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UT_SolidAngle.cpp
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UT_SolidAngle.cpp
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/*
* Copyright (c) 2018 Side Effects Software Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
* COMMENTS:
* Functions and structures for computing solid angles.
*/
#include "UT_SolidAngle.h"
#include "UT_BVHImpl.h"
#include "UT_SmallArray.h"
#include "UT_FixedVector.h"
#include "VM_SIMD.h"
#include "SYS_Types.h"
#include <igl/parallel_for.h>
#include <type_traits>
#include <utility>
#define SOLID_ANGLE_TIME_PRECOMPUTE 0
#if SOLID_ANGLE_TIME_PRECOMPUTE
#include <UT/UT_StopWatch.h>
#endif
#define SOLID_ANGLE_DEBUG 0
#if SOLID_ANGLE_DEBUG
#include <UT/UT_Debug.h>
#endif
#define TAYLOR_SERIES_ORDER 2
namespace igl { namespace FastWindingNumber {
namespace HDK_Sample {
template<typename T,typename S>
struct UT_SolidAngle<T,S>::BoxData
{
void clear()
{
// Set everything to zero
memset(this,0,sizeof(*this));
}
using Type = typename std::conditional<BVH_N==4 && std::is_same<T,float>::value, v4uf, UT_FixedVector<T,BVH_N>>::type;
using SType = typename std::conditional<BVH_N==4 && std::is_same<S,float>::value, v4uf, UT_FixedVector<S,BVH_N>>::type;
/// An upper bound on the squared distance from myAverageP to the farthest point in the box.
SType myMaxPDist2;
/// Centre of mass of the mesh surface in this box
UT_FixedVector<Type,3> myAverageP;
/// Unnormalized, area-weighted normal of the mesh in this box
UT_FixedVector<Type,3> myN;
#if TAYLOR_SERIES_ORDER >= 1
/// Values for Omega_1
/// @{
UT_FixedVector<Type,3> myNijDiag; // Nxx, Nyy, Nzz
Type myNxy_Nyx; // Nxy+Nyx
Type myNyz_Nzy; // Nyz+Nzy
Type myNzx_Nxz; // Nzx+Nxz
/// @}
#endif
#if TAYLOR_SERIES_ORDER >= 2
/// Values for Omega_2
/// @{
UT_FixedVector<Type,3> myNijkDiag; // Nxxx, Nyyy, Nzzz
Type mySumPermuteNxyz; // (Nxyz+Nxzy+Nyzx+Nyxz+Nzxy+Nzyx) = 2*(Nxyz+Nyzx+Nzxy)
Type my2Nxxy_Nyxx; // Nxxy+Nxyx+Nyxx = 2Nxxy+Nyxx
Type my2Nxxz_Nzxx; // Nxxz+Nxzx+Nzxx = 2Nxxz+Nzxx
Type my2Nyyz_Nzyy; // Nyyz+Nyzy+Nzyy = 2Nyyz+Nzyy
Type my2Nyyx_Nxyy; // Nyyx+Nyxy+Nxyy = 2Nyyx+Nxyy
Type my2Nzzx_Nxzz; // Nzzx+Nzxz+Nxzz = 2Nzzx+Nxzz
Type my2Nzzy_Nyzz; // Nzzy+Nzyz+Nyzz = 2Nzzy+Nyzz
/// @}
#endif
};
template<typename T,typename S>
inline UT_SolidAngle<T,S>::UT_SolidAngle()
: myTree()
, myNBoxes(0)
, myOrder(2)
, myData(nullptr)
, myNTriangles(0)
, myTrianglePoints(nullptr)
, myNPoints(0)
, myPositions(nullptr)
{}
template<typename T,typename S>
inline UT_SolidAngle<T,S>::~UT_SolidAngle()
{
// Default destruction works, but this needs to be outlined
// to avoid having to include UT_BVHImpl.h in the header,
// (for the UT_UniquePtr destructor.)
}
template<typename T,typename S>
inline void UT_SolidAngle<T,S>::init(
const int ntriangles,
const int *const triangle_points,
const int npoints,
const UT_Vector3T<S> *const positions,
const int order)
{
#if SOLID_ANGLE_DEBUG
UTdebugFormat("");
UTdebugFormat("");
UTdebugFormat("Building BVH for {} ntriangles on {} points:", ntriangles, npoints);
#endif
myOrder = order;
myNTriangles = ntriangles;
myTrianglePoints = triangle_points;
myNPoints = npoints;
myPositions = positions;
#if SOLID_ANGLE_TIME_PRECOMPUTE
UT_StopWatch timer;
timer.start();
#endif
UT_SmallArray<UT::Box<S,3>> triangle_boxes;
triangle_boxes.setSizeNoInit(ntriangles);
if (ntriangles < 16*1024)
{
const int *cur_triangle_points = triangle_points;
for (int i = 0; i < ntriangles; ++i, cur_triangle_points += 3)
{
UT::Box<S,3> &box = triangle_boxes[i];
box.initBounds(positions[cur_triangle_points[0]]);
box.enlargeBounds(positions[cur_triangle_points[1]]);
box.enlargeBounds(positions[cur_triangle_points[2]]);
}
}
else
{
igl::parallel_for(ntriangles,
[triangle_points,&triangle_boxes,positions](int i)
{
const int *cur_triangle_points = triangle_points + i*3;
UT::Box<S,3> &box = triangle_boxes[i];
box.initBounds(positions[cur_triangle_points[0]]);
box.enlargeBounds(positions[cur_triangle_points[1]]);
box.enlargeBounds(positions[cur_triangle_points[2]]);
});
}
#if SOLID_ANGLE_TIME_PRECOMPUTE
double time = timer.stop();
UTdebugFormat("{} s to create bounding boxes.", time);
timer.start();
#endif
myTree.template init<UT::BVH_Heuristic::BOX_AREA,S,3>(triangle_boxes.array(), ntriangles);
#if SOLID_ANGLE_TIME_PRECOMPUTE
time = timer.stop();
UTdebugFormat("{} s to initialize UT_BVH structure. {} nodes", time, myTree.getNumNodes());
#endif
//myTree.debugDump();
const int nnodes = myTree.getNumNodes();
myNBoxes = nnodes;
BoxData *box_data = new BoxData[nnodes];
myData.reset(box_data);
// Some data are only needed during initialization.
struct LocalData
{
// Bounding box
UT::Box<S,3> myBox;
// P and N are needed from each child for computing Nij.
