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InnerVertexPlacement.cpp
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Christophe Geuzaine authored
This reverts commit 07cc55d9
Christophe Geuzaine authoredThis reverts commit 07cc55d9
SOrientedBoundingBox.cpp 18.39 KiB
// Gmsh - Copyright (C) 1997-2012 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to <gmsh@geuz.org>.
//
// Contributor(s):
// Bastien Gorissen
//
#include <math.h>
#include <time.h>
#include <stdlib.h>
#include "SOrientedBoundingBox.h"
#include "fullMatrix.h"
#include "DivideAndConquer.h"
#include "SBoundingBox3d.h"
double SOrientedBoundingRectangle::area()
{
double b = size->at(0);
double B = size->at(1);
return (b*B);
}
SOrientedBoundingRectangle::SOrientedBoundingRectangle()
{
center = new std::vector<double>(2,0);
size = new std::vector<double>(2,0);
axisX = new std::vector<double>(2,0);
axisY = new std::vector<double>(2,0);
}
SOrientedBoundingRectangle::~SOrientedBoundingRectangle()
{
delete center;
delete size;
delete axisX;
delete axisY;
}
SOrientedBoundingBox::SOrientedBoundingBox()
{
center = SVector3();
size = SVector3();
axisX = SVector3();
axisY = SVector3();
axisZ = SVector3();
}
SOrientedBoundingBox::SOrientedBoundingBox(SVector3 ¢er_,
double sizeX,
double sizeY,
double sizeZ,
const SVector3 &axisX_,
const SVector3 &axisY_,
const SVector3 &axisZ_)
{
center = center_;
size = SVector3(sizeX, sizeY, sizeZ);
axisX = axisX_;
axisX.normalize();
axisY = axisY_;
axisY.normalize();
axisZ = axisZ_;
axisZ.normalize();
double dx = 0.5 * size[0];
double dy = 0.5 * size[1];
double dz = 0.5 * size[2];
p1x = center[0] - (axisX[0]*dx) - (axisY[0]*dy) - (axisZ[0]*dz);
p1y = center[1] - (axisX[1]*dx) - (axisY[1]*dy) - (axisZ[1]*dz);
p1z = center[2] - (axisX[2]*dx) - (axisY[2]*dy) - (axisZ[2]*dz);
p2x = center[0] + (axisX[0]*dx) - (axisY[0]*dy) - (axisZ[0]*dz);
p2y = center[1] + (axisX[1]*dx) - (axisY[1]*dy) - (axisZ[1]*dz);
p2z = center[2] + (axisX[2]*dx) - (axisY[2]*dy) - (axisZ[2]*dz);
p3x = center[0] - (axisX[0]*dx) + (axisY[0]*dy) - (axisZ[0]*dz);
p3y = center[1] - (axisX[1]*dx) + (axisY[1]*dy) - (axisZ[1]*dz);
p3z = center[2] - (axisX[2]*dx) + (axisY[2]*dy) - (axisZ[2]*dz);
p4x = center[0] + (axisX[0]*dx) + (axisY[0]*dy) - (axisZ[0]*dz);
p4y = center[1] + (axisX[1]*dx) + (axisY[1]*dy) - (axisZ[1]*dz);
p4z = center[2] + (axisX[2]*dx) + (axisY[2]*dy) - (axisZ[2]*dz);
p5x = center[0] - (axisX[0]*dx) - (axisY[0]*dy) + (axisZ[0]*dz);
p5y = center[1] - (axisX[1]*dx) - (axisY[1]*dy) + (axisZ[1]*dz);
p5z = center[2] - (axisX[2]*dx) - (axisY[2]*dy) + (axisZ[2]*dz);
p6x = center[0] + (axisX[0]*dx) - (axisY[0]*dy) + (axisZ[0]*dz);
p6y = center[1] + (axisX[1]*dx) - (axisY[1]*dy) + (axisZ[1]*dz);
p6z = center[2] + (axisX[2]*dx) - (axisY[2]*dy) + (axisZ[2]*dz);
