OpenVDB 11.0.0

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Operators.h
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1// Copyright Contributors to the OpenVDB Project
2// SPDX-License-Identifier: MPL-2.0
3
4/// @file math/Operators.h
5
6#ifndef OPENVDB_MATH_OPERATORS_HAS_BEEN_INCLUDED
7#define OPENVDB_MATH_OPERATORS_HAS_BEEN_INCLUDED
8
9#include "FiniteDifference.h"
10#include "Stencils.h"
11#include "Maps.h"
12#include "Transform.h"
13#include <cmath> // for std::sqrt()
14
15
16 namespace openvdb {
17 OPENVDB_USE_VERSION_NAMESPACE
18 namespace OPENVDB_VERSION_NAME {
19 namespace math {
20
21// Simple tools to help determine when type conversions are needed
22 template<typename Vec3T> struct is_vec3d { static const bool value = false; };
23 template<> struct is_vec3d<Vec3d> { static const bool value = true; };
24
25 template<typename T> struct is_double { static const bool value = false; };
26 template<> struct is_double<double> { static const bool value = true; };
27
28
29/// @brief Adapter to associate a map with a world-space operator,
30/// giving it the same call signature as an index-space operator
31/// @todo For now, the operator's result type must be specified explicitly,
32/// but eventually it should be possible, via traits, to derive the result type
33/// from the operator type.
34 template<typename MapType, typename OpType, typename ResultType>
35 struct MapAdapter {
36 MapAdapter(const MapType& m): map(m) {}
37
38 template<typename AccessorType>
39 inline ResultType
40 result(const AccessorType& grid, const Coord& ijk) { return OpType::result(map, grid, ijk); }
41
42 template<typename StencilType>
43 inline ResultType
44 result(const StencilType& stencil) { return OpType::result(map, stencil); }
45
46 const MapType map;
47};
48
49
50/// Adapter for vector-valued index-space operators to return the vector magnitude
51 template<typename OpType>
52 struct ISOpMagnitude {
53 template<typename AccessorType>
54 static inline double result(const AccessorType& grid, const Coord& ijk) {
55 return double(OpType::result(grid, ijk).length());
56 }
57
58 template<typename StencilType>
59 static inline double result(const StencilType& stencil) {
60 return double(OpType::result(stencil).length());
61 }
62};
63
64/// Adapter for vector-valued world-space operators to return the vector magnitude
65 template<typename OpType, typename MapT>
66 struct OpMagnitude {
67 template<typename AccessorType>
68 static inline double result(const MapT& map, const AccessorType& grid, const Coord& ijk) {
69 return double(OpType::result(map, grid, ijk).length());
70 }
71
72 template<typename StencilType>
73 static inline double result(const MapT& map, const StencilType& stencil) {
74 return double(OpType::result(map, stencil).length());
75 }
76};
77
78/// @cond OPENVDB_DOCS_INTERNAL
79
80 namespace internal {
81
82// This additional layer is necessary for Visual C++ to compile.
83 template<typename T>
84 struct ReturnValue {
85 using ValueType = typename T::ValueType;
86 using Vec3Type = math::Vec3<ValueType>;
87};
88
89} // namespace internal
90
91/// @endcond
92
93// ---- Operators defined in index space
94
95
96//@{
97/// @brief Gradient operators defined in index space of various orders
98 template<DScheme DiffScheme>
99 struct ISGradient
100{
101 // random access version
102 template<typename Accessor> static Vec3<typename Accessor::ValueType>
103 result(const Accessor& grid, const Coord& ijk)
104 {
105 using ValueType = typename Accessor::ValueType;
106 using Vec3Type = Vec3<ValueType>;
107 return Vec3Type( D1<DiffScheme>::inX(grid, ijk),
108 D1<DiffScheme>::inY(grid, ijk),
109 D1<DiffScheme>::inZ(grid, ijk) );
110 }
111
112 // stencil access version
113 template<typename StencilT> static Vec3<typename StencilT::ValueType>
114 result(const StencilT& stencil)
115 {
116 using ValueType = typename StencilT::ValueType;
117 using Vec3Type = Vec3<ValueType>;
118 return Vec3Type( D1<DiffScheme>::inX(stencil),
119 D1<DiffScheme>::inY(stencil),
120 D1<DiffScheme>::inZ(stencil) );
121 }
122};
123//@}
124
125/// struct that relates the BiasedGradientScheme to the
126/// forward and backward difference methods used, as well as to
127/// the correct stencil type for index space use
128 template<BiasedGradientScheme bgs>
129 struct BIAS_SCHEME {
130 static const DScheme FD = FD_1ST;
131 static const DScheme BD = BD_1ST;
132
133 template<typename GridType, bool IsSafe = true>
134 struct ISStencil {
135 using StencilType = SevenPointStencil<GridType, IsSafe>;
136 };
137};
138
139 template<> struct BIAS_SCHEME<FIRST_BIAS>
140{
141 static const DScheme FD = FD_1ST;
142 static const DScheme BD = BD_1ST;
143
144 template<typename GridType, bool IsSafe = true>
145 struct ISStencil {
146 using StencilType = SevenPointStencil<GridType, IsSafe>;
147 };
148};
149
150 template<> struct BIAS_SCHEME<SECOND_BIAS>
151{
152 static const DScheme FD = FD_2ND;
153 static const DScheme BD = BD_2ND;
154
155 template<typename GridType, bool IsSafe = true>
156 struct ISStencil {
157 using StencilType = ThirteenPointStencil<GridType, IsSafe>;
158 };
159};
160 template<> struct BIAS_SCHEME<THIRD_BIAS>
161{
162 static const DScheme FD = FD_3RD;
163 static const DScheme BD = BD_3RD;
164
165 template<typename GridType, bool IsSafe = true>
166 struct ISStencil {
167 using StencilType = NineteenPointStencil<GridType, IsSafe>;
168 };
169};
170 template<> struct BIAS_SCHEME<WENO5_BIAS>
171{
172 static const DScheme FD = FD_WENO5;
173 static const DScheme BD = BD_WENO5;
174
175 template<typename GridType, bool IsSafe = true>
176 struct ISStencil {
177 using StencilType = NineteenPointStencil<GridType, IsSafe>;
178 };
179};
180 template<> struct BIAS_SCHEME<HJWENO5_BIAS>
181{
182 static const DScheme FD = FD_HJWENO5;
183 static const DScheme BD = BD_HJWENO5;
184
185 template<typename GridType, bool IsSafe = true>
186 struct ISStencil {
187 using StencilType = NineteenPointStencil<GridType, IsSafe>;
188 };
189};
190
191
192//@{
193/// @brief Biased Gradient Operators, using upwinding defined by the @c Vec3Bias input
194
195 template<BiasedGradientScheme GradScheme, typename Vec3Bias>
196 struct ISGradientBiased
197{
198 static const DScheme FD = BIAS_SCHEME<GradScheme>::FD;
199 static const DScheme BD = BIAS_SCHEME<GradScheme>::BD;
200
201 // random access version
202 template<typename Accessor>
203 static Vec3<typename Accessor::ValueType>
204 result(const Accessor& grid, const Coord& ijk, const Vec3Bias& V)
205 {
206 using ValueType = typename Accessor::ValueType;
207 using Vec3Type = Vec3<ValueType>;
208
209 return Vec3Type(V[0]<0 ? D1<FD>::inX(grid,ijk) : D1<BD>::inX(grid,ijk),
210 V[1]<0 ? D1<FD>::inY(grid,ijk) : D1<BD>::inY(grid,ijk),
211 V[2]<0 ? D1<FD>::inZ(grid,ijk) : D1<BD>::inZ(grid,ijk) );
212 }
213
214 // stencil access version
215 template<typename StencilT>
216 static Vec3<typename StencilT::ValueType>
217 result(const StencilT& stencil, const Vec3Bias& V)
218 {
219 using ValueType = typename StencilT::ValueType;
220 using Vec3Type = Vec3<ValueType>;
221
222 return Vec3Type(V[0]<0 ? D1<FD>::inX(stencil) : D1<BD>::inX(stencil),
223 V[1]<0 ? D1<FD>::inY(stencil) : D1<BD>::inY(stencil),
224 V[2]<0 ? D1<FD>::inZ(stencil) : D1<BD>::inZ(stencil) );
225 }
226};
227
228
229 template<BiasedGradientScheme GradScheme>
230 struct ISGradientNormSqrd
231{
232 static const DScheme FD = BIAS_SCHEME<GradScheme>::FD;
233 static const DScheme BD = BIAS_SCHEME<GradScheme>::BD;
234
235
236 // random access version
237 template<typename Accessor>
238 static typename Accessor::ValueType
239 result(const Accessor& grid, const Coord& ijk)
240 {
241 using ValueType = typename Accessor::ValueType;
242 using Vec3Type = math::Vec3<ValueType>;
243
244 Vec3Type up = ISGradient<FD>::result(grid, ijk);
245 Vec3Type down = ISGradient<BD>::result(grid, ijk);
246 return math::GodunovsNormSqrd(grid.getValue(ijk)>0, down, up);
247 }
248
249 // stencil access version
250 template<typename StencilT>
251 static typename StencilT::ValueType
252 result(const StencilT& stencil)
253 {
254 using ValueType = typename StencilT::ValueType;
255 using Vec3Type = math::Vec3<ValueType>;
256
257 Vec3Type up = ISGradient<FD>::result(stencil);
258 Vec3Type down = ISGradient<BD>::result(stencil);
259 return math::GodunovsNormSqrd(stencil.template getValue<0, 0, 0>()>0, down, up);
260 }
261};
262
263#ifdef DWA_OPENVDB // for SIMD - note will do the computations in float
264 template<>
265 struct ISGradientNormSqrd<HJWENO5_BIAS>
266{
267 // random access version
268 template<typename Accessor>
269 static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
270 {
271 struct GetValue
272 {
273 const Accessor& acc;
274 GetValue(const Accessor& acc_): acc(acc_) {}
275 // Return the grid value at ijk converted to simd::Float4::value_type (= float).
276 inline simd::Float4::value_type operator()(const Coord& ijk_) {
277 return static_cast<simd::Float4::value_type>(acc.getValue(ijk_));
278 }
279 }
280 valueAt(grid);
281
282 // SSE optimized
283 const simd::Float4
284 v1(valueAt(ijk.offsetBy(-2, 0, 0)) - valueAt(ijk.offsetBy(-3, 0, 0)),
285 valueAt(ijk.offsetBy( 0,-2, 0)) - valueAt(ijk.offsetBy( 0,-3, 0)),
286 valueAt(ijk.offsetBy( 0, 0,-2)) - valueAt(ijk.offsetBy( 0, 0,-3)), 0),
287 v2(valueAt(ijk.offsetBy(-1, 0, 0)) - valueAt(ijk.offsetBy(-2, 0, 0)),
288 valueAt(ijk.offsetBy( 0,-1, 0)) - valueAt(ijk.offsetBy( 0,-2, 0)),
289 valueAt(ijk.offsetBy( 0, 0,-1)) - valueAt(ijk.offsetBy( 0, 0,-2)), 0),
290 v3(valueAt(ijk ) - valueAt(ijk.offsetBy(-1, 0, 0)),
291 valueAt(ijk ) - valueAt(ijk.offsetBy( 0,-1, 0)),
292 valueAt(ijk ) - valueAt(ijk.offsetBy( 0, 0,-1)), 0),
293 v4(valueAt(ijk.offsetBy( 1, 0, 0)) - valueAt(ijk ),
294 valueAt(ijk.offsetBy( 0, 1, 0)) - valueAt(ijk ),
295 valueAt(ijk.offsetBy( 0, 0, 1)) - valueAt(ijk ), 0),
296 v5(valueAt(ijk.offsetBy( 2, 0, 0)) - valueAt(ijk.offsetBy( 1, 0, 0)),
297 valueAt(ijk.offsetBy( 0, 2, 0)) - valueAt(ijk.offsetBy( 0, 1, 0)),
298 valueAt(ijk.offsetBy( 0, 0, 2)) - valueAt(ijk.offsetBy( 0, 0, 1)), 0),
299 v6(valueAt(ijk.offsetBy( 3, 0, 0)) - valueAt(ijk.offsetBy( 2, 0, 0)),
300 valueAt(ijk.offsetBy( 0, 3, 0)) - valueAt(ijk.offsetBy( 0, 2, 0)),
301 valueAt(ijk.offsetBy( 0, 0, 3)) - valueAt(ijk.offsetBy( 0, 0, 2)), 0),
302 down = math::WENO5(v1, v2, v3, v4, v5),
303 up = math::WENO5(v6, v5, v4, v3, v2);
304
305 return math::GodunovsNormSqrd(grid.getValue(ijk)>0, down, up);
306 }
307
308 // stencil access version
309 template<typename StencilT>
310 static typename StencilT::ValueType result(const StencilT& s)
311 {
312 using F4Val = simd::Float4::value_type;
313
314 // SSE optimized
315 const simd::Float4
316 v1(F4Val(s.template getValue<-2, 0, 0>()) - F4Val(s.template getValue<-3, 0, 0>()),
317 F4Val(s.template getValue< 0,-2, 0>()) - F4Val(s.template getValue< 0,-3, 0>()),