UT_Vector3T<T> myAverageP;
UT_Vector3T<T> myAreaP;
UT_Vector3T<T> myN;
// Unsigned area is needed for computing the average position.
T myArea;
#if TAYLOR_SERIES_ORDER >= 1
// These are needed for computing Nijk.
UT_Vector3T<T> myNijDiag;
T myNxy; T myNyx;
T myNyz; T myNzy;
T myNzx; T myNxz;
#endif
#if TAYLOR_SERIES_ORDER >= 2
UT_Vector3T<T> myNijkDiag; // Nxxx, Nyyy, Nzzz
T mySumPermuteNxyz; // (Nxyz+Nxzy+Nyzx+Nyxz+Nzxy+Nzyx) = 2*(Nxyz+Nyzx+Nzxy)
T my2Nxxy_Nyxx; // Nxxy+Nxyx+Nyxx = 2Nxxy+Nyxx
T my2Nxxz_Nzxx; // Nxxz+Nxzx+Nzxx = 2Nxxz+Nzxx
T my2Nyyz_Nzyy; // Nyyz+Nyzy+Nzyy = 2Nyyz+Nzyy
T my2Nyyx_Nxyy; // Nyyx+Nyxy+Nxyy = 2Nyyx+Nxyy
T my2Nzzx_Nxzz; // Nzzx+Nzxz+Nxzz = 2Nzzx+Nxzz
T my2Nzzy_Nyzz; // Nzzy+Nzyz+Nyzz = 2Nzzy+Nyzz
#endif
};
struct PrecomputeFunctors
{
BoxData *const myBoxData;
const UT::Box<S,3> *const myTriangleBoxes;
const int *const myTrianglePoints;
const UT_Vector3T<S> *const myPositions;
const int myOrder;
PrecomputeFunctors(
BoxData *box_data,
const UT::Box<S,3> *triangle_boxes,
const int *triangle_points,
const UT_Vector3T<S> *positions,
const int order)
: myBoxData(box_data)
, myTriangleBoxes(triangle_boxes)
, myTrianglePoints(triangle_points)
, myPositions(positions)
, myOrder(order)
{}
constexpr SYS_FORCE_INLINE bool pre(const int nodei, LocalData *data_for_parent) const
{
return true;
}
void item(const int itemi, const int parent_nodei, LocalData &data_for_parent) const
{
const UT_Vector3T<S> *const positions = myPositions;
const int *const cur_triangle_points = myTrianglePoints + 3*itemi;
const UT_Vector3T<T> a = positions[cur_triangle_points[0]];
const UT_Vector3T<T> b = positions[cur_triangle_points[1]];
const UT_Vector3T<T> c = positions[cur_triangle_points[2]];
const UT_Vector3T<T> ab = b-a;
const UT_Vector3T<T> ac = c-a;
const UT::Box<S,3> &triangle_box = myTriangleBoxes[itemi];
data_for_parent.myBox.initBounds(triangle_box.getMin(), triangle_box.getMax());
// Area-weighted normal (unnormalized)
const UT_Vector3T<T> N = T(0.5)*cross(ab,ac);
const T area2 = N.length2();
const T area = SYSsqrt(area2);
const UT_Vector3T<T> P = (a+b+c)/3;
data_for_parent.myAverageP = P;
data_for_parent.myAreaP = P*area;
data_for_parent.myN = N;
#if SOLID_ANGLE_DEBUG
UTdebugFormat("");
UTdebugFormat("Triangle {}: P = {}; N = {}; area = {}", itemi, P, N, area);
UTdebugFormat(" box = {}", data_for_parent.myBox);
#endif
data_for_parent.myArea = area;
#if TAYLOR_SERIES_ORDER >= 1
const int order = myOrder;
if (order < 1)
return;
// NOTE: Due to P being at the centroid, triangles have Nij = 0
// contributions to Nij.
data_for_parent.myNijDiag = T(0);
data_for_parent.myNxy = 0; data_for_parent.myNyx = 0;
data_for_parent.myNyz = 0; data_for_parent.myNzy = 0;
data_for_parent.myNzx = 0; data_for_parent.myNxz = 0;
#endif
#if TAYLOR_SERIES_ORDER >= 2
if (order < 2)
return;
// If it's zero-length, the results are zero, so we can skip.
if (area == 0)
{
data_for_parent.myNijkDiag = T(0);
data_for_parent.mySumPermuteNxyz = 0;
data_for_parent.my2Nxxy_Nyxx = 0;
data_for_parent.my2Nxxz_Nzxx = 0;
data_for_parent.my2Nyyz_Nzyy = 0;
data_for_parent.my2Nyyx_Nxyy = 0;
data_for_parent.my2Nzzx_Nxzz = 0;
data_for_parent.my2Nzzy_Nyzz = 0;
return;
}
// We need to use the NORMALIZED normal to multiply the integrals by.
UT_Vector3T<T> n = N/area;
// Figure out the order of a, b, and c in x, y, and z
// for use in computing the integrals for Nijk.