p7x = center[0] - (axisX[0]*dx) + (axisY[0]*dy) + (axisZ[0]*dz);
p7y = center[1] - (axisX[1]*dx) + (axisY[1]*dy) + (axisZ[1]*dz);
p7z = center[2] - (axisX[2]*dx) + (axisY[2]*dy) + (axisZ[2]*dz);
p8x = center[0] + (axisX[0]*dx) + (axisY[0]*dy) + (axisZ[0]*dz);
p8y = center[1] + (axisX[1]*dx) + (axisY[1]*dy) + (axisZ[1]*dz);
p8z = center[2] + (axisX[2]*dx) + (axisY[2]*dy) + (axisZ[2]*dz);
}
SOrientedBoundingBox::SOrientedBoundingBox(SOrientedBoundingBox* other)
{
size = other->getSize();
axisX = other->getAxis(0);
axisY = other->getAxis(1);
axisZ = other->getAxis(2);
center = other->getCenter();
double dx = 0.5*size[0];
double dy = 0.5*size[1];
double dz = 0.5*size[2];
p1x = center[0] - (axisX[0]*dx) - (axisY[0]*dy) - (axisZ[0]*dz);
p1y = center[1] - (axisX[1]*dx) - (axisY[1]*dy) - (axisZ[1]*dz);
p1z = center[2] - (axisX[2]*dx) - (axisY[2]*dy) - (axisZ[2]*dz);
p2x = center[0] + (axisX[0]*dx) - (axisY[0]*dy) - (axisZ[0]*dz);
p2y = center[1] + (axisX[1]*dx) - (axisY[1]*dy) - (axisZ[1]*dz);
p2z = center[2] + (axisX[2]*dx) - (axisY[2]*dy) - (axisZ[2]*dz);
p3x = center[0] - (axisX[0]*dx) + (axisY[0]*dy) - (axisZ[0]*dz);
p3y = center[1] - (axisX[1]*dx) + (axisY[1]*dy) - (axisZ[1]*dz);
p3z = center[2] - (axisX[2]*dx) + (axisY[2]*dy) - (axisZ[2]*dz);
p4x = center[0] + (axisX[0]*dx) + (axisY[0]*dy) - (axisZ[0]*dz);
p4y = center[1] + (axisX[1]*dx) + (axisY[1]*dy) - (axisZ[1]*dz);
p4z = center[2] + (axisX[2]*dx) + (axisY[2]*dy) - (axisZ[2]*dz);
p5x = center[0] - (axisX[0]*dx) - (axisY[0]*dy) + (axisZ[0]*dz);
p5y = center[1] - (axisX[1]*dx) - (axisY[1]*dy) + (axisZ[1]*dz);
p5z = center[2] - (axisX[2]*dx) - (axisY[2]*dy) + (axisZ[2]*dz);
p6x = center[0] + (axisX[0]*dx) - (axisY[0]*dy) + (axisZ[0]*dz);
p6y = center[1] + (axisX[1]*dx) - (axisY[1]*dy) + (axisZ[1]*dz);
p6z = center[2] + (axisX[2]*dx) - (axisY[2]*dy) + (axisZ[2]*dz);
p7x = center[0] - (axisX[0]*dx) + (axisY[0]*dy) + (axisZ[0]*dz);
p7y = center[1] - (axisX[1]*dx) + (axisY[1]*dy) + (axisZ[1]*dz);
p7z = center[2] - (axisX[2]*dx) + (axisY[2]*dy) + (axisZ[2]*dz);
p8x = center[0] + (axisX[0]*dx) + (axisY[0]*dy) + (axisZ[0]*dz);
p8y = center[1] + (axisX[1]*dx) + (axisY[1]*dy) + (axisZ[1]*dz);
p8z = center[2] + (axisX[2]*dx) + (axisY[2]*dy) + (axisZ[2]*dz);
}
double SOrientedBoundingBox::getMaxSize()
{
return (std::max(size[0], std::max(size[1], size[2])));
}
double SOrientedBoundingBox::getMinSize()
{
return (std::min(size[0], std::min(size[1], size[2])));
}
SVector3 SOrientedBoundingBox::getAxis(int axis)
{
SVector3 ret;
switch (axis) {
case 0: ret=axisX; break;
case 1: ret=axisY; break;
case 2: ret=axisZ; break;
}
return ret;
}
bool SOrientedBoundingBox::intersects(SOrientedBoundingBox& obb)
{
SVector3 collide_axes[15];
for (int i = 0; i < 3; i ++) {