318 F4Val(s.template getValue< 0, 0,-2>()) - F4Val(s.template getValue< 0, 0,-3>()), 0),
319 v2(F4Val(s.template getValue<-1, 0, 0>()) - F4Val(s.template getValue<-2, 0, 0>()),
320 F4Val(s.template getValue< 0,-1, 0>()) - F4Val(s.template getValue< 0,-2, 0>()),
321 F4Val(s.template getValue< 0, 0,-1>()) - F4Val(s.template getValue< 0, 0,-2>()), 0),
322 v3(F4Val(s.template getValue< 0, 0, 0>()) - F4Val(s.template getValue<-1, 0, 0>()),
323 F4Val(s.template getValue< 0, 0, 0>()) - F4Val(s.template getValue< 0,-1, 0>()),
324 F4Val(s.template getValue< 0, 0, 0>()) - F4Val(s.template getValue< 0, 0,-1>()), 0),
325 v4(F4Val(s.template getValue< 1, 0, 0>()) - F4Val(s.template getValue< 0, 0, 0>()),
326 F4Val(s.template getValue< 0, 1, 0>()) - F4Val(s.template getValue< 0, 0, 0>()),
327 F4Val(s.template getValue< 0, 0, 1>()) - F4Val(s.template getValue< 0, 0, 0>()), 0),
328 v5(F4Val(s.template getValue< 2, 0, 0>()) - F4Val(s.template getValue< 1, 0, 0>()),
329 F4Val(s.template getValue< 0, 2, 0>()) - F4Val(s.template getValue< 0, 1, 0>()),
330 F4Val(s.template getValue< 0, 0, 2>()) - F4Val(s.template getValue< 0, 0, 1>()), 0),
331 v6(F4Val(s.template getValue< 3, 0, 0>()) - F4Val(s.template getValue< 2, 0, 0>()),
332 F4Val(s.template getValue< 0, 3, 0>()) - F4Val(s.template getValue< 0, 2, 0>()),
333 F4Val(s.template getValue< 0, 0, 3>()) - F4Val(s.template getValue< 0, 0, 2>()), 0),
334 down = math::WENO5(v1, v2, v3, v4, v5),
335 up = math::WENO5(v6, v5, v4, v3, v2);
336
337 return math::GodunovsNormSqrd(s.template getValue<0, 0, 0>()>0, down, up);
338 }
339};
340#endif //DWA_OPENVDB // for SIMD - note will do the computations in float
341//@}
342
343
344//@{
345/// @brief Laplacian defined in index space, using various center-difference stencils
346 template<DDScheme DiffScheme>
347 struct ISLaplacian
348{
349 // random access version
350 template<typename Accessor>
351 static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk);
352
353 // stencil access version
354 template<typename StencilT>
355 static typename StencilT::ValueType result(const StencilT& stencil);
356};
357
358
359 template<>
360 struct ISLaplacian<CD_SECOND>
361{
362 // random access version
363 template<typename Accessor>
364 static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
365 {
366 return grid.getValue(ijk.offsetBy(1,0,0)) + grid.getValue(ijk.offsetBy(-1, 0, 0)) +
367 grid.getValue(ijk.offsetBy(0,1,0)) + grid.getValue(ijk.offsetBy(0, -1, 0)) +
368 grid.getValue(ijk.offsetBy(0,0,1)) + grid.getValue(ijk.offsetBy(0, 0,-1))
369 - 6*grid.getValue(ijk);
370 }
371
372 // stencil access version
373 template<typename StencilT>
374 static typename StencilT::ValueType result(const StencilT& stencil)
375 {
376 return stencil.template getValue< 1, 0, 0>() + stencil.template getValue<-1, 0, 0>() +
377 stencil.template getValue< 0, 1, 0>() + stencil.template getValue< 0,-1, 0>() +
378 stencil.template getValue< 0, 0, 1>() + stencil.template getValue< 0, 0,-1>()
379 - 6*stencil.template getValue< 0, 0, 0>();
380 }
381};
382
383 template<>
384 struct ISLaplacian<CD_FOURTH>
385{
386 // random access version
387 template<typename Accessor>
388 static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
389 {
390 using ValueT = typename Accessor::ValueType;
391 return static_cast<ValueT>(
392 (-1./12.)*(
393 grid.getValue(ijk.offsetBy(2,0,0)) + grid.getValue(ijk.offsetBy(-2, 0, 0)) +
394 grid.getValue(ijk.offsetBy(0,2,0)) + grid.getValue(ijk.offsetBy( 0,-2, 0)) +
395 grid.getValue(ijk.offsetBy(0,0,2)) + grid.getValue(ijk.offsetBy( 0, 0,-2)) )
396 + (4./3.)*(
397 grid.getValue(ijk.offsetBy(1,0,0)) + grid.getValue(ijk.offsetBy(-1, 0, 0)) +
398 grid.getValue(ijk.offsetBy(0,1,0)) + grid.getValue(ijk.offsetBy( 0,-1, 0)) +
399 grid.getValue(ijk.offsetBy(0,0,1)) + grid.getValue(ijk.offsetBy( 0, 0,-1)) )
400 - 7.5*grid.getValue(ijk));
401 }
402
403 // stencil access version
404 template<typename StencilT>
405 static typename StencilT::ValueType result(const StencilT& stencil)
406 {
407 using ValueT = typename StencilT::ValueType;
408 return static_cast<ValueT>(
409 (-1./12.)*(
410 stencil.template getValue< 2, 0, 0>() + stencil.template getValue<-2, 0, 0>() +
411 stencil.template getValue< 0, 2, 0>() + stencil.template getValue< 0,-2, 0>() +
412 stencil.template getValue< 0, 0, 2>() + stencil.template getValue< 0, 0,-2>() )
413 + (4./3.)*(
414 stencil.template getValue< 1, 0, 0>() + stencil.template getValue<-1, 0, 0>() +
415 stencil.template getValue< 0, 1, 0>() + stencil.template getValue< 0,-1, 0>() +
416 stencil.template getValue< 0, 0, 1>() + stencil.template getValue< 0, 0,-1>() )
417 - 7.5*stencil.template getValue< 0, 0, 0>());
418 }
419};
420
421 template<>
422 struct ISLaplacian<CD_SIXTH>
423{
424 // random access version
425 template<typename Accessor>
426 static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
427 {
428 using ValueT = typename Accessor::ValueType;
429 return static_cast<ValueT>(
430 (1./90.)*(
431 grid.getValue(ijk.offsetBy(3,0,0)) + grid.getValue(ijk.offsetBy(-3, 0, 0)) +
432 grid.getValue(ijk.offsetBy(0,3,0)) + grid.getValue(ijk.offsetBy( 0,-3, 0)) +
433 grid.getValue(ijk.offsetBy(0,0,3)) + grid.getValue(ijk.offsetBy( 0, 0,-3)) )
434 - (3./20.)*(
435 grid.getValue(ijk.offsetBy(2,0,0)) + grid.getValue(ijk.offsetBy(-2, 0, 0)) +
436 grid.getValue(ijk.offsetBy(0,2,0)) + grid.getValue(ijk.offsetBy( 0,-2, 0)) +
437 grid.getValue(ijk.offsetBy(0,0,2)) + grid.getValue(ijk.offsetBy( 0, 0,-2)) )
438 + 1.5 *(
439 grid.getValue(ijk.offsetBy(1,0,0)) + grid.getValue(ijk.offsetBy(-1, 0, 0)) +
440 grid.getValue(ijk.offsetBy(0,1,0)) + grid.getValue(ijk.offsetBy( 0,-1, 0)) +
441 grid.getValue(ijk.offsetBy(0,0,1)) + grid.getValue(ijk.offsetBy( 0, 0,-1)) )
442 - (3*49/18.)*grid.getValue(ijk));
443 }
444
445 // stencil access version
446 template<typename StencilT>
447 static typename StencilT::ValueType result(const StencilT& stencil)
448 {
449 using ValueT = typename StencilT::ValueType;
450 return static_cast<ValueT>(
451 (1./90.)*(
452 stencil.template getValue< 3, 0, 0>() + stencil.template getValue<-3, 0, 0>() +
453 stencil.template getValue< 0, 3, 0>() + stencil.template getValue< 0,-3, 0>() +
454 stencil.template getValue< 0, 0, 3>() + stencil.template getValue< 0, 0,-3>() )
455 - (3./20.)*(
456 stencil.template getValue< 2, 0, 0>() + stencil.template getValue<-2, 0, 0>() +
457 stencil.template getValue< 0, 2, 0>() + stencil.template getValue< 0,-2, 0>() +
458 stencil.template getValue< 0, 0, 2>() + stencil.template getValue< 0, 0,-2>() )
459 + 1.5 *(
460 stencil.template getValue< 1, 0, 0>() + stencil.template getValue<-1, 0, 0>() +
461 stencil.template getValue< 0, 1, 0>() + stencil.template getValue< 0,-1, 0>() +
462 stencil.template getValue< 0, 0, 1>() + stencil.template getValue< 0, 0,-1>() )
463 - (3*49/18.)*stencil.template getValue< 0, 0, 0>());
464 }
465};
466//@}
467
468
469//@{
470/// Divergence operator defined in index space using various first derivative schemes
471 template<DScheme DiffScheme>
472 struct ISDivergence
473{
474 // random access version
475 template<typename Accessor> static typename Accessor::ValueType::value_type
476 result(const Accessor& grid, const Coord& ijk)
477 {
478 return D1Vec<DiffScheme>::inX(grid, ijk, 0) +
479 D1Vec<DiffScheme>::inY(grid, ijk, 1) +
480 D1Vec<DiffScheme>::inZ(grid, ijk, 2);
481 }
482
483 // stencil access version
484 template<typename StencilT> static typename StencilT::ValueType::value_type
485 result(const StencilT& stencil)
486 {
487 return D1Vec<DiffScheme>::inX(stencil, 0) +
488 D1Vec<DiffScheme>::inY(stencil, 1) +
489 D1Vec<DiffScheme>::inZ(stencil, 2);
490 }
491};
492//@}
493
494
495//@{
496/// Curl operator defined in index space using various first derivative schemes
497 template<DScheme DiffScheme>
498 struct ISCurl
499{
500 // random access version
501 template<typename Accessor>
502 static typename Accessor::ValueType result(const Accessor& grid, const Coord& ijk)
503 {
504 using Vec3Type = typename Accessor::ValueType;
505 return Vec3Type( D1Vec<DiffScheme>::inY(grid, ijk, 2) - //dw/dy - dv/dz
506 D1Vec<DiffScheme>::inZ(grid, ijk, 1),
507 D1Vec<DiffScheme>::inZ(grid, ijk, 0) - //du/dz - dw/dx
508 D1Vec<DiffScheme>::inX(grid, ijk, 2),
509 D1Vec<DiffScheme>::inX(grid, ijk, 1) - //dv/dx - du/dy
510 D1Vec<DiffScheme>::inY(grid, ijk, 0) );
511 }
512
513 // stencil access version
514 template<typename StencilT>
515 static typename StencilT::ValueType result(const StencilT& stencil)
516 {
517 using Vec3Type = typename StencilT::ValueType;
518 return Vec3Type( D1Vec<DiffScheme>::inY(stencil, 2) - //dw/dy - dv/dz
519 D1Vec<DiffScheme>::inZ(stencil, 1),
520 D1Vec<DiffScheme>::inZ(stencil, 0) - //du/dz - dw/dx
521 D1Vec<DiffScheme>::inX(stencil, 2),
522 D1Vec<DiffScheme>::inX(stencil, 1) - //dv/dx - du/dy
523 D1Vec<DiffScheme>::inY(stencil, 0) );
524 }
525};
526//@}
527
528
529//@{
530/// Compute the mean curvature in index space
531 template<DDScheme DiffScheme2, DScheme DiffScheme1>
532 struct ISMeanCurvature
533{
534 /// @brief Random access version
535 /// @return @c true if the gradient is nonzero, in which case the mean curvature
536 /// is returned in two parts, @a alpha and @a beta, where @a alpha is the numerator
537 /// in &nabla; &middot; (&nabla;&Phi; / |&nabla;&Phi;|) and @a beta is |&nabla;&Phi;|.
538 template<typename Accessor>
539 static bool result(const Accessor& grid, const Coord& ijk,
540 typename Accessor::ValueType& alpha,
541 typename Accessor::ValueType& beta)
542 {
543 using ValueType = typename Accessor::ValueType;
544
545 const ValueType Dx = D1<DiffScheme1>::inX(grid, ijk);
546 const ValueType Dy = D1<DiffScheme1>::inY(grid, ijk);
547 const ValueType Dz = D1<DiffScheme1>::inZ(grid, ijk);
548
549 const ValueType Dx2 = Dx*Dx;
550 const ValueType Dy2 = Dy*Dy;
551 const ValueType Dz2 = Dz*Dz;
552 const ValueType normGrad = Dx2 + Dy2 + Dz2;
553 if (normGrad <= math::Tolerance<ValueType>::value()) {
554 alpha = beta = 0;
555 return false;
556 }
557
558 const ValueType Dxx = D2<DiffScheme2>::inX(grid, ijk);
559 const ValueType Dyy = D2<DiffScheme2>::inY(grid, ijk);
560 const ValueType Dzz = D2<DiffScheme2>::inZ(grid, ijk);
561
562 const ValueType Dxy = D2<DiffScheme2>::inXandY(grid, ijk);
563 const ValueType Dyz = D2<DiffScheme2>::inYandZ(grid, ijk);
564 const ValueType Dxz = D2<DiffScheme2>::inXandZ(grid, ijk);
565
566 // for return
567 alpha = (Dx2*(Dyy+Dzz)+Dy2*(Dxx+Dzz)+Dz2*(Dxx+Dyy)-2*(Dx*(Dy*Dxy+Dz*Dxz)+Dy*Dz*Dyz));
568 beta = ValueType(std::sqrt(double(normGrad))); // * 1/dx
569 return true;
570 }
571
572 /// @brief Stencil access version
573 /// @return @c true if the gradient is nonzero, in which case the mean curvature
574 /// is returned in two parts, @a alpha and @a beta, where @a alpha is the numerator
575 /// in &nabla; &middot; (&nabla;&Phi; / |&nabla;&Phi;|) and @a beta is |&nabla;&Phi;|.