UT_Vector3T<T> values[3] = {a, b, c};
int order_x[3] = {0,1,2};
if (a[0] > b[0])
std::swap(order_x[0],order_x[1]);
if (values[order_x[0]][0] > c[0])
std::swap(order_x[0],order_x[2]);
if (values[order_x[1]][0] > values[order_x[2]][0])
std::swap(order_x[1],order_x[2]);
T dx = values[order_x[2]][0] - values[order_x[0]][0];
int order_y[3] = {0,1,2};
if (a[1] > b[1])
std::swap(order_y[0],order_y[1]);
if (values[order_y[0]][1] > c[1])
std::swap(order_y[0],order_y[2]);
if (values[order_y[1]][1] > values[order_y[2]][1])
std::swap(order_y[1],order_y[2]);
T dy = values[order_y[2]][1] - values[order_y[0]][1];
int order_z[3] = {0,1,2};
if (a[2] > b[2])
std::swap(order_z[0],order_z[1]);
if (values[order_z[0]][2] > c[2])
std::swap(order_z[0],order_z[2]);
if (values[order_z[1]][2] > values[order_z[2]][2])
std::swap(order_z[1],order_z[2]);
T dz = values[order_z[2]][2] - values[order_z[0]][2];
auto &&compute_integrals = [](
const UT_Vector3T<T> &a,
const UT_Vector3T<T> &b,
const UT_Vector3T<T> &c,
const UT_Vector3T<T> &P,
T *integral_ii,
T *integral_ij,
T *integral_ik,
const int i)
{
#if SOLID_ANGLE_DEBUG
UTdebugFormat(" Splitting on {}; a = {}; b = {}; c = {}", char('x'+i), a, b, c);
#endif
// NOTE: a, b, and c must be in order of the i axis.
// We're splitting the triangle at the middle i coordinate.
const UT_Vector3T<T> oab = b - a;
const UT_Vector3T<T> oac = c - a;
const UT_Vector3T<T> ocb = b - c;
UT_ASSERT_MSG_P(oac[i] > 0, "This should have been checked by the caller.");
const T t = oab[i]/oac[i];
UT_ASSERT_MSG_P(t >= 0 && t <= 1, "Either sorting must have gone wrong, or there are input NaNs.");
const int j = (i==2) ? 0 : (i+1);
const int k = (j==2) ? 0 : (j+1);
const T jdiff = t*oac[j] - oab[j];
const T kdiff = t*oac[k] - oab[k];
UT_Vector3T<T> cross_a;
cross_a[0] = (jdiff*oab[k] - kdiff*oab[j]);
cross_a[1] = kdiff*oab[i];
cross_a[2] = jdiff*oab[i];
UT_Vector3T<T> cross_c;
cross_c[0] = (jdiff*ocb[k] - kdiff*ocb[j]);
cross_c[1] = kdiff*ocb[i];
cross_c[2] = jdiff*ocb[i];
const T area_scale_a = cross_a.length();
const T area_scale_c = cross_c.length();
const T Pai = a[i] - P[i];
const T Pci = c[i] - P[i];
// Integral over the area of the triangle of (pi^2)dA,
// by splitting the triangle into two at b, the a side
// and the c side.
const T int_ii_a = area_scale_a*(T(0.5)*Pai*Pai + T(2.0/3.0)*Pai*oab[i] + T(0.25)*oab[i]*oab[i]);
const T int_ii_c = area_scale_c*(T(0.5)*Pci*Pci + T(2.0/3.0)*Pci*ocb[i] + T(0.25)*ocb[i]*ocb[i]);
*integral_ii = int_ii_a + int_ii_c;
#if SOLID_ANGLE_DEBUG
UTdebugFormat(" integral_{}{}_a = {}; integral_{}{}_c = {}", char('x'+i), char('x'+i), int_ii_a, char('x'+i), char('x'+i), int_ii_c);
#endif
int jk = j;
T *integral = integral_ij;
T diff = jdiff;
while (true) // This only does 2 iterations, one for j and one for k
{
if (integral)
{
T obmidj = b[jk] + T(0.5)*diff;
T oabmidj = obmidj - a[jk];
T ocbmidj = obmidj - c[jk];
T Paj = a[jk] - P[jk];
T Pcj = c[jk] - P[jk];
// Integral over the area of the triangle of (pi*pj)dA
const T int_ij_a = area_scale_a*(T(0.5)*Pai*Paj + T(1.0/3.0)*Pai*oabmidj + T(1.0/3.0)*Paj*oab[i] + T(0.25)*oab[i]*oabmidj);
const T int_ij_c = area_scale_c*(T(0.5)*Pci*Pcj + T(1.0/3.0)*Pci*ocbmidj + T(1.0/3.0)*Pcj*ocb[i] + T(0.25)*ocb[i]*ocbmidj);
*integral = int_ij_a + int_ij_c;
#if SOLID_ANGLE_DEBUG
UTdebugFormat(" integral_{}{}_a = {}; integral_{}{}_c = {}", char('x'+i), char('x'+jk), int_ij_a, char('x'+i), char('x'+jk), int_ij_c);
#endif
}
if (jk == k)
break;
jk = k;
integral = integral_ik;
diff = kdiff;
}
};
T integral_xx = 0;
T integral_xy = 0;
T integral_yy = 0;
T integral_yz = 0;
T integral_zz = 0;
T integral_zx = 0;
// Note that if the span of any axis is zero, the integral must be zero,
// since there's a factor of (p_i-P_i), i.e. value minus average,
// and every value must be equal to the average, giving zero.
