PhysicsBasedAnimationToolkit 0.0.10
Cross-platform C++20 library of algorithms and data structures commonly used in computer graphics research on physically-based simulation.
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DistanceQueries.h
Go to the documentation of this file.
1
10
11#ifndef PBAT_GEOMETRY_DISTANCEQUERIES_H
12#define PBAT_GEOMETRY_DISTANCEQUERIES_H
13
14#include "ClosestPointQueries.h"
15#include "OverlapQueries.h"
16#include "pbat/HostDevice.h"
17#include "pbat/math/linalg/mini/Mini.h"
18
19#include <algorithm>
20
21namespace pbat {
22namespace geometry {
26namespace DistanceQueries {
27
28namespace mini = math::linalg::mini;
29
42template <
43 mini::CMatrix TMatrixL1,
44 mini::CMatrix TMatrixU1,
45 mini::CMatrix TMatrixL2,
46 mini::CMatrix TMatrixU2>
47PBAT_HOST_DEVICE auto AxisAlignedBoundingBoxes(
48 TMatrixL1 const& L1,
49 TMatrixU1 const& U1,
50 TMatrixL2 const& L2,
51 TMatrixU2 const& U2) -> typename TMatrixL1::ScalarType;
52
63template <mini::CMatrix TMatrixP, mini::CMatrix TMatrixL, mini::CMatrix TMatrixU>
64PBAT_HOST_DEVICE auto
65PointAxisAlignedBoundingBox(TMatrixP const& P, TMatrixL const& L, TMatrixU const& U) ->
66 typename TMatrixP::ScalarType;
67
80template <
81 mini::CMatrix TMatrixP,
82 mini::CMatrix TMatrixA,
83 mini::CMatrix TMatrixB,
84 mini::CMatrix TMatrixC>
85PBAT_HOST_DEVICE auto
86PointTriangle(TMatrixP const& P, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C) ->
87 typename TMatrixP::ScalarType;
88
103template <
104 mini::CMatrix TMatrixP,
105 mini::CMatrix TMatrixA,
106 mini::CMatrix TMatrixB,
107 mini::CMatrix TMatrixC,
108 mini::CMatrix TMatrixD>
109PBAT_HOST_DEVICE auto PointTetrahedron(
110 TMatrixP const& P,
111 TMatrixA const& A,
112 TMatrixB const& B,
113 TMatrixC const& C,
114 TMatrixD const& D) -> typename TMatrixP::ScalarType;
115
126template <mini::CMatrix TMatrixX, mini::CMatrix TMatrixP, mini::CMatrix TMatrixN>
127PBAT_HOST_DEVICE auto PointPlane(TMatrixX const& X, TMatrixP const& P, TMatrixN const& n) ->
128 typename TMatrixX::ScalarType;
129
142template <
143 mini::CMatrix TMatrixX,
144 mini::CMatrix TMatrixA,
145 mini::CMatrix TMatrixB,
146 mini::CMatrix TMatrixC>
147PBAT_HOST_DEVICE auto
148PointPlane(TMatrixX const& X, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C) ->
149 typename TMatrixX::ScalarType;
150
164template <
165 mini::CMatrix TMatrixX,
166 mini::CMatrix TMatrixA,
167 mini::CMatrix TMatrixB,
168 mini::CMatrix TMatrixC>
169PBAT_HOST_DEVICE auto SphereTriangle(
170 TMatrixX const& X,
171 typename TMatrixX::ScalarType R,
172 TMatrixA const& A,
173 TMatrixB const& B,
174 TMatrixC const& C) -> typename TMatrixX::ScalarType;
175
176template <
177 mini::CMatrix TMatrixL1,
178 mini::CMatrix TMatrixU1,
179 mini::CMatrix TMatrixL2,
180 mini::CMatrix TMatrixU2>
181PBAT_HOST_DEVICE auto AxisAlignedBoundingBoxes(
182 TMatrixL1 const& L1,
183 TMatrixU1 const& U1,
184 TMatrixL2 const& L2,
185 TMatrixU2 const& U2) -> typename TMatrixL1::ScalarType
186{
187 using ScalarType = typename TMatrixL1::ScalarType;
188 auto constexpr kDims = TMatrixL1::kRows;
189 mini::SVector<ScalarType, kDims> LI = Max(L1, L2);
190 mini::SVector<ScalarType, kDims> UI = Min(U1, U2);
191 auto LGU = LI > UI;
192 mini::SVector<ScalarType, kDims> DI = LI - UI;
193 ScalarType d2 = Dot(Cast<ScalarType>(LGU), Squared(DI));
194 return d2;
195}
196
197template <mini::CMatrix TMatrixP, mini::CMatrix TMatrixL, mini::CMatrix TMatrixU>
198PBAT_HOST_DEVICE auto
199PointAxisAlignedBoundingBox(TMatrixP const& P, TMatrixL const& L, TMatrixU const& U) ->
200 typename TMatrixP::ScalarType
201{
202 // If point is inside AABB, then distance is 0.