576 template<typename StencilT>
577 static bool result(const StencilT& stencil,
578 typename StencilT::ValueType& alpha,
579 typename StencilT::ValueType& beta)
580 {
581 using ValueType = typename StencilT::ValueType;
582 const ValueType Dx = D1<DiffScheme1>::inX(stencil);
583 const ValueType Dy = D1<DiffScheme1>::inY(stencil);
584 const ValueType Dz = D1<DiffScheme1>::inZ(stencil);
585
586 const ValueType Dx2 = Dx*Dx;
587 const ValueType Dy2 = Dy*Dy;
588 const ValueType Dz2 = Dz*Dz;
589 const ValueType normGrad = Dx2 + Dy2 + Dz2;
590 if (normGrad <= math::Tolerance<ValueType>::value()) {
591 alpha = beta = 0;
592 return false;
593 }
594
595 const ValueType Dxx = D2<DiffScheme2>::inX(stencil);
596 const ValueType Dyy = D2<DiffScheme2>::inY(stencil);
597 const ValueType Dzz = D2<DiffScheme2>::inZ(stencil);
598
599 const ValueType Dxy = D2<DiffScheme2>::inXandY(stencil);
600 const ValueType Dyz = D2<DiffScheme2>::inYandZ(stencil);
601 const ValueType Dxz = D2<DiffScheme2>::inXandZ(stencil);
602
603 // for return
604 alpha = (Dx2*(Dyy+Dzz)+Dy2*(Dxx+Dzz)+Dz2*(Dxx+Dyy)-2*(Dx*(Dy*Dxy+Dz*Dxz)+Dy*Dz*Dyz));
605 beta = ValueType(std::sqrt(double(normGrad))); // * 1/dx
606 return true;
607 }
608};
609
610////////////////////////////////////////////////////////
611
612// --- Operators defined in the Range of a given map
613
614//@{
615/// @brief Center difference gradient operators, defined with respect to
616/// the range-space of the @c map
617/// @note This will need to be divided by two in the case of CD_2NDT
618 template<typename MapType, DScheme DiffScheme>
619 struct Gradient
620{
621 // random access version
622 template<typename Accessor>
623 static typename internal::ReturnValue<Accessor>::Vec3Type
624 result(const MapType& map, const Accessor& grid, const Coord& ijk)
625 {
626 using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
627
628 Vec3d iGradient( ISGradient<DiffScheme>::result(grid, ijk) );
629 return Vec3Type(map.applyIJT(iGradient, ijk.asVec3d()));
630 }
631
632 // stencil access version
633 template<typename StencilT>
634 static typename internal::ReturnValue<StencilT>::Vec3Type
635 result(const MapType& map, const StencilT& stencil)
636 {
637 using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
638
639 Vec3d iGradient( ISGradient<DiffScheme>::result(stencil) );
640 return Vec3Type(map.applyIJT(iGradient, stencil.getCenterCoord().asVec3d()));
641 }
642};
643
644// Partial template specialization of Gradient
645// translation, any order
646 template<DScheme DiffScheme>
647 struct Gradient<TranslationMap, DiffScheme>
648{
649 // random access version
650 template<typename Accessor>
651 static typename internal::ReturnValue<Accessor>::Vec3Type
652 result(const TranslationMap&, const Accessor& grid, const Coord& ijk)
653 {
654 return ISGradient<DiffScheme>::result(grid, ijk);
655 }
656
657 // stencil access version
658 template<typename StencilT>
659 static typename internal::ReturnValue<StencilT>::Vec3Type
660 result(const TranslationMap&, const StencilT& stencil)
661 {
662 return ISGradient<DiffScheme>::result(stencil);
663 }
664};
665
666/// Full template specialization of Gradient
667/// uniform scale, 2nd order
668 template<>
669 struct Gradient<UniformScaleMap, CD_2ND>
670{
671 // random access version
672 template<typename Accessor>
673 static typename internal::ReturnValue<Accessor>::Vec3Type
674 result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
675 {
676 using ValueType = typename internal::ReturnValue<Accessor>::ValueType;
677 using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
678
679 Vec3Type iGradient( ISGradient<CD_2NDT>::result(grid, ijk) );
680 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
681 return iGradient * inv2dx;
682 }
683
684 // stencil access version
685 template<typename StencilT>
686 static typename internal::ReturnValue<StencilT>::Vec3Type
687 result(const UniformScaleMap& map, const StencilT& stencil)
688 {
689 using ValueType = typename internal::ReturnValue<StencilT>::ValueType;
690 using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
691
692 Vec3Type iGradient( ISGradient<CD_2NDT>::result(stencil) );
693 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
694 return iGradient * inv2dx;
695 }
696};
697
698/// Full template specialization of Gradient
699/// uniform scale translate, 2nd order
700 template<>
701 struct Gradient<UniformScaleTranslateMap, CD_2ND>
702{
703 // random access version
704 template<typename Accessor>
705 static typename internal::ReturnValue<Accessor>::Vec3Type
706 result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
707 {
708 using ValueType = typename internal::ReturnValue<Accessor>::ValueType;
709 using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
710
711 Vec3Type iGradient( ISGradient<CD_2NDT>::result(grid, ijk) );
712 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
713 return iGradient * inv2dx;
714 }
715
716 // stencil access version
717 template<typename StencilT>
718 static typename internal::ReturnValue<StencilT>::Vec3Type
719 result(const UniformScaleTranslateMap& map, const StencilT& stencil)
720 {
721 using ValueType = typename internal::ReturnValue<StencilT>::ValueType;
722 using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
723
724 Vec3Type iGradient( ISGradient<CD_2NDT>::result(stencil) );
725 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
726 return iGradient * inv2dx;
727 }
728};
729
730/// Full template specialization of Gradient
731/// scale, 2nd order
732 template<>
733 struct Gradient<ScaleMap, CD_2ND>
734{
735 // random access version
736 template<typename Accessor>
737 static typename internal::ReturnValue<Accessor>::Vec3Type
738 result(const ScaleMap& map, const Accessor& grid, const Coord& ijk)
739 {
740 using ValueType = typename internal::ReturnValue<Accessor>::ValueType;
741 using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
742
743 Vec3Type iGradient( ISGradient<CD_2NDT>::result(grid, ijk) );
744 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
745 const auto gradient0 = iGradient[0] * map.getInvTwiceScale()[0];
746 const auto gradient1 = iGradient[1] * map.getInvTwiceScale()[1];
747 const auto gradient2 = iGradient[2] * map.getInvTwiceScale()[2];
748 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
749 return Vec3Type(ValueType(gradient0),
750 ValueType(gradient1),
751 ValueType(gradient2));
752 }
753
754 // stencil access version
755 template<typename StencilT>
756 static typename internal::ReturnValue<StencilT>::Vec3Type
757 result(const ScaleMap& map, const StencilT& stencil)
758 {
759 using ValueType = typename internal::ReturnValue<StencilT>::ValueType;
760 using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
761
762 Vec3Type iGradient( ISGradient<CD_2NDT>::result(stencil) );
763 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
764 const auto gradient0 = iGradient[0] * map.getInvTwiceScale()[0];
765 const auto gradient1 = iGradient[1] * map.getInvTwiceScale()[1];
766 const auto gradient2 = iGradient[2] * map.getInvTwiceScale()[2];
767 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
768 return Vec3Type(ValueType(gradient0),
769 ValueType(gradient1),
770 ValueType(gradient2));
771 }
772};
773
774/// Full template specialization of Gradient
775/// scale translate, 2nd order
776 template<>
777 struct Gradient<ScaleTranslateMap, CD_2ND>
778{
779 // random access version
780 template<typename Accessor>
781 static typename internal::ReturnValue<Accessor>::Vec3Type
782 result(const ScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
783 {
784 using ValueType = typename internal::ReturnValue<Accessor>::ValueType;
785 using Vec3Type = typename internal::ReturnValue<Accessor>::Vec3Type;
786
787 Vec3Type iGradient( ISGradient<CD_2NDT>::result(grid, ijk) );
788 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
789 const auto gradient0 = iGradient[0] * map.getInvTwiceScale()[0];
790 const auto gradient1 = iGradient[1] * map.getInvTwiceScale()[1];
791 const auto gradient2 = iGradient[2] * map.getInvTwiceScale()[2];
792 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
793 return Vec3Type(ValueType(gradient0),
794 ValueType(gradient1),
795 ValueType(gradient2));
796 }
797
798 // Stencil access version
799 template<typename StencilT>
800 static typename internal::ReturnValue<StencilT>::Vec3Type
801 result(const ScaleTranslateMap& map, const StencilT& stencil)
802 {
803 using ValueType = typename internal::ReturnValue<StencilT>::ValueType;
804 using Vec3Type = typename internal::ReturnValue<StencilT>::Vec3Type;
805
806 Vec3Type iGradient( ISGradient<CD_2NDT>::result(stencil) );
807 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
808 const auto gradient0 = iGradient[0] * map.getInvTwiceScale()[0];
809 const auto gradient1 = iGradient[1] * map.getInvTwiceScale()[1];
810 const auto gradient2 = iGradient[2] * map.getInvTwiceScale()[2];
811 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
812 return Vec3Type(ValueType(gradient0),
813 ValueType(gradient1),
814 ValueType(gradient2));
815 }
816};
817//@}
818
819
820//@{
821/// @brief Biased gradient operators, defined with respect to the range-space of the map
822/// @note This will need to be divided by two in the case of CD_2NDT
823 template<typename MapType, BiasedGradientScheme GradScheme>
824 struct GradientBiased
825{
826 // random access version
827 template<typename Accessor> static math::Vec3<typename Accessor::ValueType>
828 result(const MapType& map, const Accessor& grid, const Coord& ijk,
829 const Vec3<typename Accessor::ValueType>& V)
830 {
831 using ValueType = typename Accessor::ValueType;
832 using Vec3Type = math::Vec3<ValueType>;
833
834 Vec3d iGradient( ISGradientBiased<GradScheme, Vec3Type>::result(grid, ijk, V) );
835 return Vec3Type(map.applyIJT(iGradient, ijk.asVec3d()));
836 }
837
838 // stencil access version
839 template<typename StencilT> static math::Vec3<typename StencilT::ValueType>
840 result(const MapType& map, const StencilT& stencil,
841 const Vec3<typename StencilT::ValueType>& V)
842 {
843 using ValueType = typename StencilT::ValueType;
844 using Vec3Type = math::Vec3<ValueType>;
845
846 Vec3d iGradient( ISGradientBiased<GradScheme, Vec3Type>::result(stencil, V) );
847 return Vec3Type(map.applyIJT(iGradient, stencil.getCenterCoord().asVec3d()));
848 }
849};
850//@}
851
852
853////////////////////////////////////////////////////////
854
855// Computes |Grad[Phi]| using upwinding
856 template<typename MapType, BiasedGradientScheme GradScheme>
857 struct GradientNormSqrd
858{
859 static const DScheme FD = BIAS_SCHEME<GradScheme>::FD;
860 static const DScheme BD = BIAS_SCHEME<GradScheme>::BD;
861
862
863 // random access version
864 template<typename Accessor>
865 static typename Accessor::ValueType
866 result(const MapType& map, const Accessor& grid, const Coord& ijk)
867 {
868 using ValueType = typename Accessor::ValueType;
869 using Vec3Type = math::Vec3<ValueType>;
870
871 Vec3Type up = Gradient<MapType, FD>::result(map, grid, ijk);
872 Vec3Type down = Gradient<MapType, BD>::result(map, grid, ijk);
873 return math::GodunovsNormSqrd(grid.getValue(ijk)>0, down, up);
874 }
875
876 // stencil access version
877 template<typename StencilT>
878 static typename StencilT::ValueType
879 result(const MapType& map, const StencilT& stencil)
880 {
881 using ValueType = typename StencilT::ValueType;
882 using Vec3Type = math::Vec3<ValueType>;
883
884 Vec3Type up = Gradient<MapType, FD>::result(map, stencil);
885 Vec3Type down = Gradient<MapType, BD>::result(map, stencil);
886 return math::GodunovsNormSqrd(stencil.template getValue<0, 0, 0>()>0, down, up);
887 }
888};
889
890/// Partial template specialization of GradientNormSqrd
891 template<BiasedGradientScheme GradScheme>
892 struct GradientNormSqrd<UniformScaleMap, GradScheme>
893{
894 // random access version
895 template<typename Accessor>
896 static typename Accessor::ValueType
897 result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
898 {
899 using ValueType = typename Accessor::ValueType;
900
901 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
902 return invdxdx * ISGradientNormSqrd<GradScheme>::result(grid, ijk);
903 }
904
905 // stencil access version
906 template<typename StencilT>
907 static typename StencilT::ValueType
908 result(const UniformScaleMap& map, const StencilT& stencil)
909 {
910 using ValueType = typename StencilT::ValueType;
911
912 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
913 return invdxdx * ISGradientNormSqrd<GradScheme>::result(stencil);
914 }
915};
916
917/// Partial template specialization of GradientNormSqrd
918 template<BiasedGradientScheme GradScheme>
919 struct GradientNormSqrd<UniformScaleTranslateMap, GradScheme>
920{
921 // random access version
922 template<typename Accessor>
923 static typename Accessor::ValueType
924 result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
925 {
926 using ValueType = typename Accessor::ValueType;
927
928 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
929 return invdxdx * ISGradientNormSqrd<GradScheme>::result(grid, ijk);
930 }
931
932 // stencil access version
933 template<typename StencilT>
934 static typename StencilT::ValueType
935 result(const UniformScaleTranslateMap& map, const StencilT& stencil)
936 {
937 using ValueType = typename StencilT::ValueType;
938
939 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
940 return invdxdx * ISGradientNormSqrd<GradScheme>::result(stencil);
941 }
942};
943
944
945//@{
946/// @brief Compute the divergence of a vector-valued grid using differencing
947/// of various orders, the result defined with respect to the range-space of the map.
948 template<typename MapType, DScheme DiffScheme>
949 struct Divergence
950{
951 // random access version
952 template<typename Accessor> static typename Accessor::ValueType::value_type
953 result(const MapType& map, const Accessor& grid, const Coord& ijk)
954 {
955 using ValueType = typename Accessor::ValueType::value_type;
956
957 ValueType div(0);
958 for (int i=0; i < 3; i++) {
959 Vec3d vec( D1Vec<DiffScheme>::inX(grid, ijk, i),
960 D1Vec<DiffScheme>::inY(grid, ijk, i),
961 D1Vec<DiffScheme>::inZ(grid, ijk, i) );
962 div += ValueType(map.applyIJT(vec, ijk.asVec3d())[i]);
963 }
964 return div;
965 }
966
967 // stencil access version
968 template<typename StencilT> static typename StencilT::ValueType::value_type
969 result(const MapType& map, const StencilT& stencil)
970 {
971 using ValueType = typename StencilT::ValueType::value_type;
972
973 ValueType div(0);
974 for (int i=0; i < 3; i++) {
975 Vec3d vec( D1Vec<DiffScheme>::inX(stencil, i),
976 D1Vec<DiffScheme>::inY(stencil, i),
977 D1Vec<DiffScheme>::inZ(stencil, i) );
978 div += ValueType(map.applyIJT(vec, stencil.getCenterCoord().asVec3d())[i]);
979 }
980 return div;
981 }
982};
983
984/// Partial template specialization of Divergence
985/// translation, any scheme
986 template<DScheme DiffScheme>
987 struct Divergence<TranslationMap, DiffScheme>
988{
989 // random access version
990 template<typename Accessor> static typename Accessor::ValueType::value_type
991 result(const TranslationMap&, const Accessor& grid, const Coord& ijk)
992 {
993 using ValueType = typename Accessor::ValueType::value_type;
994
995 ValueType div(0);
996 div =ISDivergence<DiffScheme>::result(grid, ijk);
997 return div;
998 }
999
1000 // stencil access version
1001 template<typename StencilT> static typename StencilT::ValueType::value_type
1002 result(const TranslationMap&, const StencilT& stencil)
1003 {
1004 using ValueType = typename StencilT::ValueType::value_type;
1005
1006 ValueType div(0);
1007 div =ISDivergence<DiffScheme>::result(stencil);
1008 return div;
1009 }
1010};
1011
1012/// Partial template specialization of Divergence
1013/// uniform scale, any scheme
1014 template<DScheme DiffScheme>
1015 struct Divergence<UniformScaleMap, DiffScheme>
1016{
1017 // random access version
1018 template<typename Accessor> static typename Accessor::ValueType::value_type
1019 result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
1020 {
1021 using ValueType = typename Accessor::ValueType::value_type;
1022
1023 ValueType div(0);
1024
1025 div =ISDivergence<DiffScheme>::result(grid, ijk);
1026 ValueType invdx = ValueType(map.getInvScale()[0]);
1027 return div * invdx;
1028 }
1029
1030 // stencil access version