if (dx > 0)
{
compute_integrals(
values[order_x[0]], values[order_x[1]], values[order_x[2]], P,
&integral_xx, ((dx >= dy && dy > 0) ? &integral_xy : nullptr), ((dx >= dz && dz > 0) ? &integral_zx : nullptr), 0);
}
if (dy > 0)
{
compute_integrals(
values[order_y[0]], values[order_y[1]], values[order_y[2]], P,
&integral_yy, ((dy >= dz && dz > 0) ? &integral_yz : nullptr), ((dx < dy && dx > 0) ? &integral_xy : nullptr), 1);
}
if (dz > 0)
{
compute_integrals(
values[order_z[0]], values[order_z[1]], values[order_z[2]], P,
&integral_zz, ((dx < dz && dx > 0) ? &integral_zx : nullptr), ((dy < dz && dy > 0) ? &integral_yz : nullptr), 2);
}
UT_Vector3T<T> Niii;
Niii[0] = integral_xx;
Niii[1] = integral_yy;
Niii[2] = integral_zz;
Niii *= n;
data_for_parent.myNijkDiag = Niii;
data_for_parent.mySumPermuteNxyz = 2*(n[0]*integral_yz + n[1]*integral_zx + n[2]*integral_xy);
T Nxxy = n[0]*integral_xy;
T Nxxz = n[0]*integral_zx;
T Nyyz = n[1]*integral_yz;
T Nyyx = n[1]*integral_xy;
T Nzzx = n[2]*integral_zx;
T Nzzy = n[2]*integral_yz;
data_for_parent.my2Nxxy_Nyxx = 2*Nxxy + n[1]*integral_xx;
data_for_parent.my2Nxxz_Nzxx = 2*Nxxz + n[2]*integral_xx;
data_for_parent.my2Nyyz_Nzyy = 2*Nyyz + n[2]*integral_yy;
data_for_parent.my2Nyyx_Nxyy = 2*Nyyx + n[0]*integral_yy;
data_for_parent.my2Nzzx_Nxzz = 2*Nzzx + n[0]*integral_zz;
data_for_parent.my2Nzzy_Nyzz = 2*Nzzy + n[1]*integral_zz;
#if SOLID_ANGLE_DEBUG
UTdebugFormat(" integral_xx = {}; yy = {}; zz = {}", integral_xx, integral_yy, integral_zz);
UTdebugFormat(" integral_xy = {}; yz = {}; zx = {}", integral_xy, integral_yz, integral_zx);
#endif
#endif
}
void post(const int nodei, const int parent_nodei, LocalData *data_for_parent, const int nchildren, const LocalData *child_data_array) const
{
// NOTE: Although in the general case, data_for_parent may be null for the root call,
// this functor assumes that it's non-null, so the call below must pass a non-null pointer.
BoxData ¤t_box_data = myBoxData[nodei];
UT_Vector3T<T> N = child_data_array[0].myN;
((T*)¤t_box_data.myN[0])[0] = N[0];
((T*)¤t_box_data.myN[1])[0] = N[1];
((T*)¤t_box_data.myN[2])[0] = N[2];
UT_Vector3T<T> areaP = child_data_array[0].myAreaP;
T area = child_data_array[0].myArea;
UT_Vector3T<T> local_P = child_data_array[0].myAverageP;
((T*)¤t_box_data.myAverageP[0])[0] = local_P[0];
((T*)¤t_box_data.myAverageP[1])[0] = local_P[1];
((T*)¤t_box_data.myAverageP[2])[0] = local_P[2];
for (int i = 1; i < nchildren; ++i)
{
const UT_Vector3T<T> local_N = child_data_array[i].myN;
N += local_N;
((T*)¤t_box_data.myN[0])[i] = local_N[0];
((T*)¤t_box_data.myN[1])[i] = local_N[1];
((T*)¤t_box_data.myN[2])[i] = local_N[2];
areaP += child_data_array[i].myAreaP;
area += child_data_array[i].myArea;
const UT_Vector3T<T> local_P = child_data_array[i].myAverageP;
((T*)¤t_box_data.myAverageP[0])[i] = local_P[0];
((T*)¤t_box_data.myAverageP[1])[i] = local_P[1];
((T*)¤t_box_data.myAverageP[2])[i] = local_P[2];
}
for (int i = nchildren; i < BVH_N; ++i)
{
// Set to zero, just to avoid false positives for uses of uninitialized memory.
((T*)¤t_box_data.myN[0])[i] = 0;
((T*)¤t_box_data.myN[1])[i] = 0;
((T*)¤t_box_data.myN[2])[i] = 0;
((T*)¤t_box_data.myAverageP[0])[i] = 0;
((T*)¤t_box_data.myAverageP[1])[i] = 0;
((T*)¤t_box_data.myAverageP[2])[i] = 0;
}
data_for_parent->myN = N;
data_for_parent->myAreaP = areaP;
data_for_parent->myArea = area;
UT::Box<S,3> box(child_data_array[0].myBox);
for (int i = 1; i < nchildren; ++i)
box.enlargeBounds(child_data_array[i].myBox);
// Normalize P
UT_Vector3T<T> averageP;
if (area > 0)
averageP = areaP/area;
else
averageP = T(0.5)*(box.getMin() + box.getMax());
data_for_parent->myAverageP = averageP;
data_for_parent->myBox = box;
for (int i = 0; i < nchildren; ++i)
{
const UT::Box<S,3> &local_box(child_data_array[i].myBox);
const UT_Vector3T<T> &local_P = child_data_array[i].myAverageP;
const UT_Vector3T<T> maxPDiff = SYSmax(local_P-UT_Vector3T<T>(local_box.getMin()), UT_Vector3T<T>(local_box.getMax())-local_P);
((T*)¤t_box_data.myMaxPDist2)[i] = maxPDiff.length2();
}
for (int i = nchildren; i < BVH_N; ++i)
{
// This child is non-existent. If we set myMaxPDist2 to infinity, it will never
// use the approximation, and the traverseVector function can check for EMPTY.