203 bool const bIsInsideBox = OverlapQueries::PointAxisAlignedBoundingBox(P, L, U);
204 if (bIsInsideBox)
205 return 0.;
206 // Otherwise compute distance to boundary
207 auto const CP = ClosestPointQueries::PointOnAxisAlignedBoundingBox(P, L, U);
208 return SquaredNorm(P - CP);
209}
210
211template <
212 mini::CMatrix TMatrixP,
213 mini::CMatrix TMatrixA,
214 mini::CMatrix TMatrixB,
215 mini::CMatrix TMatrixC>
216PBAT_HOST_DEVICE auto
217PointTriangle(TMatrixP const& P, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C) ->
218 typename TMatrixP::ScalarType
219{
220 auto const PP = ClosestPointQueries::PointInTriangle(P, A, B, C);
221 return SquaredNorm(P - PP);
222}
223
224template <
225 mini::CMatrix TMatrixP,
226 mini::CMatrix TMatrixA,
227 mini::CMatrix TMatrixB,
228 mini::CMatrix TMatrixC,
229 mini::CMatrix TMatrixD>
230PBAT_HOST_DEVICE auto PointTetrahedron(
231 TMatrixP const& P,
232 TMatrixA const& A,
233 TMatrixB const& B,
234 TMatrixC const& C,
235 TMatrixD const& D) -> typename TMatrixP::ScalarType
236{
237 bool const bPointInTetrahedron = OverlapQueries::PointTetrahedron3D(P, A, B, C, D);
238 if (bPointInTetrahedron)
239 return 0.;
240
241 using ScalarType = typename TMatrixP::ScalarType;
242 mini::SVector<ScalarType, 4> sd{
243 PointTriangle(P, A, B, D),
244 PointTriangle(P, B, C, D),
245 PointTriangle(P, C, A, D),
246 PointTriangle(P, A, C, B)};
247 ScalarType const min = Min(sd);
248 return min;
249}
250
251template <mini::CMatrix TMatrixX, mini::CMatrix TMatrixP, mini::CMatrix TMatrixN>
252PBAT_HOST_DEVICE auto PointPlane(TMatrixX const& X, TMatrixP const& P, TMatrixN const& n) ->
253 typename TMatrixX::ScalarType
254{
255 return Dot(X - P, n);
256}
257
258template <
259 mini::CMatrix TMatrixX,
260 mini::CMatrix TMatrixA,
261 mini::CMatrix TMatrixB,
262 mini::CMatrix TMatrixC>
263PBAT_HOST_DEVICE auto
264PointPlane(TMatrixX const& X, TMatrixA const& A, TMatrixB const& B, TMatrixC const& C) ->
265 typename TMatrixX::ScalarType
266{
267 auto const n = Cross(B - A, C - A);
268 return PointPlane(X, A, n);
269}
270
271template <
272 mini::CMatrix TMatrixX,
273 mini::CMatrix TMatrixA,
274 mini::CMatrix TMatrixB,
275 mini::CMatrix TMatrixC>
276PBAT_HOST_DEVICE auto SphereTriangle(
277 TMatrixX const& X,
278 typename TMatrixX::ScalarType R,
279 TMatrixA const& A,
280 TMatrixB const& B,
281 TMatrixC const& C) -> typename TMatrixX::ScalarType
282{
283 auto const sd2c = PointTriangle(X, A, B, C);
284 return sd2c - R * R;
285}
286
287} // namespace DistanceQueries
288} // namespace geometry
289} // namespace pbat
290
291#endif // PBAT_GEOMETRY_DISTANCEQUERIES_H
ClosestPointQueries.h
This file contains functions to answer closest point queries.
