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LinkNumberComputing.cpp
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/*
(c) 2012 Fengtao Fan
*/
#include "LinkNumberComputing.h"
#include "SegmentIntersection.h"
#include "ANNSearch.h"
#include <vector>
#include <algorithm>
#define MY_LOCAL_PI 3.14159265
/*local functions used for LinkNumberComputing*/
char SegSegInt(double a[2], double b[2],
double c[2], double d[2],
double p[2]);
double angle_between_projected_segment_and_X_axis_LinkNumber_simple(Vector3 &segment) {// sgement is normalized
return acos(segment[0]);
}
double angle_between_projected_segment_and_X_axis_LinkNumber(Vector3 &segment) {
double angle = 0.0;
if (segment[0] == 0.0) {
if (segment[1] == 0.0) {
angle = 0.0;
} else {
if (segment[1] > 0) {
angle = MY_LOCAL_PI * 0.5;
} else {
angle = MY_LOCAL_PI * 1.5;
}
}
} else {//
if (segment[0] > 0) {// first and fourth quater
if (segment[1] == 0.0) {
angle = 0.0;
} else {
if (segment[1] > 0) {
angle = atan(segment[1] / segment[0]);
} else {
angle = 2.0 * MY_LOCAL_PI + atan(segment[1] / segment[0]);
}
}
} else {// (segment[0] < 0)
if (segment[1] == 0.0) {
angle = MY_LOCAL_PI;
} else {
angle = MY_LOCAL_PI + atan(segment[1] / segment[0]);
}
}
}
return angle;
}
double LowestProjectionDistance(Vector3 &unitAxisDir,
_Polygon &leftPlg,
_Polygon &rightPlg) {
double lowestDist = 0.0;
double currentDist = 0.0;
if (leftPlg.vecPoints.empty() || rightPlg.vecPoints.empty()) {
std::cout << "NO POINTS IN ONE PLYGON" << std::endl;
}
// calculate the first projection distance
lowestDist = unitAxisDir * leftPlg.vecPoints[0];
// process the left polygon
for (unsigned int i = 1; i < leftPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
currentDist = unitAxisDir * leftPlg.vecPoints[i];
if (lowestDist > currentDist)
lowestDist = currentDist;
}
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
currentDist = unitAxisDir * rightPlg.vecPoints[i];
if (lowestDist > currentDist)
lowestDist = currentDist;
}
return lowestDist;
}
void ProjectingToPlane_LinkNumber(Vector3 &basePt, Vector3 &unitNormalDir, Vector3 &inPt, Vector3 &outPt) {
Vector3 segDir = inPt - basePt;
double projDist = (segDir * unitNormalDir);
outPt = inPt - projDist * unitNormalDir;
return;
}
void RotateAlongAxis_LinkNumber(double u, double v, double w,
double x, double y, double z,
double theta,
Vector3 &outRes) {
//rotation vector along the origin
//<u, v, w> is the rotation axis, a unit vector
// theta is the rotation angle
//<x, y, z> is the input vector,
double uvwxyz = (u * x + v * y + w * z);
double cos_a = cos(theta);
double sin_a = sin(theta);
outRes[0] = u * uvwxyz * (1 - cos_a) + x * cos_a + (-w * y + v * z) * sin_a;
outRes[1] = v * uvwxyz * (1 - cos_a) + y * cos_a + (w * x - u * z) * sin_a;
outRes[2] = w * uvwxyz * (1 - cos_a) + z * cos_a + (-v * x + u * y) * sin_a;
return;
}
void angle_between_projected_segment_and_X_axis_LinkNumber(double u, double v, double w,
double x, double y, double z,
Vector3 &outRes) {
double uvw = 1.0 / sqrt(u * u + v * v + w * w);
double uv = 1.0 / sqrt(u * u + v * v);
outRes[0] = ((u * w * x + w * v * y) * uv - (z) / uv) * uvw;
outRes[1] = (u * y - v * x) * uv;