((T*)¤t_box_data.myMaxPDist2)[i] = std::numeric_limits<T>::infinity();
}
#if TAYLOR_SERIES_ORDER >= 1
const int order = myOrder;
if (order >= 1)
{
// We now have the current box's P, so we can adjust Nij and Nijk
data_for_parent->myNijDiag = child_data_array[0].myNijDiag;
data_for_parent->myNxy = 0;
data_for_parent->myNyx = 0;
data_for_parent->myNyz = 0;
data_for_parent->myNzy = 0;
data_for_parent->myNzx = 0;
data_for_parent->myNxz = 0;
#if TAYLOR_SERIES_ORDER >= 2
data_for_parent->myNijkDiag = child_data_array[0].myNijkDiag;
data_for_parent->mySumPermuteNxyz = child_data_array[0].mySumPermuteNxyz;
data_for_parent->my2Nxxy_Nyxx = child_data_array[0].my2Nxxy_Nyxx;
data_for_parent->my2Nxxz_Nzxx = child_data_array[0].my2Nxxz_Nzxx;
data_for_parent->my2Nyyz_Nzyy = child_data_array[0].my2Nyyz_Nzyy;
data_for_parent->my2Nyyx_Nxyy = child_data_array[0].my2Nyyx_Nxyy;
data_for_parent->my2Nzzx_Nxzz = child_data_array[0].my2Nzzx_Nxzz;
data_for_parent->my2Nzzy_Nyzz = child_data_array[0].my2Nzzy_Nyzz;
#endif
for (int i = 1; i < nchildren; ++i)
{
data_for_parent->myNijDiag += child_data_array[i].myNijDiag;
#if TAYLOR_SERIES_ORDER >= 2
data_for_parent->myNijkDiag += child_data_array[i].myNijkDiag;
data_for_parent->mySumPermuteNxyz += child_data_array[i].mySumPermuteNxyz;
data_for_parent->my2Nxxy_Nyxx += child_data_array[i].my2Nxxy_Nyxx;
data_for_parent->my2Nxxz_Nzxx += child_data_array[i].my2Nxxz_Nzxx;
data_for_parent->my2Nyyz_Nzyy += child_data_array[i].my2Nyyz_Nzyy;
data_for_parent->my2Nyyx_Nxyy += child_data_array[i].my2Nyyx_Nxyy;
data_for_parent->my2Nzzx_Nxzz += child_data_array[i].my2Nzzx_Nxzz;
data_for_parent->my2Nzzy_Nyzz += child_data_array[i].my2Nzzy_Nyzz;
#endif
}
for (int j = 0; j < 3; ++j)
((T*)¤t_box_data.myNijDiag[j])[0] = child_data_array[0].myNijDiag[j];
((T*)¤t_box_data.myNxy_Nyx)[0] = child_data_array[0].myNxy + child_data_array[0].myNyx;
((T*)¤t_box_data.myNyz_Nzy)[0] = child_data_array[0].myNyz + child_data_array[0].myNzy;
((T*)¤t_box_data.myNzx_Nxz)[0] = child_data_array[0].myNzx + child_data_array[0].myNxz;
for (int j = 0; j < 3; ++j)
((T*)¤t_box_data.myNijkDiag[j])[0] = child_data_array[0].myNijkDiag[j];
((T*)¤t_box_data.mySumPermuteNxyz)[0] = child_data_array[0].mySumPermuteNxyz;
((T*)¤t_box_data.my2Nxxy_Nyxx)[0] = child_data_array[0].my2Nxxy_Nyxx;
((T*)¤t_box_data.my2Nxxz_Nzxx)[0] = child_data_array[0].my2Nxxz_Nzxx;
((T*)¤t_box_data.my2Nyyz_Nzyy)[0] = child_data_array[0].my2Nyyz_Nzyy;
((T*)¤t_box_data.my2Nyyx_Nxyy)[0] = child_data_array[0].my2Nyyx_Nxyy;
((T*)¤t_box_data.my2Nzzx_Nxzz)[0] = child_data_array[0].my2Nzzx_Nxzz;
((T*)¤t_box_data.my2Nzzy_Nyzz)[0] = child_data_array[0].my2Nzzy_Nyzz;
for (int i = 1; i < nchildren; ++i)
{
for (int j = 0; j < 3; ++j)
((T*)¤t_box_data.myNijDiag[j])[i] = child_data_array[i].myNijDiag[j];
((T*)¤t_box_data.myNxy_Nyx)[i] = child_data_array[i].myNxy + child_data_array[i].myNyx;
((T*)¤t_box_data.myNyz_Nzy)[i] = child_data_array[i].myNyz + child_data_array[i].myNzy;
((T*)¤t_box_data.myNzx_Nxz)[i] = child_data_array[i].myNzx + child_data_array[i].myNxz;
for (int j = 0; j < 3; ++j)
((T*)¤t_box_data.myNijkDiag[j])[i] = child_data_array[i].myNijkDiag[j];
((T*)¤t_box_data.mySumPermuteNxyz)[i] = child_data_array[i].mySumPermuteNxyz;
((T*)¤t_box_data.my2Nxxy_Nyxx)[i] = child_data_array[i].my2Nxxy_Nyxx;
((T*)¤t_box_data.my2Nxxz_Nzxx)[i] = child_data_array[i].my2Nxxz_Nzxx;
((T*)¤t_box_data.my2Nyyz_Nzyy)[i] = child_data_array[i].my2Nyyz_Nzyy;
((T*)¤t_box_data.my2Nyyx_Nxyy)[i] = child_data_array[i].my2Nyyx_Nxyy;
((T*)¤t_box_data.my2Nzzx_Nxzz)[i] = child_data_array[i].my2Nzzx_Nxzz;
((T*)¤t_box_data.my2Nzzy_Nyzz)[i] = child_data_array[i].my2Nzzy_Nyzz;
}
for (int i = nchildren; i < BVH_N; ++i)
{
// Set to zero, just to avoid false positives for uses of uninitialized memory.