Mini.h
This file includes all the mini linear algebra headers.
OverlapQueries.h
This file contains functions to answer overlap queries.
pbat::geometry::ClosestPointQueries::PointOnAxisAlignedBoundingBox
PBAT_HOST_DEVICE auto PointOnAxisAlignedBoundingBox(TMatrixX const &X, TMatrixL const &L, TMatrixU const &U) -> mini::SVector< typename TMatrixX::ScalarType, TMatrixX::kRows >
Obtain the point on the axis-aligned bounding box (AABB) defined by the lower and upper corners close...
Definition ClosestPointQueries.h:280
pbat::geometry::ClosestPointQueries::PointInTriangle
PBAT_HOST_DEVICE auto PointInTriangle(TMatrixP const &P, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C) -> mini::SVector< typename TMatrixP::ScalarType, TMatrixP::kRows >
Obtain the point on the triangle ABC closest to the point P.
Definition ClosestPointQueries.h:384
pbat::geometry::DistanceQueries
This namespace contains functions to answer distance queries.
Definition DistanceQueries.h:26
pbat::geometry::DistanceQueries::AxisAlignedBoundingBoxes
PBAT_HOST_DEVICE auto AxisAlignedBoundingBoxes(TMatrixL1 const &L1, TMatrixU1 const &U1, TMatrixL2 const &L2, TMatrixU2 const &U2) -> typename TMatrixL1::ScalarType
Obtain squared distance between 2 axis-aligned bounding boxes.
Definition DistanceQueries.h:181
pbat::geometry::DistanceQueries::SphereTriangle
PBAT_HOST_DEVICE auto SphereTriangle(TMatrixX const &X, typename TMatrixX::ScalarType R, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C) -> typename TMatrixX::ScalarType
Obtains the squared distance between sphere (X,R) and triangle ABC.
Definition DistanceQueries.h:276
pbat::geometry::DistanceQueries::PointTetrahedron
PBAT_HOST_DEVICE auto PointTetrahedron(TMatrixP const &P, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C, TMatrixD const &D) -> typename TMatrixP::ScalarType
Obtain squared distance between point P and tetrahedron ABCD.
Definition DistanceQueries.h:230
pbat::geometry::DistanceQueries::PointTriangle
PBAT_HOST_DEVICE auto PointTriangle(TMatrixP const &P, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C) -> typename TMatrixP::ScalarType
Obtain squared distance between point P and triangle ABC.
Definition DistanceQueries.h:217
pbat::geometry::DistanceQueries::PointAxisAlignedBoundingBox
PBAT_HOST_DEVICE auto PointAxisAlignedBoundingBox(TMatrixP const &P, TMatrixL const &L, TMatrixU const &U) -> typename TMatrixP::ScalarType
Obtain squared distance between point P and axis-aligned box (L,U)
Definition DistanceQueries.h:199
pbat::geometry::DistanceQueries::PointPlane
PBAT_HOST_DEVICE auto PointPlane(TMatrixX const &X, TMatrixP const &P, TMatrixN const &n) -> typename TMatrixX::ScalarType
Obtains the signed distance of X w.r.t. plane (P,n)
Definition DistanceQueries.h:252
pbat::geometry::OverlapQueries::PointTetrahedron3D
PBAT_HOST_DEVICE bool PointTetrahedron3D(TMatrixP const &P, TMatrixA const &A, TMatrixB const &B, TMatrixC const &C, TMatrixD const &D)
Checks if point P is contained in tetrahedron ABCD, in at least 3D.
Definition OverlapQueries.h:562
pbat::geometry::OverlapQueries::PointAxisAlignedBoundingBox
PBAT_HOST_DEVICE bool PointAxisAlignedBoundingBox(TMatrixP const &P, TMatrixL const &L, TMatrixU const &U)
Tests for overlap between point P and axis-aligned bounding box (L,U)
Definition OverlapQueries.h:536
pbat::geometry
Geometric queries, quantities and data structures.
Definition AabbKdTreeHierarchy.h:23
pbat::math::linalg::mini
Mini linear algebra related functionality.
Definition Assign.h:12
pbat
The main namespace of the library.
Definition Aliases.h:15