1031 template<typename StencilT> static typename StencilT::ValueType::value_type
1032 result(const UniformScaleMap& map, const StencilT& stencil)
1033 {
1034 using ValueType = typename StencilT::ValueType::value_type;
1035
1036 ValueType div(0);
1037
1038 div =ISDivergence<DiffScheme>::result(stencil);
1039 ValueType invdx = ValueType(map.getInvScale()[0]);
1040 return div * invdx;
1041 }
1042};
1043
1044/// Partial template specialization of Divergence
1045/// uniform scale and translation, any scheme
1046 template<DScheme DiffScheme>
1047 struct Divergence<UniformScaleTranslateMap, DiffScheme>
1048{
1049 // random access version
1050 template<typename Accessor> static typename Accessor::ValueType::value_type
1051 result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
1052 {
1053 using ValueType = typename Accessor::ValueType::value_type;
1054
1055 ValueType div(0);
1056
1057 div =ISDivergence<DiffScheme>::result(grid, ijk);
1058 ValueType invdx = ValueType(map.getInvScale()[0]);
1059 return div * invdx;
1060 }
1061
1062 // stencil access version
1063 template<typename StencilT> static typename StencilT::ValueType::value_type
1064 result(const UniformScaleTranslateMap& map, const StencilT& stencil)
1065 {
1066 using ValueType = typename StencilT::ValueType::value_type;
1067
1068 ValueType div(0);
1069
1070 div =ISDivergence<DiffScheme>::result(stencil);
1071 ValueType invdx = ValueType(map.getInvScale()[0]);
1072 return div * invdx;
1073 }
1074};
1075
1076/// Full template specialization of Divergence
1077/// uniform scale 2nd order
1078 template<>
1079 struct Divergence<UniformScaleMap, CD_2ND>
1080{
1081 // random access version
1082 template<typename Accessor> static typename Accessor::ValueType::value_type
1083 result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
1084 {
1085 using ValueType = typename Accessor::ValueType::value_type;
1086
1087 ValueType div(0);
1088 div =ISDivergence<CD_2NDT>::result(grid, ijk);
1089 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
1090 return div * inv2dx;
1091 }
1092
1093 // stencil access version
1094 template<typename StencilT> static typename StencilT::ValueType::value_type
1095 result(const UniformScaleMap& map, const StencilT& stencil)
1096 {
1097 using ValueType = typename StencilT::ValueType::value_type;
1098
1099 ValueType div(0);
1100 div =ISDivergence<CD_2NDT>::result(stencil);
1101 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
1102 return div * inv2dx;
1103 }
1104};
1105
1106/// Full template specialization of Divergence
1107/// uniform scale translate 2nd order
1108 template<>
1109 struct Divergence<UniformScaleTranslateMap, CD_2ND>
1110{
1111 // random access version
1112 template<typename Accessor> static typename Accessor::ValueType::value_type
1113 result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
1114 {
1115 using ValueType = typename Accessor::ValueType::value_type;
1116
1117 ValueType div(0);
1118
1119 div =ISDivergence<CD_2NDT>::result(grid, ijk);
1120 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
1121 return div * inv2dx;
1122 }
1123
1124 // stencil access version
1125 template<typename StencilT> static typename StencilT::ValueType::value_type
1126 result(const UniformScaleTranslateMap& map, const StencilT& stencil)
1127 {
1128 using ValueType = typename StencilT::ValueType::value_type;
1129
1130 ValueType div(0);
1131
1132 div =ISDivergence<CD_2NDT>::result(stencil);
1133 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
1134 return div * inv2dx;
1135 }
1136};
1137
1138/// Partial template specialization of Divergence
1139/// scale, any scheme
1140 template<DScheme DiffScheme>
1141 struct Divergence<ScaleMap, DiffScheme>
1142{
1143 // random access version
1144 template<typename Accessor> static typename Accessor::ValueType::value_type
1145 result(const ScaleMap& map, const Accessor& grid, const Coord& ijk)
1146 {
1147 using ValueType = typename Accessor::ValueType::value_type;
1148
1149 ValueType div = ValueType(
1150 D1Vec<DiffScheme>::inX(grid, ijk, 0) * (map.getInvScale()[0]) +
1151 D1Vec<DiffScheme>::inY(grid, ijk, 1) * (map.getInvScale()[1]) +
1152 D1Vec<DiffScheme>::inZ(grid, ijk, 2) * (map.getInvScale()[2]));
1153 return div;
1154 }
1155
1156 // stencil access version
1157 template<typename StencilT> static typename StencilT::ValueType::value_type
1158 result(const ScaleMap& map, const StencilT& stencil)
1159 {
1160 using ValueType = typename StencilT::ValueType::value_type;
1161
1162 ValueType div(0);
1163 div = ValueType(
1164 D1Vec<DiffScheme>::inX(stencil, 0) * (map.getInvScale()[0]) +
1165 D1Vec<DiffScheme>::inY(stencil, 1) * (map.getInvScale()[1]) +
1166 D1Vec<DiffScheme>::inZ(stencil, 2) * (map.getInvScale()[2]) );
1167 return div;
1168 }
1169};
1170
1171/// Partial template specialization of Divergence
1172/// scale translate, any scheme
1173 template<DScheme DiffScheme>
1174 struct Divergence<ScaleTranslateMap, DiffScheme>
1175{
1176 // random access version
1177 template<typename Accessor> static typename Accessor::ValueType::value_type
1178 result(const ScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
1179 {
1180 using ValueType = typename Accessor::ValueType::value_type;
1181
1182 ValueType div = ValueType(
1183 D1Vec<DiffScheme>::inX(grid, ijk, 0) * (map.getInvScale()[0]) +
1184 D1Vec<DiffScheme>::inY(grid, ijk, 1) * (map.getInvScale()[1]) +
1185 D1Vec<DiffScheme>::inZ(grid, ijk, 2) * (map.getInvScale()[2]));
1186 return div;
1187 }
1188
1189 // stencil access version
1190 template<typename StencilT> static typename StencilT::ValueType::value_type
1191 result(const ScaleTranslateMap& map, const StencilT& stencil)
1192 {
1193 using ValueType = typename StencilT::ValueType::value_type;
1194
1195 ValueType div(0);
1196 div = ValueType(
1197 D1Vec<DiffScheme>::inX(stencil, 0) * (map.getInvScale()[0]) +
1198 D1Vec<DiffScheme>::inY(stencil, 1) * (map.getInvScale()[1]) +
1199 D1Vec<DiffScheme>::inZ(stencil, 2) * (map.getInvScale()[2]) );
1200 return div;
1201 }
1202};
1203
1204/// Full template specialization Divergence
1205/// scale 2nd order
1206 template<>
1207 struct Divergence<ScaleMap, CD_2ND>
1208{
1209 // random access version
1210 template<typename Accessor> static typename Accessor::ValueType::value_type
1211 result(const ScaleMap& map, const Accessor& grid, const Coord& ijk)
1212 {
1213 using ValueType = typename Accessor::ValueType::value_type;
1214
1215 ValueType div = ValueType(
1216 D1Vec<CD_2NDT>::inX(grid, ijk, 0) * (map.getInvTwiceScale()[0]) +
1217 D1Vec<CD_2NDT>::inY(grid, ijk, 1) * (map.getInvTwiceScale()[1]) +
1218 D1Vec<CD_2NDT>::inZ(grid, ijk, 2) * (map.getInvTwiceScale()[2]) );
1219 return div;
1220 }
1221
1222 // stencil access version
1223 template<typename StencilT> static typename StencilT::ValueType::value_type
1224 result(const ScaleMap& map, const StencilT& stencil)
1225 {
1226 using ValueType = typename StencilT::ValueType::value_type;
1227
1228 ValueType div = ValueType(
1229 D1Vec<CD_2NDT>::inX(stencil, 0) * (map.getInvTwiceScale()[0]) +
1230 D1Vec<CD_2NDT>::inY(stencil, 1) * (map.getInvTwiceScale()[1]) +
1231 D1Vec<CD_2NDT>::inZ(stencil, 2) * (map.getInvTwiceScale()[2]) );
1232 return div;
1233 }
1234};
1235
1236/// Full template specialization of Divergence
1237/// scale and translate, 2nd order
1238 template<>
1239 struct Divergence<ScaleTranslateMap, CD_2ND>
1240{
1241 // random access version
1242 template<typename Accessor> static typename Accessor::ValueType::value_type
1243 result(const ScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
1244 {
1245 using ValueType = typename Accessor::ValueType::value_type;
1246
1247 ValueType div = ValueType(
1248 D1Vec<CD_2NDT>::inX(grid, ijk, 0) * (map.getInvTwiceScale()[0]) +
1249 D1Vec<CD_2NDT>::inY(grid, ijk, 1) * (map.getInvTwiceScale()[1]) +
1250 D1Vec<CD_2NDT>::inZ(grid, ijk, 2) * (map.getInvTwiceScale()[2]) );
1251 return div;
1252 }
1253
1254 // stencil access version
1255 template<typename StencilT> static typename StencilT::ValueType::value_type
1256 result(const ScaleTranslateMap& map, const StencilT& stencil)
1257 {
1258 using ValueType = typename StencilT::ValueType::value_type;
1259
1260 ValueType div = ValueType(
1261 D1Vec<CD_2NDT>::inX(stencil, 0) * (map.getInvTwiceScale()[0]) +
1262 D1Vec<CD_2NDT>::inY(stencil, 1) * (map.getInvTwiceScale()[1]) +
1263 D1Vec<CD_2NDT>::inZ(stencil, 2) * (map.getInvTwiceScale()[2]) );
1264 return div;
1265 }
1266};
1267//@}
1268
1269
1270//@{
1271/// @brief Compute the curl of a vector-valued grid using differencing
1272/// of various orders in the space defined by the range of the map.
1273 template<typename MapType, DScheme DiffScheme>
1274 struct Curl
1275{
1276 // random access version
1277 template<typename Accessor> static typename Accessor::ValueType
1278 result(const MapType& map, const Accessor& grid, const Coord& ijk)
1279 {
1280 using Vec3Type = typename Accessor::ValueType;
1281 Vec3Type mat[3];
1282 for (int i = 0; i < 3; i++) {
1283 Vec3d vec(
1284 D1Vec<DiffScheme>::inX(grid, ijk, i),
1285 D1Vec<DiffScheme>::inY(grid, ijk, i),
1286 D1Vec<DiffScheme>::inZ(grid, ijk, i));
1287 // dF_i/dx_j (x_1 = x, x_2 = y, x_3 = z)
1288 mat[i] = Vec3Type(map.applyIJT(vec, ijk.asVec3d()));
1289 }
1290 return Vec3Type(mat[2][1] - mat[1][2], // dF_3/dx_2 - dF_2/dx_3
1291 mat[0][2] - mat[2][0], // dF_1/dx_3 - dF_3/dx_1
1292 mat[1][0] - mat[0][1]); // dF_2/dx_1 - dF_1/dx_2
1293 }
1294
1295 // stencil access version
1296 template<typename StencilT> static typename StencilT::ValueType
1297 result(const MapType& map, const StencilT& stencil)
1298 {
1299 using Vec3Type = typename StencilT::ValueType;
1300 Vec3Type mat[3];
1301 for (int i = 0; i < 3; i++) {
1302 Vec3d vec(
1303 D1Vec<DiffScheme>::inX(stencil, i),
1304 D1Vec<DiffScheme>::inY(stencil, i),
1305 D1Vec<DiffScheme>::inZ(stencil, i));
1306 // dF_i/dx_j (x_1 = x, x_2 = y, x_3 = z)
1307 mat[i] = Vec3Type(map.applyIJT(vec, stencil.getCenterCoord().asVec3d()));
1308 }
1309 return Vec3Type(mat[2][1] - mat[1][2], // dF_3/dx_2 - dF_2/dx_3
1310 mat[0][2] - mat[2][0], // dF_1/dx_3 - dF_3/dx_1
1311 mat[1][0] - mat[0][1]); // dF_2/dx_1 - dF_1/dx_2
1312 }
1313};
1314
1315/// Partial template specialization of Curl
1316 template<DScheme DiffScheme>
1317 struct Curl<UniformScaleMap, DiffScheme>
1318{
1319 // random access version
1320 template<typename Accessor> static typename Accessor::ValueType
1321 result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
1322 {
1323 using Vec3Type = typename Accessor::ValueType;
1324 using ValueType = typename Vec3Type::value_type;
1325 return ISCurl<DiffScheme>::result(grid, ijk) * ValueType(map.getInvScale()[0]);
1326 }
1327
1328 // Stencil access version
1329 template<typename StencilT> static typename StencilT::ValueType
1330 result(const UniformScaleMap& map, const StencilT& stencil)
1331 {
1332 using Vec3Type = typename StencilT::ValueType;
1333 using ValueType = typename Vec3Type::value_type;
1334 return ISCurl<DiffScheme>::result(stencil) * ValueType(map.getInvScale()[0]);
1335 }
1336};
1337
1338/// Partial template specialization of Curl
1339 template<DScheme DiffScheme>
1340 struct Curl<UniformScaleTranslateMap, DiffScheme>
1341{
1342 // random access version
1343 template<typename Accessor> static typename Accessor::ValueType
1344 result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
1345 {
1346 using Vec3Type = typename Accessor::ValueType;
1347 using ValueType = typename Vec3Type::value_type;
1348
1349 return ISCurl<DiffScheme>::result(grid, ijk) * ValueType(map.getInvScale()[0]);
1350 }
1351
1352 // stencil access version
1353 template<typename StencilT> static typename StencilT::ValueType
1354 result(const UniformScaleTranslateMap& map, const StencilT& stencil)
1355 {
1356 using Vec3Type = typename StencilT::ValueType;
1357 using ValueType = typename Vec3Type::value_type;
1358
1359 return ISCurl<DiffScheme>::result(stencil) * ValueType(map.getInvScale()[0]);
1360 }
1361};
1362
1363/// Full template specialization of Curl
1364 template<>
1365 struct Curl<UniformScaleMap, CD_2ND>
1366{
1367 // random access version
1368 template<typename Accessor> static typename Accessor::ValueType
1369 result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
1370 {
1371 using Vec3Type = typename Accessor::ValueType;
1372 using ValueType = typename Vec3Type::value_type;
1373
1374 return ISCurl<CD_2NDT>::result(grid, ijk) * ValueType(map.getInvTwiceScale()[0]);
1375 }
1376
1377 // stencil access version
1378 template<typename StencilT> static typename StencilT::ValueType
1379 result(const UniformScaleMap& map, const StencilT& stencil)
1380 {
1381 using Vec3Type = typename StencilT::ValueType;
1382 using ValueType = typename Vec3Type::value_type;
1383
1384 return ISCurl<CD_2NDT>::result(stencil) * ValueType(map.getInvTwiceScale()[0]);
1385 }
1386};
1387
1388/// Full template specialization of Curl
1389 template<>
1390 struct Curl<UniformScaleTranslateMap, CD_2ND>
1391{
1392 // random access version
1393 template<typename Accessor> static typename Accessor::ValueType
1394 result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
1395 {
1396 using Vec3Type = typename Accessor::ValueType;
1397 using ValueType = typename Vec3Type::value_type;
1398
1399 return ISCurl<CD_2NDT>::result(grid, ijk) * ValueType(map.getInvTwiceScale()[0]);
1400 }
1401
1402 // stencil access version
1403 template<typename StencilT> static typename StencilT::ValueType
1404 result(const UniformScaleTranslateMap& map, const StencilT& stencil)
1405 {
1406 using Vec3Type = typename StencilT::ValueType;
1407 using ValueType = typename Vec3Type::value_type;
1408
1409 return ISCurl<CD_2NDT>::result(stencil) * ValueType(map.getInvTwiceScale()[0]);
1410 }
1411};
1412//@}
1413
1414
1415//@{
1416/// @brief Compute the Laplacian at a given location in a grid using finite differencing
1417/// of various orders. The result is defined in the range of the map.
1418 template<typename MapType, DDScheme DiffScheme>
1419 struct Laplacian
1420{
1421 // random access version
1422 template<typename Accessor>
1423 static typename Accessor::ValueType result(const MapType& map,
1424 const Accessor& grid, const Coord& ijk)
1425 {
1426 using ValueType = typename Accessor::ValueType;
1427 // all the second derivatives in index space
1428 ValueType iddx = D2<DiffScheme>::inX(grid, ijk);
1429 ValueType iddy = D2<DiffScheme>::inY(grid, ijk);
1430 ValueType iddz = D2<DiffScheme>::inZ(grid, ijk);
1431
1432 ValueType iddxy = D2<DiffScheme>::inXandY(grid, ijk);
1433 ValueType iddyz = D2<DiffScheme>::inYandZ(grid, ijk);
1434 ValueType iddxz = D2<DiffScheme>::inXandZ(grid, ijk);
1435
1436 // second derivatives in index space
1437 Mat3d d2_is(iddx, iddxy, iddxz,
1438 iddxy, iddy, iddyz,
1439 iddxz, iddyz, iddz);
1440
1441 Mat3d d2_rs; // to hold the second derivative matrix in range space
1442 if (is_linear<MapType>::value) {
1443 d2_rs = map.applyIJC(d2_is);
1444 } else {
1445 // compute the first derivatives with 2nd order accuracy.
1446 Vec3d d1_is(static_cast<double>(D1<CD_2ND>::inX(grid, ijk)),
1447 static_cast<double>(D1<CD_2ND>::inY(grid, ijk)),
1448 static_cast<double>(D1<CD_2ND>::inZ(grid, ijk)));
1449
1450 d2_rs = map.applyIJC(d2_is, d1_is, ijk.asVec3d());
1451 }
1452
1453 // the trace of the second derivative (range space) matrix is laplacian
1454 return ValueType(d2_rs(0,0) + d2_rs(1,1) + d2_rs(2,2));
1455 }
1456
1457 // stencil access version
1458 template<typename StencilT>
1459 static typename StencilT::ValueType result(const MapType& map, const StencilT& stencil)
1460 {
1461 using ValueType = typename StencilT::ValueType;
1462 // all the second derivatives in index space
1463 ValueType iddx = D2<DiffScheme>::inX(stencil);
1464 ValueType iddy = D2<DiffScheme>::inY(stencil);
1465 ValueType iddz = D2<DiffScheme>::inZ(stencil);
1466
1467 ValueType iddxy = D2<DiffScheme>::inXandY(stencil);
1468 ValueType iddyz = D2<DiffScheme>::inYandZ(stencil);
1469 ValueType iddxz = D2<DiffScheme>::inXandZ(stencil);
1470
1471 // second derivatives in index space
1472 Mat3d d2_is(iddx, iddxy, iddxz,
1473 iddxy, iddy, iddyz,
1474 iddxz, iddyz, iddz);
1475
1476 Mat3d d2_rs; // to hold the second derivative matrix in range space
1477 if (is_linear<MapType>::value) {
1478 d2_rs = map.applyIJC(d2_is);
1479 } else {
1480 // compute the first derivatives with 2nd order accuracy.