for (int j = 0; j < 3; ++j)
((T*)¤t_box_data.myNijDiag[j])[i] = 0;
((T*)¤t_box_data.myNxy_Nyx)[i] = 0;
((T*)¤t_box_data.myNyz_Nzy)[i] = 0;
((T*)¤t_box_data.myNzx_Nxz)[i] = 0;
for (int j = 0; j < 3; ++j)
((T*)¤t_box_data.myNijkDiag[j])[i] = 0;
((T*)¤t_box_data.mySumPermuteNxyz)[i] = 0;
((T*)¤t_box_data.my2Nxxy_Nyxx)[i] = 0;
((T*)¤t_box_data.my2Nxxz_Nzxx)[i] = 0;
((T*)¤t_box_data.my2Nyyz_Nzyy)[i] = 0;
((T*)¤t_box_data.my2Nyyx_Nxyy)[i] = 0;
((T*)¤t_box_data.my2Nzzx_Nxzz)[i] = 0;
((T*)¤t_box_data.my2Nzzy_Nyzz)[i] = 0;
}
for (int i = 0; i < nchildren; ++i)
{
const LocalData &child_data = child_data_array[i];
UT_Vector3T<T> displacement = child_data.myAverageP - UT_Vector3T<T>(data_for_parent->myAverageP);
UT_Vector3T<T> N = child_data.myN;
// Adjust Nij for the change in centre P
data_for_parent->myNijDiag += N*displacement;
T Nxy = child_data.myNxy + N[0]*displacement[1];
T Nyx = child_data.myNyx + N[1]*displacement[0];
T Nyz = child_data.myNyz + N[1]*displacement[2];
T Nzy = child_data.myNzy + N[2]*displacement[1];
T Nzx = child_data.myNzx + N[2]*displacement[0];
T Nxz = child_data.myNxz + N[0]*displacement[2];
data_for_parent->myNxy += Nxy;
data_for_parent->myNyx += Nyx;
data_for_parent->myNyz += Nyz;
data_for_parent->myNzy += Nzy;
data_for_parent->myNzx += Nzx;
data_for_parent->myNxz += Nxz;
#if TAYLOR_SERIES_ORDER >= 2
if (order >= 2)
{
// Adjust Nijk for the change in centre P
data_for_parent->myNijkDiag += T(2)*displacement*child_data.myNijDiag + displacement*displacement*child_data.myN;
data_for_parent->mySumPermuteNxyz += (displacement[0]*(Nyz+Nzy) + displacement[1]*(Nzx+Nxz) + displacement[2]*(Nxy+Nyx));
data_for_parent->my2Nxxy_Nyxx +=
2*(displacement[1]*child_data.myNijDiag[0] + displacement[0]*child_data.myNxy + N[0]*displacement[0]*displacement[1])
+ 2*child_data.myNyx*displacement[0] + N[1]*displacement[0]*displacement[0];
data_for_parent->my2Nxxz_Nzxx +=
2*(displacement[2]*child_data.myNijDiag[0] + displacement[0]*child_data.myNxz + N[0]*displacement[0]*displacement[2])
+ 2*child_data.myNzx*displacement[0] + N[2]*displacement[0]*displacement[0];
data_for_parent->my2Nyyz_Nzyy +=
2*(displacement[2]*child_data.myNijDiag[1] + displacement[1]*child_data.myNyz + N[1]*displacement[1]*displacement[2])
+ 2*child_data.myNzy*displacement[1] + N[2]*displacement[1]*displacement[1];
data_for_parent->my2Nyyx_Nxyy +=
2*(displacement[0]*child_data.myNijDiag[1] + displacement[1]*child_data.myNyx + N[1]*displacement[1]*displacement[0])
+ 2*child_data.myNxy*displacement[1] + N[0]*displacement[1]*displacement[1];
data_for_parent->my2Nzzx_Nxzz +=
2*(displacement[0]*child_data.myNijDiag[2] + displacement[2]*child_data.myNzx + N[2]*displacement[2]*displacement[0])
+ 2*child_data.myNxz*displacement[2] + N[0]*displacement[2]*displacement[2];
data_for_parent->my2Nzzy_Nyzz +=
2*(displacement[1]*child_data.myNijDiag[2] + displacement[2]*child_data.myNzy + N[2]*displacement[2]*displacement[1])
+ 2*child_data.myNyz*displacement[2] + N[1]*displacement[2]*displacement[2];
}
#endif
}
}
#endif
#if SOLID_ANGLE_DEBUG
UTdebugFormat("");
UTdebugFormat("Node {}: nchildren = {}; maxP = {}", nodei, nchildren, SYSsqrt(current_box_data.myMaxPDist2));
UTdebugFormat(" P = {}; N = {}", current_box_data.myAverageP, current_box_data.myN);
#if TAYLOR_SERIES_ORDER >= 1
UTdebugFormat(" Nii = {}", current_box_data.myNijDiag);
UTdebugFormat(" Nxy+Nyx = {}; Nyz+Nzy = {}; Nyz+Nzy = {}", current_box_data.myNxy_Nyx, current_box_data.myNyz_Nzy, current_box_data.myNzx_Nxz);
#if TAYLOR_SERIES_ORDER >= 2
UTdebugFormat(" Niii = {}; 2(Nxyz+Nyzx+Nzxy) = {}", current_box_data.myNijkDiag, current_box_data.mySumPermuteNxyz);
UTdebugFormat(" 2Nxxy+Nyxx = {}; 2Nxxz+Nzxx = {}", current_box_data.my2Nxxy_Nyxx, current_box_data.my2Nxxz_Nzxx);
UTdebugFormat(" 2Nyyz+Nzyy = {}; 2Nyyx+Nxyy = {}", current_box_data.my2Nyyz_Nzyy, current_box_data.my2Nyyx_Nxyy);
UTdebugFormat(" 2Nzzx+Nxzz = {}; 2Nzzy+Nyzz = {}", current_box_data.my2Nzzx_Nxzz, current_box_data.my2Nzzy_Nyzz);
#endif
#endif
#endif
}
};
#if SOLID_ANGLE_TIME_PRECOMPUTE
timer.start();
#endif
const PrecomputeFunctors functors(box_data, triangle_boxes.array(), triangle_points, positions, order);
// NOTE: post-functor relies on non-null data_for_parent, so we have to pass one.