collide_axes[i] = getAxis(i);
collide_axes[i+3] = obb.getAxis(i);
}
SVector3 sizes[2];
sizes[0] = getSize();
sizes[1] = obb.getSize();
for(unsigned int i=0 ; i<3 ; i++) {
for(unsigned int j=3 ; j<6 ; j++) {
collide_axes[3*i+j+3] = crossprod(collide_axes[i],collide_axes[j]);
}
}
SVector3 T = obb.getCenter() - getCenter();
for(unsigned int i=0 ; i<15 ; i++) {
double val = 0.0;
for(unsigned int j=0 ; j<6 ; j++) {
val += 0.5*(sizes[j<3?0:1])(j % 3) * fabs(dot(collide_axes[j],collide_axes[i]));
}
if (fabs(dot(collide_axes[i],T )) > val)
return false;
}
return true;
}
SOrientedBoundingBox* SOrientedBoundingBox::buildOBB(std::vector<SPoint3> vertices)
{
int num_vertices = vertices.size();
// First organize the data
fullMatrix<double> data(3,num_vertices);
int tmp = 0;
for (int i = 0; i < num_vertices; i++) {
bool okay = true;
for (int j = 0; j < tmp; j++) {
if((data(0,j) == vertices[i].x()) &&
(data(1,j) == vertices[i].y()) &&
(data(2,j) == vertices[i].z())) {
okay = false;
break;
}
}
if (okay) {
data(0,tmp) = vertices[i].x();
data(1,tmp) = vertices[i].y();
data(2,tmp) = vertices[i].z();
tmp++;
}
}
num_vertices = tmp;
// Compute the empirical means
fullVector<double> mean(3);
for (int i = 0; i < 3; i++) {
mean(i) = 0;
for (int j = 0; j < num_vertices; j++) {
mean(i) += data(i,j);
}
mean(i) /= (double)num_vertices;
}
// Get the deviation from the mean
fullMatrix<double> B(3,num_vertices);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < num_vertices; j++) {
B(i,j) = data(i,j) - mean(i);
}
}
// Compute the covariance matrix
fullMatrix<double> covariance(3,3);
B.mult(B.transpose(), covariance);
covariance.scale(1./(num_vertices-1));
/*
Msg::Debug("Covariance matrix");
Msg::Debug("%f %f %f", covariance(0,0),covariance(0,1),covariance(0,2) );
Msg::Debug("%f %f %f", covariance(1,0),covariance(1,1),covariance(1,2) );
Msg::Debug("%f %f %f", covariance(2,0),covariance(2,1),covariance(2,2) );
*/
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
if (fabs(covariance(i,j))< 10e-16)
covariance(i,j) = 0;
}
}
fullMatrix<double> left_eigv(3,3);
fullMatrix<double> right_eigv(3,3);
fullVector<double> real_eig(3);
fullVector<double> img_eig(3);
covariance.eig(real_eig, img_eig, left_eigv, right_eigv,true);
// Now, project the data in the new basis.
fullMatrix<double> projected(3,num_vertices);
left_eigv.transpose().mult(data,projected);
// Get the size of the box in the new direction
fullVector<double> mins(3);
fullVector<double> maxs(3);
for (int i = 0; i < 3; i++) {
mins(i) = DBL_MAX;
maxs(i) = -DBL_MAX;
for (int j = 0; j < num_vertices; j++) {
maxs(i) =std::max(maxs(i),projected(i,j));
mins(i) = std::min(mins(i),projected(i,j));
}
}
double means[3];
double sizes[3];
// Note: the size is computed in the box's coordinates!