1481 Vec3d d1_is(D1<CD_2ND>::inX(stencil),
1482 D1<CD_2ND>::inY(stencil),
1483 D1<CD_2ND>::inZ(stencil) );
1484
1485 d2_rs = map.applyIJC(d2_is, d1_is, stencil.getCenterCoord().asVec3d());
1486 }
1487
1488 // the trace of the second derivative (range space) matrix is laplacian
1489 return ValueType(d2_rs(0,0) + d2_rs(1,1) + d2_rs(2,2));
1490 }
1491};
1492
1493
1494 template<DDScheme DiffScheme>
1495 struct Laplacian<TranslationMap, DiffScheme>
1496{
1497 // random access version
1498 template<typename Accessor>
1499 static typename Accessor::ValueType result(const TranslationMap&,
1500 const Accessor& grid, const Coord& ijk)
1501 {
1502 return ISLaplacian<DiffScheme>::result(grid, ijk);
1503 }
1504
1505 // stencil access version
1506 template<typename StencilT>
1507 static typename StencilT::ValueType result(const TranslationMap&, const StencilT& stencil)
1508 {
1509 return ISLaplacian<DiffScheme>::result(stencil);
1510 }
1511};
1512
1513
1514// The Laplacian is invariant to rotation or reflection.
1515 template<DDScheme DiffScheme>
1516 struct Laplacian<UnitaryMap, DiffScheme>
1517{
1518 // random access version
1519 template<typename Accessor>
1520 static typename Accessor::ValueType result(const UnitaryMap&,
1521 const Accessor& grid, const Coord& ijk)
1522 {
1523 return ISLaplacian<DiffScheme>::result(grid, ijk);
1524 }
1525
1526 // stencil access version
1527 template<typename StencilT>
1528 static typename StencilT::ValueType result(const UnitaryMap&, const StencilT& stencil)
1529 {
1530 return ISLaplacian<DiffScheme>::result(stencil);
1531 }
1532};
1533
1534
1535 template<DDScheme DiffScheme>
1536 struct Laplacian<UniformScaleMap, DiffScheme>
1537{
1538 // random access version
1539 template<typename Accessor> static typename Accessor::ValueType
1540 result(const UniformScaleMap& map, const Accessor& grid, const Coord& ijk)
1541 {
1542 using ValueType = typename Accessor::ValueType;
1543 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
1544 return ISLaplacian<DiffScheme>::result(grid, ijk) * invdxdx;
1545 }
1546
1547 // stencil access version
1548 template<typename StencilT> static typename StencilT::ValueType
1549 result(const UniformScaleMap& map, const StencilT& stencil)
1550 {
1551 using ValueType = typename StencilT::ValueType;
1552 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
1553 return ISLaplacian<DiffScheme>::result(stencil) * invdxdx;
1554 }
1555};
1556
1557
1558 template<DDScheme DiffScheme>
1559 struct Laplacian<UniformScaleTranslateMap, DiffScheme>
1560{
1561 // random access version
1562 template<typename Accessor> static typename Accessor::ValueType
1563 result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
1564 {
1565 using ValueType = typename Accessor::ValueType;
1566 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
1567 return ISLaplacian<DiffScheme>::result(grid, ijk) * invdxdx;
1568 }
1569
1570 // stencil access version
1571 template<typename StencilT> static typename StencilT::ValueType
1572 result(const UniformScaleTranslateMap& map, const StencilT& stencil)
1573 {
1574 using ValueType = typename StencilT::ValueType;
1575 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
1576 return ISLaplacian<DiffScheme>::result(stencil) * invdxdx;
1577 }
1578};
1579
1580
1581 template<DDScheme DiffScheme>
1582 struct Laplacian<ScaleMap, DiffScheme>
1583{
1584 // random access version
1585 template<typename Accessor> static typename Accessor::ValueType
1586 result(const ScaleMap& map, const Accessor& grid, const Coord& ijk)
1587 {
1588 using ValueType = typename Accessor::ValueType;
1589
1590 // compute the second derivatives in index space
1591 ValueType iddx = D2<DiffScheme>::inX(grid, ijk);
1592 ValueType iddy = D2<DiffScheme>::inY(grid, ijk);
1593 ValueType iddz = D2<DiffScheme>::inZ(grid, ijk);
1594 const Vec3d& invScaleSqr = map.getInvScaleSqr();
1595 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
1596 // scale them by the appropriate 1/dx^2, 1/dy^2, 1/dz^2 and sum
1597 const ValueType value = iddx * invScaleSqr[0] + iddy * invScaleSqr[1] + iddz * invScaleSqr[2];
1598 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
1599 return value;
1600 }
1601
1602 // stencil access version
1603 template<typename StencilT> static typename StencilT::ValueType
1604 result(const ScaleMap& map, const StencilT& stencil)
1605 {
1606 using ValueType = typename StencilT::ValueType;
1607
1608 // compute the second derivatives in index space
1609 ValueType iddx = D2<DiffScheme>::inX(stencil);
1610 ValueType iddy = D2<DiffScheme>::inY(stencil);
1611 ValueType iddz = D2<DiffScheme>::inZ(stencil);
1612 const Vec3d& invScaleSqr = map.getInvScaleSqr();
1613 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
1614 // scale them by the appropriate 1/dx^2, 1/dy^2, 1/dz^2 and sum
1615 const ValueType value = iddx * invScaleSqr[0] + iddy * invScaleSqr[1] + iddz * invScaleSqr[2];
1616 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
1617 return value;
1618 }
1619};
1620
1621
1622 template<DDScheme DiffScheme>
1623 struct Laplacian<ScaleTranslateMap, DiffScheme>
1624{
1625 // random access version
1626 template<typename Accessor> static typename Accessor::ValueType
1627 result(const ScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
1628 {
1629 using ValueType = typename Accessor::ValueType;
1630 // compute the second derivatives in index space
1631 ValueType iddx = D2<DiffScheme>::inX(grid, ijk);
1632 ValueType iddy = D2<DiffScheme>::inY(grid, ijk);
1633 ValueType iddz = D2<DiffScheme>::inZ(grid, ijk);
1634 const Vec3d& invScaleSqr = map.getInvScaleSqr();
1635 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
1636 // scale them by the appropriate 1/dx^2, 1/dy^2, 1/dz^2 and sum
1637 const ValueType value = iddx * invScaleSqr[0] + iddy * invScaleSqr[1] + iddz * invScaleSqr[2];
1638 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
1639 return value;
1640 }
1641
1642 // stencil access version
1643 template<typename StencilT> static typename StencilT::ValueType
1644 result(const ScaleTranslateMap& map, const StencilT& stencil)
1645 {
1646 using ValueType = typename StencilT::ValueType;
1647 // compute the second derivatives in index space
1648 ValueType iddx = D2<DiffScheme>::inX(stencil);
1649 ValueType iddy = D2<DiffScheme>::inY(stencil);
1650 ValueType iddz = D2<DiffScheme>::inZ(stencil);
1651 const Vec3d& invScaleSqr = map.getInvScaleSqr();
1652 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
1653 // scale them by the appropriate 1/dx^2, 1/dy^2, 1/dz^2 and sum
1654 const ValueType value = iddx * invScaleSqr[0] + iddy * invScaleSqr[1] + iddz * invScaleSqr[2];
1655 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
1656 return value;
1657 }
1658};
1659
1660
1661/// @brief Compute the closest-point transform to a level set.
1662/// @return the closest point to the surface from which the level set was derived,
1663/// in the domain space of the map (e.g., voxel space).
1664 template<typename MapType, DScheme DiffScheme>
1665 struct CPT
1666{
1667 // random access version
1668 template<typename Accessor> static math::Vec3<typename Accessor::ValueType>
1669 result(const MapType& map, const Accessor& grid, const Coord& ijk)
1670 {
1671 using ValueType = typename Accessor::ValueType;
1672 using Vec3Type = Vec3<ValueType>;
1673
1674 // current distance
1675 ValueType d = grid.getValue(ijk);
1676 // compute gradient in physical space where it is a unit normal
1677 // since the grid holds a distance level set.
1678 Vec3d vectorFromSurface(d*Gradient<MapType,DiffScheme>::result(map, grid, ijk));
1679 if (is_linear<MapType>::value) {
1680 Vec3d result = ijk.asVec3d() - map.applyInverseMap(vectorFromSurface);
1681 return Vec3Type(result);
1682 } else {
1683 Vec3d location = map.applyMap(ijk.asVec3d());
1684 Vec3d result = map.applyInverseMap(location - vectorFromSurface);
1685 return Vec3Type(result);
1686 }
1687 }
1688
1689 // stencil access version
1690 template<typename StencilT> static math::Vec3<typename StencilT::ValueType>
1691 result(const MapType& map, const StencilT& stencil)
1692 {
1693 using ValueType = typename StencilT::ValueType;
1694 using Vec3Type = Vec3<ValueType>;
1695
1696 // current distance
1697 ValueType d = stencil.template getValue<0, 0, 0>();
1698 // compute gradient in physical space where it is a unit normal
1699 // since the grid holds a distance level set.
1700 Vec3d vectorFromSurface(d*Gradient<MapType, DiffScheme>::result(map, stencil));
1701 if (is_linear<MapType>::value) {
1702 Vec3d result = stencil.getCenterCoord().asVec3d()
1703 - map.applyInverseMap(vectorFromSurface);
1704 return Vec3Type(result);
1705 } else {
1706 Vec3d location = map.applyMap(stencil.getCenterCoord().asVec3d());
1707 Vec3d result = map.applyInverseMap(location - vectorFromSurface);
1708 return Vec3Type(result);
1709 }
1710 }
1711};
1712
1713
1714/// @brief Compute the closest-point transform to a level set.
1715/// @return the closest point to the surface from which the level set was derived,
1716/// in the range space of the map (e.g., in world space)
1717 template<typename MapType, DScheme DiffScheme>
1718 struct CPT_RANGE
1719{
1720 // random access version
1721 template<typename Accessor> static Vec3<typename Accessor::ValueType>
1722 result(const MapType& map, const Accessor& grid, const Coord& ijk)
1723 {
1724 using ValueType = typename Accessor::ValueType;
1725 using Vec3Type = Vec3<ValueType>;
1726 // current distance
1727 ValueType d = grid.getValue(ijk);
1728 // compute gradient in physical space where it is a unit normal
1729 // since the grid holds a distance level set.
1730 Vec3Type vectorFromSurface =
1731 d*Gradient<MapType,DiffScheme>::result(map, grid, ijk);
1732 Vec3d result = map.applyMap(ijk.asVec3d()) - vectorFromSurface;
1733
1734 return Vec3Type(result);
1735 }
1736
1737 // stencil access version
1738 template<typename StencilT> static Vec3<typename StencilT::ValueType>
1739 result(const MapType& map, const StencilT& stencil)
1740 {
1741 using ValueType = typename StencilT::ValueType;
1742 using Vec3Type = Vec3<ValueType>;
1743 // current distance
1744 ValueType d = stencil.template getValue<0, 0, 0>();
1745 // compute gradient in physical space where it is a unit normal
1746 // since the grid holds a distance level set.
1747 Vec3Type vectorFromSurface =
1748 d*Gradient<MapType, DiffScheme>::result(map, stencil);
1749 Vec3d result = map.applyMap(stencil.getCenterCoord().asVec3d()) - vectorFromSurface;
1750
1751 return Vec3Type(result);
1752 }
1753};
1754
1755
1756/// @brief Compute the mean curvature.
1757/// @details The mean curvature is returned in two parts, @a alpha and @a beta,
1758/// where @a alpha is the numerator in &nabla; &middot; (&nabla;&Phi; / |&nabla;&Phi;|)
1759/// and @a beta is |&nabla;&Phi;|.
1760 template<typename MapType, DDScheme DiffScheme2, DScheme DiffScheme1>
1761 struct MeanCurvature
1762{
1763 /// @brief Random access version
1764 /// @return @c true if the gradient is nonzero, in which case the mean curvature
1765 /// is returned in two parts, @a alpha and @a beta, where @a alpha is the numerator
1766 /// in &nabla; &middot; (&nabla;&Phi; / |&nabla;&Phi;|) and @a beta is |&nabla;&Phi;|.
1767 template<typename Accessor>
1768 static bool compute(const MapType& map, const Accessor& grid, const Coord& ijk,
1769 double& alpha, double& beta)
1770 {
1771 using ValueType = typename Accessor::ValueType;
1772
1773 // compute the gradient in index and world space
1774 Vec3d d1_is(static_cast<double>(D1<DiffScheme1>::inX(grid, ijk)),
1775 static_cast<double>(D1<DiffScheme1>::inY(grid, ijk)),
1776 static_cast<double>(D1<DiffScheme1>::inZ(grid, ijk))), d1_ws;
1777 if (is_linear<MapType>::value) {//resolved at compiletime
1778 d1_ws = map.applyIJT(d1_is);
1779 } else {
1780 d1_ws = map.applyIJT(d1_is, ijk.asVec3d());
1781 }
1782 const double Dx2 = d1_ws(0)*d1_ws(0);
1783 const double Dy2 = d1_ws(1)*d1_ws(1);
1784 const double Dz2 = d1_ws(2)*d1_ws(2);
1785 const double normGrad = Dx2 + Dy2 + Dz2;
1786 if (normGrad <= math::Tolerance<double>::value()) {
1787 alpha = beta = 0;
1788 return false;
1789 }
1790
1791 // all the second derivatives in index space
1792 ValueType iddx = D2<DiffScheme2>::inX(grid, ijk);
1793 ValueType iddy = D2<DiffScheme2>::inY(grid, ijk);
1794 ValueType iddz = D2<DiffScheme2>::inZ(grid, ijk);
1795
1796 ValueType iddxy = D2<DiffScheme2>::inXandY(grid, ijk);
1797 ValueType iddyz = D2<DiffScheme2>::inYandZ(grid, ijk);
1798 ValueType iddxz = D2<DiffScheme2>::inXandZ(grid, ijk);
1799
1800 // second derivatives in index space
1801 Mat3d d2_is(iddx, iddxy, iddxz,
1802 iddxy, iddy, iddyz,
1803 iddxz, iddyz, iddz);
1804
1805 // convert second derivatives to world space
1806 Mat3d d2_ws;
1807 if (is_linear<MapType>::value) {//resolved at compiletime
1808 d2_ws = map.applyIJC(d2_is);
1809 } else {
1810 d2_ws = map.applyIJC(d2_is, d1_is, ijk.asVec3d());
1811 }
1812
1813 // assemble the nominator and denominator for mean curvature
1814 alpha = (Dx2*(d2_ws(1,1)+d2_ws(2,2))+Dy2*(d2_ws(0,0)+d2_ws(2,2))
1815 +Dz2*(d2_ws(0,0)+d2_ws(1,1))
1816 -2*(d1_ws(0)*(d1_ws(1)*d2_ws(0,1)+d1_ws(2)*d2_ws(0,2))
1817 +d1_ws(1)*d1_ws(2)*d2_ws(1,2)));
1818 beta = std::sqrt(normGrad); // * 1/dx
1819 return true;
1820 }
1821
1822 template<typename Accessor>
1823 static typename Accessor::ValueType result(const MapType& map,
1824 const Accessor& grid, const Coord& ijk)
1825 {
1826 using ValueType = typename Accessor::ValueType;
1827 double alpha, beta;
1828 return compute(map, grid, ijk, alpha, beta) ?
1829 ValueType(alpha/(2. *math::Pow3(beta))) : 0;
1830 }
1831
1832 template<typename Accessor>
1833 static typename Accessor::ValueType normGrad(const MapType& map,
1834 const Accessor& grid, const Coord& ijk)
1835 {
1836 using ValueType = typename Accessor::ValueType;
1837 double alpha, beta;
1838 return compute(map, grid, ijk, alpha, beta) ?