LocalData local_data;
myTree.template traverseParallel<LocalData>(4096, functors, &local_data);
//myTree.template traverse<LocalData>(functors);
#if SOLID_ANGLE_TIME_PRECOMPUTE
time = timer.stop();
UTdebugFormat("{} s to precompute coefficients.", time);
#endif
}
template<typename T,typename S>
inline void UT_SolidAngle<T, S>::clear()
{
myTree.clear();
myNBoxes = 0;
myOrder = 2;
myData.reset();
myNTriangles = 0;
myTrianglePoints = nullptr;
myNPoints = 0;
myPositions = nullptr;
}
template<typename T,typename S>
inline T UT_SolidAngle<T, S>::computeSolidAngle(const UT_Vector3T<T> &query_point, const T accuracy_scale) const
{
const T accuracy_scale2 = accuracy_scale*accuracy_scale;
struct SolidAngleFunctors
{
const BoxData *const myBoxData;
const UT_Vector3T<T> myQueryPoint;
const T myAccuracyScale2;
const UT_Vector3T<S> *const myPositions;
const int *const myTrianglePoints;
const int myOrder;
SolidAngleFunctors(
const BoxData *const box_data,
const UT_Vector3T<T> &query_point,
const T accuracy_scale2,
const int order,
const UT_Vector3T<S> *const positions,
const int *const triangle_points)
: myBoxData(box_data)
, myQueryPoint(query_point)
, myAccuracyScale2(accuracy_scale2)
, myOrder(order)
, myPositions(positions)
, myTrianglePoints(triangle_points)
{}
uint pre(const int nodei, T *data_for_parent) const
{
const BoxData &data = myBoxData[nodei];
const typename BoxData::Type maxP2 = data.myMaxPDist2;
UT_FixedVector<typename BoxData::Type,3> q;
q[0] = typename BoxData::Type(myQueryPoint[0]);
q[1] = typename BoxData::Type(myQueryPoint[1]);
q[2] = typename BoxData::Type(myQueryPoint[2]);
q -= data.myAverageP;
const typename BoxData::Type qlength2 = q[0]*q[0] + q[1]*q[1] + q[2]*q[2];
// If the query point is within a factor of accuracy_scale of the box radius,
// it's assumed to be not a good enough approximation, so it needs to descend.
// TODO: Is there a way to estimate the error?
static_assert((std::is_same<typename BoxData::Type,v4uf>::value), "FIXME: Implement support for other tuple types!");
v4uu descend_mask = (qlength2 <= maxP2*myAccuracyScale2);
uint descend_bitmask = _mm_movemask_ps(V4SF(descend_mask.vector));
constexpr uint allchildbits = ((uint(1)<<BVH_N)-1);
if (descend_bitmask == allchildbits)
{
*data_for_parent = 0;
return allchildbits;
}
// qlength2 must be non-zero, since it's strictly greater than something.
// We still need to be careful for NaNs, though, because the 4th power might cause problems.
const typename BoxData::Type qlength_m2 = typename BoxData::Type(1.0)/qlength2;
const typename BoxData::Type qlength_m1 = sqrt(qlength_m2);
// Normalize q to reduce issues with overflow/underflow, since we'd need the 7th power
// if we didn't normalize, and (1e-6)^-7 = 1e42, which overflows single-precision.
q *= qlength_m1;
typename BoxData::Type Omega_approx = -qlength_m2*dot(q,data.myN);
#if TAYLOR_SERIES_ORDER >= 1
const int order = myOrder;
if (order >= 1)
{
const UT_FixedVector<typename BoxData::Type,3> q2 = q*q;
const typename BoxData::Type qlength_m3 = qlength_m2*qlength_m1;
const typename BoxData::Type Omega_1 =
qlength_m3*(data.myNijDiag[0] + data.myNijDiag[1] + data.myNijDiag[2]
-typename BoxData::Type(3.0)*(dot(q2,data.myNijDiag) +
q[0]*q[1]*data.myNxy_Nyx +
q[0]*q[2]*data.myNzx_Nxz +
q[1]*q[2]*data.myNyz_Nzy));
Omega_approx += Omega_1;
#if TAYLOR_SERIES_ORDER >= 2
if (order >= 2)
{
const UT_FixedVector<typename BoxData::Type,3> q3 = q2*q;
const typename BoxData::Type qlength_m4 = qlength_m2*qlength_m2;
typename BoxData::Type temp0[3] = {
data.my2Nyyx_Nxyy+data.my2Nzzx_Nxzz,
data.my2Nzzy_Nyzz+data.my2Nxxy_Nyxx,
data.my2Nxxz_Nzxx+data.my2Nyyz_Nzyy
};
typename BoxData::Type temp1[3] = {
q[1]*data.my2Nxxy_Nyxx + q[2]*data.my2Nxxz_Nzxx,
q[2]*data.my2Nyyz_Nzyy + q[0]*data.my2Nyyx_Nxyy,
q[0]*data.my2Nzzx_Nxzz + q[1]*data.my2Nzzy_Nyzz
};
const typename BoxData::Type Omega_2 =
qlength_m4*(typename BoxData::Type(1.5)*dot(q, typename BoxData::Type(3)*data.myNijkDiag + UT_FixedVector<typename BoxData::Type,3>(temp0))
-typename BoxData::Type(7.5)*(dot(q3,data.myNijkDiag) + q[0]*q[1]*q[2]*data.mySumPermuteNxyz + dot(q2, UT_FixedVector<typename BoxData::Type,3>(temp1))));
Omega_approx += Omega_2;
}
#endif
}
#endif
// If q is so small that we got NaNs and we just have a
// small bounding box, it needs to descend.