outRes[2] = (u * x + v * y + w * z) * uvw;
}
void Rotation_to_make_uvw_become_z_axis(double u, double v, double w,
double x, double y, double z,
Vector3 &outRes) {
double uvw = 1.0 / sqrt(u * u + v * v + w * w);
double uv = 1.0 / sqrt(u * u + v * v);
outRes[0] = ((u * w * x + w * v * y) * uv - (z) / uv) * uvw;
outRes[1] = (u * y - v * x) * uv;
outRes[2] = (u * x + v * y + w * z) * uvw;
}
/**************************************/
/**************************************/
/**************************************/
void LinkNumberPairPolygon::FindingProjectionPlaneWithoutDegeneratePointProjecting_ANN() {//
const int nSegmentNumber = leftPlg.vecPoints.size() - 1 + rightPlg.vecPoints.size() - 1;
Vector3 segment;
vector<double> theta;
vector<double> phi;
// process the left polygon
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = leftPlg.vecPoints[i + 1] - leftPlg.vecPoints[i];
if (segment[2] < 0.0) {
for (int j = 0; j < 3; j++)
segment[j] = -segment[j];
}
theta.push_back(angle_between_projected_segment_and_X_axis_LinkNumber(segment));
//
if (norm2(segment) == 0.0)
phi.push_back(0.0);
else {
unitize(segment);
phi.push_back(MY_LOCAL_PI * 0.5 - acos(segment[2]));
}
}
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = rightPlg.vecPoints[i + 1] - rightPlg.vecPoints[i];
if (segment[2] < 0.0) {
for (int j = 0; j < 3; j++)
segment[j] = -segment[j];
}
theta.push_back(angle_between_projected_segment_and_X_axis_LinkNumber(segment));
//
if (norm2(segment) == 0.0)
phi.push_back(0.0);
else {
unitize(segment);
phi.push_back(MY_LOCAL_PI * 0.5 - acos(segment[2]));
}
}
//
//search the largest distance from these various existing points in the angle parametrization space
const double thetaRange = MY_LOCAL_PI * 2.0;
const double phiRange = MY_LOCAL_PI * 0.5;
const int sqrtSegNumber = int(sqrt(double(nSegmentNumber))) + 1;
const int thetaSample = 8 * sqrtSegNumber;
const int phiSample = sqrtSegNumber;
std::pair<double, double> maxAnglePair;
ANNSearch::GetMaxDistancePoint(theta, phi,
thetaRange, phiRange,
thetaSample, phiSample,
maxAnglePair.first, maxAnglePair.second);
//calculate the direction according to the theta and phi parameter
_planeNormal[0] = cos(maxAnglePair.second) * cos(maxAnglePair.first);
_planeNormal[1] = cos(maxAnglePair.second) * sin(maxAnglePair.first);
_planeNormal[2] = sin(maxAnglePair.second);
//unitize(_planeNormal);
// calculate the lowest projection along the normal axis for each point in current XYZ-coordinate system
_ptOnPlane = Vector3(0., 0., 0.);//_planeNormal * (LowestProjectionDistance(_planeNormal, leftPlg, rightPlg) - 2.0);
//
ProjectingToPlane(_ptOnPlane, _planeNormal, leftPlg.vecPoints[0], _xAxis);
ProjectingToPlane(_ptOnPlane, _planeNormal, leftPlg.vecPoints[1], _yAxis);
_xAxis -= _yAxis;
unitize(_xAxis);
// taking the cross product
_yAxis = _planeNormal ^ _xAxis;
unitize(_yAxis);
//
return;
}
//
void LinkNumberPairPolygon::OptimizeXYAxisMakeNoParaOrtho() {
//
// calculating the intersection angle delta
const int nSegmentNumber = leftPlg.vecPoints.size() - 1 + rightPlg.vecPoints.size() - 1;
std::vector<double> delta_angle(nSegmentNumber);
// process the left polygon