for(int i = 0 ; i < 3 ; i++) {
sizes[i] = maxs(i) - mins(i);
means[i] = (maxs(i) - mins(i)) / 2.;
}
/*
Msg::Debug("Sizes : %f %f %f",sizes[0],sizes[1], sizes[2]);
Msg::Debug("Eig Axis 1 : %f %f %f",left_eigv(0,0),left_eigv(1,0), left_eigv(2,0));
Msg::Debug("Eig Axis 2 : %f %f %f",left_eigv(0,1),left_eigv(1,1), left_eigv(2,1));
Msg::Debug("Eig Axis 3 : %f %f %f",left_eigv(0,2),left_eigv(1,2), left_eigv(2,2));
*/
// We take the smallest component, then project the data on the plane defined by the other twos
int smallest_comp = 0;
if (sizes[0] <= sizes[1] && sizes[0] <= sizes[2])
smallest_comp = 0;
else if (sizes[1] <= sizes[0] && sizes[1] <= sizes[2])
smallest_comp = 1;
else if (sizes[2] <= sizes[0] && sizes[2] <= sizes[1])
smallest_comp = 2;
// The projection has been done circa line 161.
// We just ignore the coordinate corresponding to smallest_comp.
std::vector<SPoint2*> points;
for (int i = 0; i < num_vertices; i++) {
SPoint2* p = new SPoint2(projected(smallest_comp==0?1:0,i), projected(smallest_comp==2?1:2,i));
bool keep = true;
for (std::vector<SPoint2*>::iterator point = points.begin();point != points.end();point++) {
if ( fabs((*p)[0] -(**point)[0]) < 10e-10 && fabs((*p)[1] -(**point)[1]) < 10e-10 ) {
keep = false;
break;
}
}
if (keep) {
points.push_back(p);
} else {
delete p;
}
}
// Find the convex hull from a delaunay triangulation of the points
DocRecord record(points.size());
record.numPoints = points.size();
srand((unsigned)time(0));
for (unsigned int i = 0; i < points.size(); i++) {
record.points[i].where.h = points[i]->x()+(10e-6)*sizes[smallest_comp==0?1:0]*(-0.5+((double)rand())/RAND_MAX);
record.points[i].where.v = points[i]->y()+(10e-6)*sizes[smallest_comp==2?1:0]*(-0.5+((double)rand())/RAND_MAX);
record.points[i].adjacent = NULL;
//Msg::Info("Points for delaunay : %f %f",record.points[i].where.h,record.points[i].where.v);
}
record.MakeMeshWithPoints();
std::vector<Segment> convex_hull;
for (int i = 0; i < record.numTriangles; i++) {
Segment segs[3];
segs[0].from = record.triangles[i].a;
segs[0].to = record.triangles[i].b;
segs[1].from = record.triangles[i].b;
segs[1].to = record.triangles[i].c;
segs[2].from = record.triangles[i].c;
segs[2].to = record.triangles[i].a;
for (int j = 0; j < 3; j++) {
bool okay = true;
for (std::vector<Segment>::iterator seg = convex_hull.begin(); seg != convex_hull.end(); seg++) {
if ( ((*seg).from == segs[j].from && (*seg).from == segs[j].to) || ((*seg).from == segs[j].to && (*seg).from == segs[j].from)) {
convex_hull.erase(seg);
okay = false;
break;
}
}
if (okay) {
convex_hull.push_back(segs[j]);
}
}
}
// Now, examinate all the directions given by the edges of the convex hull
// to find the one that lets us build the least-area bounding rectangle for then
// points.