const v4uu mask = Omega_approx.isFinite() & ~descend_mask;
Omega_approx = Omega_approx & mask;
descend_bitmask = (~_mm_movemask_ps(V4SF(mask.vector))) & allchildbits;
T sum = Omega_approx[0];
for (int i = 1; i < BVH_N; ++i)
sum += Omega_approx[i];
*data_for_parent = sum;
return descend_bitmask;
}
void item(const int itemi, const int parent_nodei, T &data_for_parent) const
{
const UT_Vector3T<S> *const positions = myPositions;
const int *const cur_triangle_points = myTrianglePoints + 3*itemi;
const UT_Vector3T<T> a = positions[cur_triangle_points[0]];
const UT_Vector3T<T> b = positions[cur_triangle_points[1]];
const UT_Vector3T<T> c = positions[cur_triangle_points[2]];
data_for_parent = UTsignedSolidAngleTri(a, b, c, myQueryPoint);
}
SYS_FORCE_INLINE void post(const int nodei, const int parent_nodei, T *data_for_parent, const int nchildren, const T *child_data_array, const uint descend_bits) const
{
T sum = (descend_bits&1) ? child_data_array[0] : 0;
for (int i = 1; i < nchildren; ++i)
sum += ((descend_bits>>i)&1) ? child_data_array[i] : 0;
*data_for_parent += sum;
}
};
const SolidAngleFunctors functors(myData.get(), query_point, accuracy_scale2, myOrder, myPositions, myTrianglePoints);
T sum;
myTree.traverseVector(functors, &sum);
return sum;
}
template<typename T,typename S>
struct UT_SubtendedAngle<T,S>::BoxData
{
void clear()
{
// Set everything to zero
memset(this,0,sizeof(*this));
}
using Type = typename std::conditional<BVH_N==4 && std::is_same<T,float>::value, v4uf, UT_FixedVector<T,BVH_N>>::type;
using SType = typename std::conditional<BVH_N==4 && std::is_same<S,float>::value, v4uf, UT_FixedVector<S,BVH_N>>::type;
/// An upper bound on the squared distance from myAverageP to the farthest point in the box.
SType myMaxPDist2;
/// Centre of mass of the mesh surface in this box
UT_FixedVector<Type,2> myAverageP;
/// Unnormalized, area-weighted normal of the mesh in this box
UT_FixedVector<Type,2> myN;
/// Values for Omega_1
/// @{
UT_FixedVector<Type,2> myNijDiag; // Nxx, Nyy
Type myNxy_Nyx; // Nxy+Nyx
/// @}
/// Values for Omega_2
/// @{
UT_FixedVector<Type,2> myNijkDiag; // Nxxx, Nyyy
Type my2Nxxy_Nyxx; // Nxxy+Nxyx+Nyxx = 2Nxxy+Nyxx
Type my2Nyyx_Nxyy; // Nyyx+Nyxy+Nxyy = 2Nyyx+Nxyy
/// @}
};
template<typename T,typename S>
inline UT_SubtendedAngle<T,S>::UT_SubtendedAngle()
: myTree()
, myNBoxes(0)
, myOrder(2)
, myData(nullptr)
, myNSegments(0)
, mySegmentPoints(nullptr)
, myNPoints(0)
, myPositions(nullptr)
{}
template<typename T,typename S>
inline UT_SubtendedAngle<T,S>::~UT_SubtendedAngle()
{
// Default destruction works, but this needs to be outlined
// to avoid having to include UT_BVHImpl.h in the header,
// (for the UT_UniquePtr destructor.)
}
template<typename T,typename S>
inline void UT_SubtendedAngle<T,S>::init(
const int nsegments,
const int *const segment_points,
const int npoints,
const UT_Vector2T<S> *const positions,
const int order)
{
#if SOLID_ANGLE_DEBUG
UTdebugFormat("");
UTdebugFormat("");
UTdebugFormat("Building BVH for {} segments on {} points:", nsegments, npoints);
#endif
myOrder = order;
myNSegments = nsegments;
mySegmentPoints = segment_points;
myNPoints = npoints;
myPositions = positions;
#if SOLID_ANGLE_TIME_PRECOMPUTE
UT_StopWatch timer;
timer.start();
#endif
UT_SmallArray<UT::Box<S,2>> segment_boxes;
segment_boxes.setSizeNoInit(nsegments);
if (nsegments < 16*1024)
{
const int *cur_segment_points = segment_points;
for (int i = 0; i < nsegments; ++i, cur_segment_points += 2)
{
UT::Box<S,2> &box = segment_boxes[i];
box.initBounds(positions[cur_segment_points[0]]);
box.enlargeBounds(positions[cur_segment_points[1]]);
}
}
else
{
igl::parallel_for(nsegments,
[segment_points,&segment_boxes,positions](int i)
{
const int *cur_segment_points = segment_points + i*2;
UT::Box<S,2> &box = segment_boxes[i];
box.initBounds(positions[cur_segment_points[0]]);
box.enlargeBounds(positions[cur_segment_points[1]]);
});
}
#if SOLID_ANGLE_TIME_PRECOMPUTE
double time = timer.stop();
UTdebugFormat("{} s to create bounding boxes.", time);
timer.start();
#endif
myTree.template init<UT::BVH_Heuristic::BOX_AREA,S,2>(segment_boxes.array(), nsegments);
#if SOLID_ANGLE_TIME_PRECOMPUTE
time = timer.stop();
UTdebugFormat("{} s to initialize UT_BVH structure. {} nodes", time, myTree.getNumNodes());
#endif
//myTree.debugDump();
const int nnodes = myTree.getNumNodes();
myNBoxes = nnodes;
BoxData *box_data = new BoxData[nnodes];
myData.reset(box_data);
// Some data are only needed during initialization.
struct LocalData
{
// Bounding box
UT::Box<S,2> myBox;
// P and N are needed from each child for computing Nij.
UT_Vector2T<T> myAverageP;
UT_Vector2T<T> myLengthP;
UT_Vector2T<T> myN;
// Unsigned length is needed for computing the average position.
T myLength;
// These are needed for computing Nijk.
UT_Vector2T<T> myNijDiag;
T myNxy; T myNyx;