Vector3 segment;
double xCoord = 0.0;
double yCoord = 0.0;
double invPI = 1.0 / MY_LOCAL_PI;
double halfPI = 0.5 * MY_LOCAL_PI;
//
// process the left polygon
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = leftPlg.vecPoints[i + 1] - leftPlg.vecPoints[i];
xCoord = segment * _xAxis;
yCoord = segment * _yAxis;
if (xCoord == 0.0) {
delta_angle[i] = 0.0;
} else {
delta_angle[i] = MY_LOCAL_PI + atan(yCoord / xCoord);
delta_angle[i] = delta_angle[i] - ((int) (delta_angle[i] * 2.0 * invPI)) * halfPI;
}
}
int prevSize = leftPlg.vecPoints.size() - 1;
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = rightPlg.vecPoints[i + 1] - rightPlg.vecPoints[i];
xCoord = segment * _xAxis;
yCoord = segment * _yAxis;
if (xCoord == 0.0) {
delta_angle[i + prevSize] = 0.0;
} else {
delta_angle[i + prevSize] = MY_LOCAL_PI + atan(yCoord / xCoord);
delta_angle[i + prevSize] =
delta_angle[i + prevSize] - ((int) (delta_angle[i + prevSize] * 2.0 * invPI)) * halfPI;
}
}
//
//
delta_angle.push_back(0.0);
delta_angle.push_back(halfPI);
// sorting the angle
std::sort(delta_angle.begin(), delta_angle.end());
//scan the array to find the max-tempty interval
double maxIntervalBegin = 0.0;
double maxIntervalEnd = 0.0;
for (unsigned int i = 1; i < delta_angle.size(); i++) {
if (delta_angle[i] - delta_angle[i - 1] > maxIntervalEnd - maxIntervalBegin) {
maxIntervalBegin = delta_angle[i - 1];
maxIntervalEnd = delta_angle[i];
}
}
//
double rotAngle = (maxIntervalBegin + maxIntervalEnd) * 0.5;
//
RotateAlongAxis_LinkNumber(_planeNormal[0], _planeNormal[1], _planeNormal[2],
_yAxis[0], _yAxis[1], _yAxis[2],
rotAngle,
_yAxis);
//
RotateAlongAxis_LinkNumber(_planeNormal[0], _planeNormal[1], _planeNormal[2],
_xAxis[0], _xAxis[1], _xAxis[2],
rotAngle,
_xAxis);
//
return;
}
//
void LinkNumberPairPolygon::OptimizeNormalMakeNoOverlapping() {
//
// calculating the intersection angle delta
const int nSegmentNumber = leftPlg.vecPoints.size() - 1 + rightPlg.vecPoints.size() - 1;
std::vector<double> delta_angle(nSegmentNumber);
// process the left polygon
Vector3 segment;
double xCoord = 0.0;
double zCoord = 0.0;
double invPI = 1.0 / MY_LOCAL_PI;
double halfPI = 0.5 * MY_LOCAL_PI;
//
// process the left polygon
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = leftPlg.vecPoints[i + 1] - leftPlg.vecPoints[i];
xCoord = segment * _xAxis;
zCoord = segment * _planeNormal;
if (zCoord == 0.0) {
delta_angle[i] = halfPI;
} else {
delta_angle[i] = atan((-xCoord) / zCoord);
if (xCoord * zCoord > 0.0) {
delta_angle[i] = halfPI - delta_angle[i];
}
//delta_angle[i] = MY_LOCAL_PI + atan((-xCoord) / zCoord);
//delta_angle[i] = delta_angle[i] - ((int)(delta_angle[i] * invPI)) * MY_LOCAL_PI;
}
}
// process the right polygon
int prevSize = leftPlg.vecPoints.size() - 1;
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = rightPlg.vecPoints[i + 1] - rightPlg.vecPoints[i];
xCoord = segment * _xAxis;
zCoord = segment * _planeNormal;
if (zCoord == 0.0) {
delta_angle[i + prevSize] = halfPI;
} else {
delta_angle[i] = atan((-xCoord) / zCoord);
if (xCoord * zCoord > 0.0) {
delta_angle[i] = halfPI - delta_angle[i];
}
//delta_angle[i + prevSize] = MY_LOCAL_PI + atan((-xCoord) / zCoord);