fullVector<double> axis(2);
axis(0) = 1;
axis(1) = 0;
fullVector<double> axis2(2);
axis2(0) = 0;
axis2(1) = 1;
SOrientedBoundingRectangle least_rectangle;
least_rectangle.center->at(0) = 0.0;
least_rectangle.center->at(1) = 0.0;
least_rectangle.size->at(0) = -1;
least_rectangle.size->at(1) = 1;
for (std::vector<Segment>::iterator seg = convex_hull.begin(); seg != convex_hull.end(); seg++) {
fullVector<double> segment(2);
//segment(0) = record.points[(*seg).from].where.h - record.points[(*seg).to].where.h;
//segment(1) = record.points[(*seg).from].where.v - record.points[(*seg).to].where.v;
segment(0) = points[(*seg).from]->x() - points[(*seg).to]->x();
segment(1) = points[(*seg).from]->y() - points[(*seg).to]->y();
segment.scale(1.0/segment.norm());
double cosine = axis(0)*segment(0) + segment(1)*axis(1);
double sine = axis(1)*segment(0) - segment(1)*axis(0);
//double sine = axis(0)*segment(1) - segment(0)*axis(1);
fullMatrix<double> rotation(2,2);
rotation(0,0) = cosine; rotation(0,1) = sine;
rotation(1,0) = -sine; rotation(1,1) = cosine;
double max_x = -DBL_MAX;
double min_x = DBL_MAX;
double max_y = -DBL_MAX;
double min_y = DBL_MAX;
for (int i = 0; i < record.numPoints; i++) {
fullVector<double> pnt(2);
//pnt(0) = record.points[i].where.h;
//pnt(1) = record.points[i].where.v;
pnt(0) = points[i]->x();
pnt(1) = points[i]->y();
fullVector<double> rot_pnt(2);
rotation.mult(pnt,rot_pnt);
if (rot_pnt(0) < min_x) min_x = rot_pnt(0);
if (rot_pnt(0) > max_x) max_x = rot_pnt(0);
if (rot_pnt(1) < min_y) min_y = rot_pnt(1);
if (rot_pnt(1) > max_y) max_y = rot_pnt(1);
}
/**/
fullVector<double> center_rot(2);
fullVector<double> center_before_rot(2);
center_before_rot(0) = (max_x+min_x)/2.0;
center_before_rot(1) = (max_y+min_y)/2.0;
fullMatrix<double> rotation_inv(2,2);
rotation_inv(0,0) = cosine; rotation_inv(0,1) = -sine;
rotation_inv(1,0) = sine; rotation_inv(1,1) = cosine;
rotation_inv.mult(center_before_rot,center_rot);
fullVector<double> axis_rot1(2);
fullVector<double> axis_rot2(2);
rotation_inv.mult(axis,axis_rot1);
rotation_inv.mult(axis2,axis_rot2);
//*/
if ((least_rectangle.area() == -1) || (max_x-min_x)*(max_y-min_y) < least_rectangle.area()) {
least_rectangle.size->at(0) = max_x-min_x;
least_rectangle.size->at(1) = max_y-min_y;
least_rectangle.center->at(0) = (max_x+min_x)/2.0;
least_rectangle.center->at(1) = (max_y+min_y)/2.0;
least_rectangle.center->at(0) = center_rot(0);
least_rectangle.center->at(1) = center_rot(1);
least_rectangle.axisX->at(0) = axis_rot1(0);
least_rectangle.axisX->at(1) = axis_rot1(1);
// least_rectangle.axisX->at(0) = segment(0);
// least_rectangle.axisX->at(1) = segment(1);
least_rectangle.axisY->at(0) = axis_rot2(0);
least_rectangle.axisY->at(1) = axis_rot2(1);
}
}
double min_pca = DBL_MAX;
double max_pca = -DBL_MAX;
for (int i = 0; i < num_vertices; i++) {
min_pca = std::min(min_pca,projected(smallest_comp,i));
max_pca = std::max(max_pca,projected(smallest_comp,i));
}
double center_pca = (max_pca+min_pca)/2.0;
double size_pca = (max_pca-min_pca);
double raw_data[3][5];
raw_data[0][0] = size_pca;