1839 ValueType(alpha/(2. *math::Pow2(beta))) : 0;
1840 }
1841
1842 /// @brief Stencil access version
1843 /// @return @c true if the gradient is nonzero, in which case the mean curvature
1844 /// is returned in two parts, @a alpha and @a beta, where @a alpha is the numerator
1845 /// in &nabla; &middot; (&nabla;&Phi; / |&nabla;&Phi;|) and @a beta is |&nabla;&Phi;|.
1846 template<typename StencilT>
1847 static bool compute(const MapType& map, const StencilT& stencil,
1848 double& alpha, double& beta)
1849 {
1850 using ValueType = typename StencilT::ValueType;
1851
1852 // compute the gradient in index and world space
1853 Vec3d d1_is(D1<DiffScheme1>::inX(stencil),
1854 D1<DiffScheme1>::inY(stencil),
1855 D1<DiffScheme1>::inZ(stencil) ), d1_ws;
1856 if (is_linear<MapType>::value) {//resolved at compiletime
1857 d1_ws = map.applyIJT(d1_is);
1858 } else {
1859 d1_ws = map.applyIJT(d1_is, stencil.getCenterCoord().asVec3d());
1860 }
1861 const double Dx2 = d1_ws(0)*d1_ws(0);
1862 const double Dy2 = d1_ws(1)*d1_ws(1);
1863 const double Dz2 = d1_ws(2)*d1_ws(2);
1864 const double normGrad = Dx2 + Dy2 + Dz2;
1865 if (normGrad <= math::Tolerance<double>::value()) {
1866 alpha = beta = 0;
1867 return false;
1868 }
1869
1870 // all the second derivatives in index space
1871 ValueType iddx = D2<DiffScheme2>::inX(stencil);
1872 ValueType iddy = D2<DiffScheme2>::inY(stencil);
1873 ValueType iddz = D2<DiffScheme2>::inZ(stencil);
1874
1875 ValueType iddxy = D2<DiffScheme2>::inXandY(stencil);
1876 ValueType iddyz = D2<DiffScheme2>::inYandZ(stencil);
1877 ValueType iddxz = D2<DiffScheme2>::inXandZ(stencil);
1878
1879 // second derivatives in index space
1880 Mat3d d2_is(iddx, iddxy, iddxz,
1881 iddxy, iddy, iddyz,
1882 iddxz, iddyz, iddz);
1883
1884 // convert second derivatives to world space
1885 Mat3d d2_ws;
1886 if (is_linear<MapType>::value) {//resolved at compiletime
1887 d2_ws = map.applyIJC(d2_is);
1888 } else {
1889 d2_ws = map.applyIJC(d2_is, d1_is, stencil.getCenterCoord().asVec3d());
1890 }
1891
1892 // for return
1893 alpha = (Dx2*(d2_ws(1,1)+d2_ws(2,2))+Dy2*(d2_ws(0,0)+d2_ws(2,2))
1894 +Dz2*(d2_ws(0,0)+d2_ws(1,1))
1895 -2*(d1_ws(0)*(d1_ws(1)*d2_ws(0,1)+d1_ws(2)*d2_ws(0,2))
1896 +d1_ws(1)*d1_ws(2)*d2_ws(1,2)));
1897 beta = std::sqrt(normGrad); // * 1/dx
1898 return true;
1899 }
1900
1901 template<typename StencilT>
1902 static typename StencilT::ValueType
1903 result(const MapType& map, const StencilT stencil)
1904 {
1905 using ValueType = typename StencilT::ValueType;
1906 double alpha, beta;
1907 return compute(map, stencil, alpha, beta) ?
1908 ValueType(alpha/(2*math::Pow3(beta))) : 0;
1909 }
1910
1911 template<typename StencilT>
1912 static typename StencilT::ValueType normGrad(const MapType& map, const StencilT stencil)
1913 {
1914 using ValueType = typename StencilT::ValueType;
1915 double alpha, beta;
1916 return compute(map, stencil, alpha, beta) ?
1917 ValueType(alpha/(2*math::Pow2(beta))) : 0;
1918 }
1919};
1920
1921
1922 template<DDScheme DiffScheme2, DScheme DiffScheme1>
1923 struct MeanCurvature<TranslationMap, DiffScheme2, DiffScheme1>
1924{
1925 // random access version
1926 template<typename Accessor>
1927 static typename Accessor::ValueType result(const TranslationMap&,
1928 const Accessor& grid, const Coord& ijk)
1929 {
1930 using ValueType = typename Accessor::ValueType;
1931
1932 ValueType alpha, beta;
1933 return ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta) ?
1934 ValueType(alpha /(2*math::Pow3(beta))) : 0;
1935 }
1936
1937 template<typename Accessor>
1938 static typename Accessor::ValueType normGrad(const TranslationMap&,
1939 const Accessor& grid, const Coord& ijk)
1940 {
1941 using ValueType = typename Accessor::ValueType;
1942
1943 ValueType alpha, beta;
1944 return ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta) ?
1945 ValueType(alpha/(2*math::Pow2(beta))) : 0;
1946 }
1947
1948 // stencil access version
1949 template<typename StencilT>
1950 static typename StencilT::ValueType result(const TranslationMap&, const StencilT& stencil)
1951 {
1952 using ValueType = typename StencilT::ValueType;
1953
1954 ValueType alpha, beta;
1955 return ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta) ?
1956 ValueType(alpha /(2*math::Pow3(beta))) : 0;
1957 }
1958
1959 template<typename StencilT>
1960 static typename StencilT::ValueType normGrad(const TranslationMap&, const StencilT& stencil)
1961 {
1962 using ValueType = typename StencilT::ValueType;
1963
1964 ValueType alpha, beta;
1965 return ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta) ?
1966 ValueType(alpha/(2*math::Pow2(beta))) : 0;
1967 }
1968};
1969
1970
1971 template<DDScheme DiffScheme2, DScheme DiffScheme1>
1972 struct MeanCurvature<UniformScaleMap, DiffScheme2, DiffScheme1>
1973{
1974 // random access version
1975 template<typename Accessor>
1976 static typename Accessor::ValueType result(const UniformScaleMap& map,
1977 const Accessor& grid, const Coord& ijk)
1978 {
1979 using ValueType = typename Accessor::ValueType;
1980
1981 ValueType alpha, beta;
1982 if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta)) {
1983 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
1984 return ValueType(alpha*inv2dx/math::Pow3(beta));
1985 }
1986 return 0;
1987 }
1988
1989 template<typename Accessor>
1990 static typename Accessor::ValueType normGrad(const UniformScaleMap& map,
1991 const Accessor& grid, const Coord& ijk)
1992 {
1993 using ValueType = typename Accessor::ValueType;
1994
1995 ValueType alpha, beta;
1996 if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta)) {
1997 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
1998 return ValueType(alpha*invdxdx/(2*math::Pow2(beta)));
1999 }
2000 return 0;
2001 }
2002
2003 // stencil access version
2004 template<typename StencilT>
2005 static typename StencilT::ValueType result(const UniformScaleMap& map, const StencilT& stencil)
2006 {
2007 using ValueType = typename StencilT::ValueType;
2008
2009 ValueType alpha, beta;
2010 if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta)) {
2011 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
2012 return ValueType(alpha*inv2dx/math::Pow3(beta));
2013 }
2014 return 0;
2015 }
2016
2017 template<typename StencilT>
2018 static typename StencilT::ValueType normGrad(const UniformScaleMap& map, const StencilT& stencil)
2019 {
2020 using ValueType = typename StencilT::ValueType;
2021
2022 ValueType alpha, beta;
2023 if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta)) {
2024 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
2025 return ValueType(alpha*invdxdx/(2*math::Pow2(beta)));
2026 }
2027 return 0;
2028 }
2029};
2030
2031
2032 template<DDScheme DiffScheme2, DScheme DiffScheme1>
2033 struct MeanCurvature<UniformScaleTranslateMap, DiffScheme2, DiffScheme1>
2034{
2035 // random access version
2036 template<typename Accessor> static typename Accessor::ValueType
2037 result(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
2038 {
2039 using ValueType = typename Accessor::ValueType;
2040
2041 ValueType alpha, beta;
2042 if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta)) {
2043 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
2044 return ValueType(alpha*inv2dx/math::Pow3(beta));
2045 }
2046 return 0;
2047 }
2048
2049 template<typename Accessor> static typename Accessor::ValueType
2050 normGrad(const UniformScaleTranslateMap& map, const Accessor& grid, const Coord& ijk)
2051 {
2052 using ValueType = typename Accessor::ValueType;
2053
2054 ValueType alpha, beta;
2055 if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(grid, ijk, alpha, beta)) {
2056 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
2057 return ValueType(alpha*invdxdx/(2*math::Pow2(beta)));
2058 }
2059 return 0;
2060 }
2061
2062 // stencil access version
2063 template<typename StencilT> static typename StencilT::ValueType
2064 result(const UniformScaleTranslateMap& map, const StencilT& stencil)
2065 {
2066 using ValueType = typename StencilT::ValueType;
2067
2068 ValueType alpha, beta;
2069 if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta)) {
2070 ValueType inv2dx = ValueType(map.getInvTwiceScale()[0]);
2071 return ValueType(alpha*inv2dx/math::Pow3(beta));
2072 }
2073 return 0;
2074 }
2075
2076 template<typename StencilT> static typename StencilT::ValueType
2077 normGrad(const UniformScaleTranslateMap& map, const StencilT& stencil)
2078 {
2079 using ValueType = typename StencilT::ValueType;
2080
2081 ValueType alpha, beta;
2082 if (ISMeanCurvature<DiffScheme2, DiffScheme1>::result(stencil, alpha, beta)) {
2083 ValueType invdxdx = ValueType(map.getInvScaleSqr()[0]);
2084 return ValueType(alpha*invdxdx/(2*math::Pow2(beta)));
2085 }
2086 return 0;
2087 }
2088};
2089
2090
2091/// @brief A wrapper that holds a MapBase::ConstPtr and exposes a reduced set
2092/// of functionality needed by the mathematical operators
2093/// @details This may be used in some <tt>Map</tt>-templated code, when the overhead of
2094/// actually resolving the @c Map type is large compared to the map work to be done.
2095 class GenericMap
2096{
2097 public:
2098 template<typename GridType>
2099 GenericMap(const GridType& g): mMap(g.transform().baseMap()) {}
2100
2101 GenericMap(const Transform& t): mMap(t.baseMap()) {}
2102 GenericMap(MapBase::Ptr map): mMap(ConstPtrCast<const MapBase>(map)) {}
2103 GenericMap(MapBase::ConstPtr map): mMap(map) {}
2104 ~GenericMap() {}
2105
2106 Vec3d applyMap(const Vec3d& in) const { return mMap->applyMap(in); }
2107 Vec3d applyInverseMap(const Vec3d& in) const { return mMap->applyInverseMap(in); }
2108
2109 Vec3d applyIJT(const Vec3d& in) const { return mMap->applyIJT(in); }
2110 Vec3d applyIJT(const Vec3d& in, const Vec3d& pos) const { return mMap->applyIJT(in, pos); }
2111 Mat3d applyIJC(const Mat3d& m) const { return mMap->applyIJC(m); }
2112 Mat3d applyIJC(const Mat3d& m, const Vec3d& v, const Vec3d& pos) const
2113 { return mMap->applyIJC(m,v,pos); }
2114
2115 double determinant() const { return mMap->determinant(); }
2116 double determinant(const Vec3d& in) const { return mMap->determinant(in); }
2117
2118 Vec3d voxelSize() const { return mMap->voxelSize(); }
2119 Vec3d voxelSize(const Vec3d&v) const { return mMap->voxelSize(v); }
2120
2121 private:
2122 MapBase::ConstPtr mMap;
2123};
2124
2125} // end math namespace
2126} // namespace OPENVDB_VERSION_NAME
2127} // end openvdb namespace
2128
2129#endif // OPENVDB_MATH_OPERATORS_HAS_BEEN_INCLUDED
FiniteDifference.h
Maps.h
OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
Bracket code with OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN/_END, to inhibit warnings about type conve...
Definition Platform.h:227
OPENVDB_NO_TYPE_CONVERSION_WARNING_END
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_END
Definition Platform.h:228
Transform.h
openvdb::v11_0::math::Coord
Signed (x, y, z) 32-bit integer coordinates.
Definition Coord.h:25
openvdb::v11_0::math::Coord::asVec3d
Vec3d asVec3d() const
Definition Coord.h:143
openvdb::v11_0::math::Coord::offsetBy
Coord offsetBy(Int32 dx, Int32 dy, Int32 dz) const
Definition Coord.h:91
openvdb::v11_0::math::GenericMap::determinant
double determinant(const Vec3d &in) const
Definition Operators.h:2116
openvdb::v11_0::math::GenericMap::voxelSize
Vec3d voxelSize() const
Definition Operators.h:2118
openvdb::v11_0::math::GenericMap::GenericMap
GenericMap(const GridType &g)
Definition Operators.h:2099
openvdb::v11_0::math::GenericMap::determinant
double determinant() const
Definition Operators.h:2115
openvdb::v11_0::math::GenericMap::applyMap
Vec3d applyMap(const Vec3d &in) const
Definition Operators.h:2106
openvdb::v11_0::math::GenericMap::GenericMap
GenericMap(MapBase::ConstPtr map)
Definition Operators.h:2103
openvdb::v11_0::math::GenericMap::applyInverseMap
Vec3d applyInverseMap(const Vec3d &in) const
Definition Operators.h:2107
openvdb::v11_0::math::GenericMap::GenericMap
GenericMap(const Transform &t)
Definition Operators.h:2101
openvdb::v11_0::math::GenericMap::applyIJC
Mat3d applyIJC(const Mat3d &m) const
Definition Operators.h:2111
openvdb::v11_0::math::GenericMap::applyIJT
Vec3d applyIJT(const Vec3d &in, const Vec3d &pos) const
Definition Operators.h:2110
openvdb::v11_0::math::GenericMap::voxelSize
Vec3d voxelSize(const Vec3d &v) const
Definition Operators.h:2119
openvdb::v11_0::math::GenericMap::applyIJT
Vec3d applyIJT(const Vec3d &in) const
Definition Operators.h:2109
openvdb::v11_0::math::GenericMap::GenericMap
GenericMap(MapBase::Ptr map)
Definition Operators.h:2102
openvdb::v11_0::math::GenericMap::~GenericMap
~GenericMap()
Definition Operators.h:2104
openvdb::v11_0::math::GenericMap::applyIJC
Mat3d applyIJC(const Mat3d &m, const Vec3d &v, const Vec3d &pos) const
Definition Operators.h:2112
openvdb::v11_0::math::MapBase
Abstract base class for maps.
Definition Maps.h:135
openvdb::v11_0::math::MapBase::Ptr
SharedPtr< MapBase > Ptr
Definition Maps.h:137
openvdb::v11_0::math::MapBase::ConstPtr
SharedPtr< const MapBase > ConstPtr
Definition Maps.h:138
openvdb::v11_0::math::NineteenPointStencil
Definition Stencils.h:822
openvdb::v11_0::math::ScaleMap
A specialized Affine transform that scales along the principal axis the scaling need not be uniform i...
Definition Maps.h:656
openvdb::v11_0::math::ScaleMap::getInvScale
const Vec3d & getInvScale() const
Return 1/(scale)
Definition Maps.h:802
openvdb::v11_0::math::ScaleMap::getInvTwiceScale
const Vec3d & getInvTwiceScale() const
Return 1/(2 scale). Used to optimize some finite difference calculations.
Definition Maps.h:800
openvdb::v11_0::math::ScaleMap::getInvScaleSqr
const Vec3d & getInvScaleSqr() const
Return the square of the scale. Used to optimize some finite difference calculations.
Definition Maps.h:798
openvdb::v11_0::math::ScaleTranslateMap
A specialized Affine transform that scales along the principal axis the scaling need not be uniform i...