raw_data[1][0] = least_rectangle.size->at(0);
raw_data[2][0] = least_rectangle.size->at(1);
raw_data[0][1] = center_pca;
raw_data[1][1] = least_rectangle.center->at(0);
raw_data[2][1] = least_rectangle.center->at(1);
for (int i = 0; i < 3; i++) {
raw_data[0][2+i] = left_eigv(i,smallest_comp);
raw_data[1][2+i] = least_rectangle.axisX->at(0)*left_eigv(i,smallest_comp==0?1:0) +
least_rectangle.axisX->at(1)*left_eigv(i,smallest_comp==2?1:2);
raw_data[2][2+i] = least_rectangle.axisY->at(0)*left_eigv(i,smallest_comp==0?1:0) +
least_rectangle.axisY->at(1)*left_eigv(i,smallest_comp==2?1:2);
}
// Msg::Info("Test 1 : %f %f",least_rectangle.center->at(0),least_rectangle.center->at(1));
// Msg::Info("Test 2 : %f %f",least_rectangle.axisY->at(0),least_rectangle.axisY->at(1));
int tri[3];
if (size_pca > least_rectangle.size->at(0)) { // P > R0
if (size_pca > least_rectangle.size->at(1)) { // P > R1
tri[0] = 0;
if (least_rectangle.size->at(0) > least_rectangle.size->at(1)) { // R0 > R1
tri[1] = 1;
tri[2] = 2;
} else { // R1 > R0
tri[1] = 2;
tri[2] = 1;
}
} else { // P < R1
tri[0] = 2;
tri[1] = 0;
tri[2] = 1;
}
} else { // P < R0
if (size_pca < least_rectangle.size->at(1)) { // P < R1
tri[2] = 0;
if (least_rectangle.size->at(0) > least_rectangle.size->at(1)) {
tri[0] = 1;
tri[1] = 2;
} else {
tri[0] = 2;
tri[1] = 1;
}
} else {
tri[0] = 1;
tri[1] = 0;
tri[2] = 2;
}
}
SVector3 size;
SVector3 center;
SVector3 Axis1;
SVector3 Axis2;
SVector3 Axis3;
for (int i = 0; i < 3; i++) {
size[i] = raw_data[tri[i]][0];
center[i] = raw_data[tri[i]][1];
Axis1[i] = raw_data[tri[0]][2+i];
Axis2[i] = raw_data[tri[1]][2+i];
Axis3[i] = raw_data[tri[2]][2+i];
}
SVector3 aux1;
SVector3 aux2;
SVector3 aux3;
for (int i = 0; i < 3; i++) {
aux1(i) = left_eigv(i,smallest_comp);
aux2(i) = left_eigv(i,smallest_comp==0?1:0);
aux3(i) = left_eigv(i,smallest_comp==2?1:2);
}
center = aux1*center_pca + aux2*least_rectangle.center->at(0) + aux3*least_rectangle.center->at(1);
//center[1] = -center[1];
/*
Msg::Info("Box center : %f %f %f",center[0],center[1],center[2]);
Msg::Info("Box size : %f %f %f",size[0],size[1],size[2]);
Msg::Info("Box axis 1 : %f %f %f",Axis1[0],Axis1[1],Axis1[2]);
Msg::Info("Box axis 2 : %f %f %f",Axis2[0],Axis2[1],Axis2[2]);
Msg::Info("Box axis 3 : %f %f %f",Axis3[0],Axis3[1],Axis3[2]);
Msg::Info("Volume : %f", size[0]*size[1]*size[2]);
*/
return (new SOrientedBoundingBox(center,
size[0], size[1], size[2], Axis1, Axis2, Axis3));
}
double SOrientedBoundingBox::compare(SOrientedBoundingBox& obb1, SOrientedBoundingBox& obb2)
{
// "center term"
double center_term = norm(obb1.getCenter() - obb2.getCenter());
// "size term"
double size_term = 0.0;
for (int i = 0; i < 3; i++) {
if ((obb1.getSize())(i) + (obb2.getSize())(i) != 0) {
size_term += fabs((obb1.getSize())(i) - (obb2.getSize())(i)) / ((obb1.getSize())(i) + (obb2.getSize())(i));
}
}
// "orientation term"
double orientation_term = 0.0;
for (int i = 0; i < 3; i++) {
orientation_term += 1 - fabs(dot(obb1.getAxis(i),obb2.getAxis(i)));
}
return (center_term + size_term + orientation_term);
}