Definition Maps.h:1163
openvdb::v11_0::math::ScaleTranslateMap::getInvScale
const Vec3d & getInvScale() const
Return 1/(scale)
Definition Maps.h:1347
openvdb::v11_0::math::ScaleTranslateMap::getInvTwiceScale
const Vec3d & getInvTwiceScale() const
Return 1/(2 scale). Used to optimize some finite difference calculations.
Definition Maps.h:1345
openvdb::v11_0::math::ScaleTranslateMap::getInvScaleSqr
const Vec3d & getInvScaleSqr() const
Return the square of the scale. Used to optimize some finite difference calculations.
Definition Maps.h:1343
openvdb::v11_0::math::SevenPointStencil
Definition Stencils.h:247
openvdb::v11_0::math::ThirteenPointStencil
Definition Stencils.h:552
openvdb::v11_0::math::Transform
Definition Transform.h:40
openvdb::v11_0::math::TranslationMap
A specialized linear transform that performs a translation.
Definition Maps.h:978
openvdb::v11_0::math::UniformScaleMap
A specialized Affine transform that scales along the principal axis the scaling is uniform in the thr...
Definition Maps.h:906
openvdb::v11_0::math::UniformScaleTranslateMap
A specialized Affine transform that uniformaly scales along the principal axis and then translates th...
Definition Maps.h:1479
openvdb::v11_0::math::UnitaryMap
A specialized linear transform that performs a unitary maping i.e. rotation and or reflection.
Definition Maps.h:1621
openvdb::v11_0::math::Vec3
Definition Vec3.h:24
openvdb::v11_0::internal
Definition openvdb.h:114
openvdb::v11_0::math::Mat3d
Mat3< double > Mat3d
Definition Mat3.h:834
openvdb::v11_0::math::GodunovsNormSqrd
Real GodunovsNormSqrd(bool isOutside, Real dP_xm, Real dP_xp, Real dP_ym, Real dP_yp, Real dP_zm, Real dP_zp)
Definition FiniteDifference.h:325
openvdb::v11_0::math::DScheme
DScheme
Different discrete schemes used in the first derivatives.
Definition FiniteDifference.h:31
openvdb::v11_0::math::FD_2ND
@ FD_2ND
Definition FiniteDifference.h:38
openvdb::v11_0::math::BD_3RD
@ BD_3RD
Definition FiniteDifference.h:42
openvdb::v11_0::math::FD_HJWENO5
@ FD_HJWENO5
Definition FiniteDifference.h:45
openvdb::v11_0::math::FD_WENO5
@ FD_WENO5
Definition FiniteDifference.h:43
openvdb::v11_0::math::BD_2ND
@ BD_2ND
Definition FiniteDifference.h:41
openvdb::v11_0::math::FD_1ST
@ FD_1ST
Definition FiniteDifference.h:37
openvdb::v11_0::math::BD_HJWENO5
@ BD_HJWENO5
Definition FiniteDifference.h:46
openvdb::v11_0::math::CD_2ND
@ CD_2ND
Definition FiniteDifference.h:34
openvdb::v11_0::math::BD_WENO5
@ BD_WENO5
Definition FiniteDifference.h:44
openvdb::v11_0::math::BD_1ST
@ BD_1ST
Definition FiniteDifference.h:40
openvdb::v11_0::math::FD_3RD
@ FD_3RD
Definition FiniteDifference.h:39
openvdb::v11_0::math::CD_SIXTH
@ CD_SIXTH
Definition FiniteDifference.h:153
openvdb::v11_0::math::CD_FOURTH
@ CD_FOURTH
Definition FiniteDifference.h:152
openvdb::v11_0::math::CD_SECOND
@ CD_SECOND
Definition FiniteDifference.h:151
openvdb::v11_0::math::Vec3d
Vec3< double > Vec3d
Definition Vec3.h:664
openvdb::v11_0::math::FIRST_BIAS
@ FIRST_BIAS
Definition FiniteDifference.h:166
openvdb::v11_0::math::THIRD_BIAS
@ THIRD_BIAS
Definition FiniteDifference.h:168
openvdb::v11_0::math::WENO5_BIAS
@ WENO5_BIAS
Definition FiniteDifference.h:169
openvdb::v11_0::math::SECOND_BIAS
@ SECOND_BIAS
Definition FiniteDifference.h:167
openvdb::v11_0::math::HJWENO5_BIAS
@ HJWENO5_BIAS
Definition FiniteDifference.h:170
openvdb::v11_0::math::Pow3
Type Pow3(Type x)
Return x3.
Definition Math.h:552
openvdb::v11_0::math::Pow2
Type Pow2(Type x)
Return x2.
Definition Math.h:548
openvdb::v11_0::ConstPtrCast
SharedPtr< T > ConstPtrCast(const SharedPtr< U > &ptr)
Return a new shared pointer that points to the same object as the given pointer but with possibly dif...
Definition Types.h:126
openvdb
Definition Exceptions.h:13
Stencils.h
Defines various finite difference stencils by means of the "curiously recurring template pattern" on ...
openvdb::v11_0::math::BIAS_SCHEME::ISStencil
Definition Operators.h:134
openvdb::v11_0::math::BIAS_SCHEME::ISStencil::StencilType
SevenPointStencil< GridType, IsSafe > StencilType
Definition Operators.h:135
openvdb::v11_0::math::BIAS_SCHEME< FIRST_BIAS >::ISStencil
Definition Operators.h:145
openvdb::v11_0::math::BIAS_SCHEME< FIRST_BIAS >::ISStencil::StencilType
SevenPointStencil< GridType, IsSafe > StencilType
Definition Operators.h:146
openvdb::v11_0::math::BIAS_SCHEME< FIRST_BIAS >::FD
static const DScheme FD
Definition Operators.h:141
openvdb::v11_0::math::BIAS_SCHEME< FIRST_BIAS >::BD
static const DScheme BD
Definition Operators.h:142
openvdb::v11_0::math::BIAS_SCHEME< HJWENO5_BIAS >::ISStencil
Definition Operators.h:186
openvdb::v11_0::math::BIAS_SCHEME< HJWENO5_BIAS >::ISStencil::StencilType
NineteenPointStencil< GridType, IsSafe > StencilType
Definition Operators.h:187
openvdb::v11_0::math::BIAS_SCHEME< HJWENO5_BIAS >::FD
static const DScheme FD
Definition Operators.h:182
openvdb::v11_0::math::BIAS_SCHEME< HJWENO5_BIAS >::BD
static const DScheme BD
Definition Operators.h:183
openvdb::v11_0::math::BIAS_SCHEME< SECOND_BIAS >::ISStencil
Definition Operators.h:156
openvdb::v11_0::math::BIAS_SCHEME< SECOND_BIAS >::ISStencil::StencilType
ThirteenPointStencil< GridType, IsSafe > StencilType
Definition Operators.h:157
openvdb::v11_0::math::BIAS_SCHEME< SECOND_BIAS >::FD
static const DScheme FD
Definition Operators.h:152
openvdb::v11_0::math::BIAS_SCHEME< SECOND_BIAS >::BD
static const DScheme BD
Definition Operators.h:153
openvdb::v11_0::math::BIAS_SCHEME< THIRD_BIAS >::ISStencil
Definition Operators.h:166
openvdb::v11_0::math::BIAS_SCHEME< THIRD_BIAS >::ISStencil::StencilType
NineteenPointStencil< GridType, IsSafe > StencilType
Definition Operators.h:167
openvdb::v11_0::math::BIAS_SCHEME< THIRD_BIAS >::FD
static const DScheme FD
Definition Operators.h:162
openvdb::v11_0::math::BIAS_SCHEME< THIRD_BIAS >::BD
static const DScheme BD
Definition Operators.h:163
openvdb::v11_0::math::BIAS_SCHEME< WENO5_BIAS >::ISStencil
Definition Operators.h:176
openvdb::v11_0::math::BIAS_SCHEME< WENO5_BIAS >::ISStencil::StencilType
NineteenPointStencil< GridType, IsSafe > StencilType
Definition Operators.h:177
openvdb::v11_0::math::BIAS_SCHEME< WENO5_BIAS >::FD
static const DScheme FD
Definition Operators.h:172
openvdb::v11_0::math::BIAS_SCHEME< WENO5_BIAS >::BD
static const DScheme BD
Definition Operators.h:173
openvdb::v11_0::math::BIAS_SCHEME
Definition Operators.h:129
openvdb::v11_0::math::BIAS_SCHEME< SpatialScheme >::FD
static const DScheme FD
Definition Operators.h:130
openvdb::v11_0::math::BIAS_SCHEME< SpatialScheme >::BD
static const DScheme BD
Definition Operators.h:131
openvdb::v11_0::math::CPT_RANGE
Compute the closest-point transform to a level set.
Definition Operators.h:1719
openvdb::v11_0::math::CPT_RANGE::result
static Vec3< typename StencilT::ValueType > result(const MapType &map, const StencilT &stencil)
Definition Operators.h:1739
openvdb::v11_0::math::CPT_RANGE::result
static Vec3< typename Accessor::ValueType > result(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1722
openvdb::v11_0::math::CPT
Compute the closest-point transform to a level set.
Definition Operators.h:1666
openvdb::v11_0::math::CPT::result
static math::Vec3< typename StencilT::ValueType > result(const MapType &map, const StencilT &stencil)
Definition Operators.h:1691
openvdb::v11_0::math::CPT::result
static math::Vec3< typename Accessor::ValueType > result(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1669
openvdb::v11_0::math::Curl< UniformScaleMap, CD_2ND >::result
static StencilT::ValueType result(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:1379
openvdb::v11_0::math::Curl< UniformScaleMap, CD_2ND >::result
static Accessor::ValueType result(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1369
openvdb::v11_0::math::Curl< UniformScaleMap, DiffScheme >::result
static StencilT::ValueType result(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:1330
openvdb::v11_0::math::Curl< UniformScaleMap, DiffScheme >::result
static Accessor::ValueType result(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1321
openvdb::v11_0::math::Curl< UniformScaleTranslateMap, CD_2ND >::result
static StencilT::ValueType result(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:1404
openvdb::v11_0::math::Curl< UniformScaleTranslateMap, CD_2ND >::result
static Accessor::ValueType result(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1394
openvdb::v11_0::math::Curl< UniformScaleTranslateMap, DiffScheme >::result
static StencilT::ValueType result(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:1354
openvdb::v11_0::math::Curl< UniformScaleTranslateMap, DiffScheme >::result
static Accessor::ValueType result(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1344
openvdb::v11_0::math::Curl
Compute the curl of a vector-valued grid using differencing of various orders in the space defined by...
Definition Operators.h:1275
openvdb::v11_0::math::Curl::result
static StencilT::ValueType result(const MapType &map, const StencilT &stencil)
Definition Operators.h:1297
openvdb::v11_0::math::Curl::result
static Accessor::ValueType result(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1278
openvdb::v11_0::math::D1::inX
static Accessor::ValueType inX(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::D1::inZ
static Accessor::ValueType inZ(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::D1::inY
static Accessor::ValueType inY(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::D1Vec::inZ
static Accessor::ValueType::value_type inZ(const Accessor &grid, const Coord &ijk, int n)
Definition FiniteDifference.h:1504
openvdb::v11_0::math::D1Vec::inX
static Accessor::ValueType::value_type inX(const Accessor &grid, const Coord &ijk, int n)
Definition FiniteDifference.h:1491
openvdb::v11_0::math::D1Vec::inY
static Accessor::ValueType::value_type inY(const Accessor &grid, const Coord &ijk, int n)
Definition FiniteDifference.h:1498
openvdb::v11_0::math::D2::inX
static Accessor::ValueType inX(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::D2::inZ
static Accessor::ValueType inZ(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::D2::inXandZ
static Accessor::ValueType inXandZ(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::D2::inYandZ
static Accessor::ValueType inYandZ(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::D2::inXandY
static Accessor::ValueType inXandY(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::D2::inY
static Accessor::ValueType inY(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::Divergence< ScaleMap, CD_2ND >::result
static Accessor::ValueType::value_type result(const ScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1211
openvdb::v11_0::math::Divergence< ScaleMap, CD_2ND >::result
static StencilT::ValueType::value_type result(const ScaleMap &map, const StencilT &stencil)
Definition Operators.h:1224
openvdb::v11_0::math::Divergence< ScaleMap, DiffScheme >::result
static Accessor::ValueType::value_type result(const ScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1145
openvdb::v11_0::math::Divergence< ScaleMap, DiffScheme >::result
static StencilT::ValueType::value_type result(const ScaleMap &map, const StencilT &stencil)
Definition Operators.h:1158
openvdb::v11_0::math::Divergence< ScaleTranslateMap, CD_2ND >::result
static StencilT::ValueType::value_type result(const ScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:1256
openvdb::v11_0::math::Divergence< ScaleTranslateMap, CD_2ND >::result
static Accessor::ValueType::value_type result(const ScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1243
openvdb::v11_0::math::Divergence< ScaleTranslateMap, DiffScheme >::result
static StencilT::ValueType::value_type result(const ScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:1191
openvdb::v11_0::math::Divergence< ScaleTranslateMap, DiffScheme >::result
static Accessor::ValueType::value_type result(const ScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1178
openvdb::v11_0::math::Divergence< TranslationMap, DiffScheme >::result
static StencilT::ValueType::value_type result(const TranslationMap &, const StencilT &stencil)
Definition Operators.h:1002
openvdb::v11_0::math::Divergence< TranslationMap, DiffScheme >::result
static Accessor::ValueType::value_type result(const TranslationMap &, const Accessor &grid, const Coord &ijk)
Definition Operators.h:991
openvdb::v11_0::math::Divergence< UniformScaleMap, CD_2ND >::result
static Accessor::ValueType::value_type result(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1083
openvdb::v11_0::math::Divergence< UniformScaleMap, CD_2ND >::result
static StencilT::ValueType::value_type result(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:1095
openvdb::v11_0::math::Divergence< UniformScaleMap, DiffScheme >::result
static Accessor::ValueType::value_type result(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1019
openvdb::v11_0::math::Divergence< UniformScaleMap, DiffScheme >::result
static StencilT::ValueType::value_type result(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:1032
openvdb::v11_0::math::Divergence< UniformScaleTranslateMap, CD_2ND >::result
static StencilT::ValueType::value_type result(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:1126
openvdb::v11_0::math::Divergence< UniformScaleTranslateMap, CD_2ND >::result
static Accessor::ValueType::value_type result(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1113
openvdb::v11_0::math::Divergence< UniformScaleTranslateMap, DiffScheme >::result
static StencilT::ValueType::value_type result(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:1064
openvdb::v11_0::math::Divergence< UniformScaleTranslateMap, DiffScheme >::result
static Accessor::ValueType::value_type result(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1051
openvdb::v11_0::math::Divergence
Compute the divergence of a vector-valued grid using differencing of various orders,...
Definition Operators.h:950
openvdb::v11_0::math::Divergence::result
static Accessor::ValueType::value_type result(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:953
openvdb::v11_0::math::Divergence::result
static StencilT::ValueType::value_type result(const MapType &map, const StencilT &stencil)
Definition Operators.h:969
openvdb::v11_0::math::Gradient< ScaleMap, CD_2ND >::result
static internal::ReturnValue< StencilT >::Vec3Type result(const ScaleMap &map, const StencilT &stencil)
Definition Operators.h:757
openvdb::v11_0::math::Gradient< ScaleMap, CD_2ND >::result
static internal::ReturnValue< Accessor >::Vec3Type result(const ScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:738
openvdb::v11_0::math::Gradient< ScaleTranslateMap, CD_2ND >::result
static internal::ReturnValue< StencilT >::Vec3Type result(const ScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:801
openvdb::v11_0::math::Gradient< ScaleTranslateMap, CD_2ND >::result
static internal::ReturnValue< Accessor >::Vec3Type result(const ScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:782
openvdb::v11_0::math::Gradient< TranslationMap, DiffScheme >::result
static internal::ReturnValue< Accessor >::Vec3Type result(const TranslationMap &, const Accessor &grid, const Coord &ijk)
Definition Operators.h:652
openvdb::v11_0::math::Gradient< TranslationMap, DiffScheme >::result
static internal::ReturnValue< StencilT >::Vec3Type result(const TranslationMap &, const StencilT &stencil)
Definition Operators.h:660
openvdb::v11_0::math::Gradient< UniformScaleMap, CD_2ND >::result
static internal::ReturnValue< StencilT >::Vec3Type result(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:687
openvdb::v11_0::math::Gradient< UniformScaleMap, CD_2ND >::result
static internal::ReturnValue< Accessor >::Vec3Type result(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:674
openvdb::v11_0::math::Gradient< UniformScaleTranslateMap, CD_2ND >::result
static internal::ReturnValue< Accessor >::Vec3Type result(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:706
openvdb::v11_0::math::Gradient< UniformScaleTranslateMap, CD_2ND >::result
static internal::ReturnValue< StencilT >::Vec3Type result(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:719
openvdb::v11_0::math::GradientBiased
Biased gradient operators, defined with respect to the range-space of the map.
Definition Operators.h:825
openvdb::v11_0::math::GradientBiased::result
static math::Vec3< typename Accessor::ValueType > result(const MapType &map, const Accessor &grid, const Coord &ijk, const Vec3< typename Accessor::ValueType > &V)
Definition Operators.h:828
openvdb::v11_0::math::GradientBiased::result
static math::Vec3< typename StencilT::ValueType > result(const MapType &map, const StencilT &stencil, const Vec3< typename StencilT::ValueType > &V)
Definition Operators.h:840
openvdb::v11_0::math::Gradient
Center difference gradient operators, defined with respect to the range-space of the map.
Definition Operators.h:620
openvdb::v11_0::math::Gradient::result
static internal::ReturnValue< Accessor >::Vec3Type result(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:624
openvdb::v11_0::math::Gradient::result
static internal::ReturnValue< StencilT >::Vec3Type result(const MapType &map, const StencilT &stencil)
Definition Operators.h:635
openvdb::v11_0::math::GradientNormSqrd< UniformScaleMap, GradScheme >::result
static StencilT::ValueType result(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:908
openvdb::v11_0::math::GradientNormSqrd< UniformScaleMap, GradScheme >::result
static Accessor::ValueType result(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:897
openvdb::v11_0::math::GradientNormSqrd< UniformScaleTranslateMap, GradScheme >::result
static StencilT::ValueType result(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:935
openvdb::v11_0::math::GradientNormSqrd< UniformScaleTranslateMap, GradScheme >::result
static Accessor::ValueType result(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:924
openvdb::v11_0::math::GradientNormSqrd
Definition Operators.h:858
openvdb::v11_0::math::GradientNormSqrd::FD
static const DScheme FD
Definition Operators.h:859
openvdb::v11_0::math::GradientNormSqrd::result
static StencilT::ValueType result(const MapType &map, const StencilT &stencil)
Definition Operators.h:879
openvdb::v11_0::math::GradientNormSqrd::BD
static const DScheme BD
Definition Operators.h:860
openvdb::v11_0::math::GradientNormSqrd::result
static Accessor::ValueType result(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:866
openvdb::v11_0::math::ISCurl
Curl operator defined in index space using various first derivative schemes.
Definition Operators.h:499
openvdb::v11_0::math::ISCurl::result
static StencilT::ValueType result(const StencilT &stencil)
Definition Operators.h:515
openvdb::v11_0::math::ISCurl::result
static Accessor::ValueType result(const Accessor &grid, const Coord &ijk)
Definition Operators.h:502
openvdb::v11_0::math::ISDivergence
Divergence operator defined in index space using various first derivative schemes.
Definition Operators.h:473
openvdb::v11_0::math::ISDivergence::result
static Accessor::ValueType::value_type result(const Accessor &grid, const Coord &ijk)
Definition Operators.h:476
openvdb::v11_0::math::ISDivergence::result
static StencilT::ValueType::value_type result(const StencilT &stencil)
Definition Operators.h:485
openvdb::v11_0::math::ISGradientBiased
Biased Gradient Operators, using upwinding defined by the Vec3Bias input.
Definition Operators.h:197
openvdb::v11_0::math::ISGradientBiased::result
static Vec3< typename Accessor::ValueType > result(const Accessor &grid, const Coord &ijk, const Vec3Bias &V)
Definition Operators.h:204
openvdb::v11_0::math::ISGradientBiased::FD
static const DScheme FD
Definition Operators.h:198
openvdb::v11_0::math::ISGradientBiased::BD
static const DScheme BD
Definition Operators.h:199
openvdb::v11_0::math::ISGradientBiased::result
static Vec3< typename StencilT::ValueType > result(const StencilT &stencil, const Vec3Bias &V)
Definition Operators.h:217
openvdb::v11_0::math::ISGradient
Gradient operators defined in index space of various orders.
Definition Operators.h:100
openvdb::v11_0::math::ISGradient::result
static Vec3< typename Accessor::ValueType > result(const Accessor &grid, const Coord &ijk)
Definition Operators.h:103
openvdb::v11_0::math::ISGradient::result
static Vec3< typename StencilT::ValueType > result(const StencilT &stencil)
Definition Operators.h:114
openvdb::v11_0::math::ISGradientNormSqrd
Definition Operators.h:231
openvdb::v11_0::math::ISGradientNormSqrd::result
static StencilT::ValueType result(const StencilT &stencil)
Definition Operators.h:252
openvdb::v11_0::math::ISGradientNormSqrd::FD
static const DScheme FD
Definition Operators.h:232
openvdb::v11_0::math::ISGradientNormSqrd::result
static Accessor::ValueType result(const Accessor &grid, const Coord &ijk)
Definition Operators.h:239
openvdb::v11_0::math::ISGradientNormSqrd::BD
static const DScheme BD
Definition Operators.h:233
openvdb::v11_0::math::ISLaplacian< CD_FOURTH >::result
static StencilT::ValueType result(const StencilT &stencil)
Definition Operators.h:405
openvdb::v11_0::math::ISLaplacian< CD_FOURTH >::result
static Accessor::ValueType result(const Accessor &grid, const Coord &ijk)
Definition Operators.h:388
openvdb::v11_0::math::ISLaplacian< CD_SECOND >::result
static StencilT::ValueType result(const StencilT &stencil)
Definition Operators.h:374
openvdb::v11_0::math::ISLaplacian< CD_SECOND >::result
static Accessor::ValueType result(const Accessor &grid, const Coord &ijk)
Definition Operators.h:364
openvdb::v11_0::math::ISLaplacian< CD_SIXTH >::result
static StencilT::ValueType result(const StencilT &stencil)
Definition Operators.h:447
openvdb::v11_0::math::ISLaplacian< CD_SIXTH >::result
static Accessor::ValueType result(const Accessor &grid, const Coord &ijk)
Definition Operators.h:426
openvdb::v11_0::math::ISLaplacian
Laplacian defined in index space, using various center-difference stencils.
Definition Operators.h:348
openvdb::v11_0::math::ISLaplacian::result
static StencilT::ValueType result(const StencilT &stencil)
openvdb::v11_0::math::ISLaplacian::result
static Accessor::ValueType result(const Accessor &grid, const Coord &ijk)
openvdb::v11_0::math::ISMeanCurvature
Compute the mean curvature in index space.
Definition Operators.h:533
openvdb::v11_0::math::ISMeanCurvature::result
static bool result(const Accessor &grid, const Coord &ijk, typename Accessor::ValueType &alpha, typename Accessor::ValueType &beta)
Random access version.
Definition Operators.h:539
openvdb::v11_0::math::ISMeanCurvature::result
static bool result(const StencilT &stencil, typename StencilT::ValueType &alpha, typename StencilT::ValueType &beta)
Stencil access version.
Definition Operators.h:577
openvdb::v11_0::math::ISOpMagnitude
Adapter for vector-valued index-space operators to return the vector magnitude.
Definition Operators.h:52
openvdb::v11_0::math::ISOpMagnitude::result
static double result(const AccessorType &grid, const Coord &ijk)
Definition Operators.h:54
openvdb::v11_0::math::ISOpMagnitude::result
static double result(const StencilType &stencil)
Definition Operators.h:59
openvdb::v11_0::math::Laplacian< ScaleMap, DiffScheme >::result
static Accessor::ValueType result(const ScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1586
openvdb::v11_0::math::Laplacian< ScaleMap, DiffScheme >::result
static StencilT::ValueType result(const ScaleMap &map, const StencilT &stencil)
Definition Operators.h:1604
openvdb::v11_0::math::Laplacian< ScaleTranslateMap, DiffScheme >::result
static Accessor::ValueType result(const ScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1627
openvdb::v11_0::math::Laplacian< ScaleTranslateMap, DiffScheme >::result
static StencilT::ValueType result(const ScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:1644
openvdb::v11_0::math::Laplacian< TranslationMap, DiffScheme >::result
static Accessor::ValueType result(const TranslationMap &, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1499
openvdb::v11_0::math::Laplacian< TranslationMap, DiffScheme >::result
static StencilT::ValueType result(const TranslationMap &, const StencilT &stencil)
Definition Operators.h:1507
openvdb::v11_0::math::Laplacian< UniformScaleMap, DiffScheme >::result
static StencilT::ValueType result(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:1549
openvdb::v11_0::math::Laplacian< UniformScaleMap, DiffScheme >::result
static Accessor::ValueType result(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1540
openvdb::v11_0::math::Laplacian< UniformScaleTranslateMap, DiffScheme >::result
static StencilT::ValueType result(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:1572
openvdb::v11_0::math::Laplacian< UniformScaleTranslateMap, DiffScheme >::result
static Accessor::ValueType result(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1563
openvdb::v11_0::math::Laplacian< UnitaryMap, DiffScheme >::result
static Accessor::ValueType result(const UnitaryMap &, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1520
openvdb::v11_0::math::Laplacian< UnitaryMap, DiffScheme >::result
static StencilT::ValueType result(const UnitaryMap &, const StencilT &stencil)
Definition Operators.h:1528
openvdb::v11_0::math::Laplacian
Compute the Laplacian at a given location in a grid using finite differencing of various orders....
Definition Operators.h:1420
openvdb::v11_0::math::Laplacian::result
static StencilT::ValueType result(const MapType &map, const StencilT &stencil)
Definition Operators.h:1459
openvdb::v11_0::math::Laplacian::result
static Accessor::ValueType result(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1423
openvdb::v11_0::math::MapAdapter::result
ResultType result(const StencilType &stencil)
Definition Operators.h:44
openvdb::v11_0::math::MapAdapter::result
ResultType result(const AccessorType &grid, const Coord &ijk)
Definition Operators.h:40
openvdb::v11_0::math::MapAdapter::map
const MapType map
Definition Operators.h:46
openvdb::v11_0::math::MapAdapter::MapAdapter
MapAdapter(const MapType &m)
Definition Operators.h:36
openvdb::v11_0::math::MeanCurvature< TranslationMap, DiffScheme2, DiffScheme1 >::result
static Accessor::ValueType result(const TranslationMap &, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1927
openvdb::v11_0::math::MeanCurvature< TranslationMap, DiffScheme2, DiffScheme1 >::result
static StencilT::ValueType result(const TranslationMap &, const StencilT &stencil)
Definition Operators.h:1950
openvdb::v11_0::math::MeanCurvature< TranslationMap, DiffScheme2, DiffScheme1 >::normGrad
static StencilT::ValueType normGrad(const TranslationMap &, const StencilT &stencil)
Definition Operators.h:1960
openvdb::v11_0::math::MeanCurvature< TranslationMap, DiffScheme2, DiffScheme1 >::normGrad
static Accessor::ValueType normGrad(const TranslationMap &, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1938
openvdb::v11_0::math::MeanCurvature< UniformScaleMap, DiffScheme2, DiffScheme1 >::normGrad
static Accessor::ValueType normGrad(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1990
openvdb::v11_0::math::MeanCurvature< UniformScaleMap, DiffScheme2, DiffScheme1 >::normGrad
static StencilT::ValueType normGrad(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:2018
openvdb::v11_0::math::MeanCurvature< UniformScaleMap, DiffScheme2, DiffScheme1 >::result
static StencilT::ValueType result(const UniformScaleMap &map, const StencilT &stencil)
Definition Operators.h:2005
openvdb::v11_0::math::MeanCurvature< UniformScaleMap, DiffScheme2, DiffScheme1 >::result
static Accessor::ValueType result(const UniformScaleMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1976
openvdb::v11_0::math::MeanCurvature< UniformScaleTranslateMap, DiffScheme2, DiffScheme1 >::result
static StencilT::ValueType result(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:2064
openvdb::v11_0::math::MeanCurvature< UniformScaleTranslateMap, DiffScheme2, DiffScheme1 >::result
static Accessor::ValueType result(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:2037
openvdb::v11_0::math::MeanCurvature< UniformScaleTranslateMap, DiffScheme2, DiffScheme1 >::normGrad
static StencilT::ValueType normGrad(const UniformScaleTranslateMap &map, const StencilT &stencil)
Definition Operators.h:2077
openvdb::v11_0::math::MeanCurvature< UniformScaleTranslateMap, DiffScheme2, DiffScheme1 >::normGrad
static Accessor::ValueType normGrad(const UniformScaleTranslateMap &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:2050
openvdb::v11_0::math::MeanCurvature
Compute the mean curvature.
Definition Operators.h:1762
openvdb::v11_0::math::MeanCurvature::normGrad
static StencilT::ValueType normGrad(const MapType &map, const StencilT stencil)
Definition Operators.h:1912
openvdb::v11_0::math::MeanCurvature::compute
static bool compute(const MapType &map, const Accessor &grid, const Coord &ijk, double &alpha, double &beta)
Random access version.
Definition Operators.h:1768
openvdb::v11_0::math::MeanCurvature::normGrad
static Accessor::ValueType normGrad(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1833
openvdb::v11_0::math::MeanCurvature::compute
static bool compute(const MapType &map, const StencilT &stencil, double &alpha, double &beta)
Stencil access version.
Definition Operators.h:1847
openvdb::v11_0::math::MeanCurvature::result
static StencilT::ValueType result(const MapType &map, const StencilT stencil)
Definition Operators.h:1903
openvdb::v11_0::math::MeanCurvature::result
static Accessor::ValueType result(const MapType &map, const Accessor &grid, const Coord &ijk)
Definition Operators.h:1823
openvdb::v11_0::math::OpMagnitude
Adapter for vector-valued world-space operators to return the vector magnitude.
Definition Operators.h:66
openvdb::v11_0::math::OpMagnitude::result
static double result(const MapT &map, const StencilType &stencil)
Definition Operators.h:73
openvdb::v11_0::math::OpMagnitude::result
static double result(const MapT &map, const AccessorType &grid, const Coord &ijk)
Definition Operators.h:68
openvdb::v11_0::math::Tolerance::value
static T value()
Definition Math.h:148
openvdb::v11_0::math::is_double< double >::value
static const bool value
Definition Operators.h:26
openvdb::v11_0::math::is_double
Definition Operators.h:25
openvdb::v11_0::math::is_double::value
static const bool value
Definition Operators.h:25
openvdb::v11_0::math::is_linear::value
static const bool value
Definition Maps.h:55
openvdb::v11_0::math::is_vec3d< Vec3d >::value
static const bool value
Definition Operators.h:23
openvdb::v11_0::math::is_vec3d
Definition Operators.h:22
openvdb::v11_0::math::is_vec3d::value
static const bool value
Definition Operators.h:22
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition version.h.in:121
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition version.h.in:212