//delta_angle[i + prevSize] = delta_angle[i] - ((int)(delta_angle[i + prevSize] * invPI)) * MY_LOCAL_PI;
}
}
//
//
delta_angle.push_back(0.0);
delta_angle.push_back(MY_LOCAL_PI);
// sorting the angle
std::sort(delta_angle.begin(), delta_angle.end());
//scan the array to find the max-tempty interval
double maxIntervalBegin = 0.0;
double maxIntervalEnd = 0.0;
for (unsigned int i = 1; i < delta_angle.size(); i++) {
if (delta_angle[i] - delta_angle[i - 1] > maxIntervalEnd - maxIntervalBegin) {
maxIntervalBegin = delta_angle[i - 1];
maxIntervalEnd = delta_angle[i];
}
}
//
double rotAngle = (maxIntervalBegin + maxIntervalEnd) * 0.5;
rotAngle = rotAngle - halfPI;
//
RotateAlongAxis_LinkNumber(_yAxis[0], _yAxis[1], _yAxis[2],
_planeNormal[0], _planeNormal[1], _planeNormal[2],
rotAngle,
_planeNormal);
//
RotateAlongAxis_LinkNumber(_yAxis[0], _yAxis[1], _yAxis[2],
_xAxis[0], _xAxis[1], _xAxis[2],
rotAngle,
_xAxis);
//
// rotate all points
//_planeNormal[0] = 0.0; _planeNormal[1] = 0.0; _planeNormal[2] = 1.0;
//_xAxis[0] = 1.0; _xAxis[1] = 1.0; _xAxis[2] = 0.0;
//_yAxis[0] = -1.0; _yAxis[1] = 1.0; _yAxis[2] = 0.0;
Vector3 tempPt;
for (unsigned int i = 0;
i < leftPlg.vecPoints.size() - 1; i++) {// rotate the points to make the new direction become Z-axis
tempPt[0] = leftPlg.vecPoints[i] * _xAxis;
tempPt[1] = leftPlg.vecPoints[i] * _yAxis;
tempPt[2] = leftPlg.vecPoints[i] * _planeNormal;
//
leftPlg.vecPoints[i] = tempPt;
}
leftPlg.vecPoints[leftPlg.vecPoints.size() - 1] = leftPlg.vecPoints[0];
// process the right polygon
for (unsigned int i = 0;
i < rightPlg.vecPoints.size() - 1; i++) {// rotate the points to make the new direction become Z-axis
tempPt[0] = rightPlg.vecPoints[i] * _xAxis;
tempPt[1] = rightPlg.vecPoints[i] * _yAxis;
tempPt[2] = rightPlg.vecPoints[i] * _planeNormal;
//
rightPlg.vecPoints[i] = tempPt;
}
rightPlg.vecPoints[rightPlg.vecPoints.size() - 1] = rightPlg.vecPoints[0];
return;
}
/*****************************/
void LinkNumberPairPolygon::FindingProjectionPlaneWithoutDegeneratePointProjecting_2(int ___int___) {//
Vector3 segment;
std::set<float> theta;
std::set<float> phi;
const int nSegmentNumber = leftPlg.vecPoints.size() - 1 + rightPlg.vecPoints.size() - 1;
// process the left polygon
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = leftPlg.vecPoints[i + 1] - leftPlg.vecPoints[i];
unitize(segment);
//
theta.insert(angle_between_projected_segment_and_X_axis_LinkNumber_simple(segment));
//
{
if (segment[2] > 0)
phi.insert(float(acos(segment[2])));
else {
phi.insert(float(acos(segment[2]) - MY_LOCAL_PI * 0.5));
}
}
}
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = rightPlg.vecPoints[i + 1] - rightPlg.vecPoints[i];
unitize(segment);
//
{
if (segment[2] > 0)
phi.insert(float(acos(segment[2])));
else {
phi.insert(float(acos(segment[2]) - MY_LOCAL_PI * 0.5));
}
}
}
std::pair<float, float> maxAnglePair;
float max_var_val = 0.0;
float max_cur_val = 0.0;
float max_pre_val = 0.0;
float pre_val = 0.0;
float cur_val = 0.0;
std::set<float>::iterator sIter;
sIter = theta.begin();
pre_val = *sIter;
for (sIter++; sIter != theta.end(); sIter++) {
cur_val = *sIter;
if (cur_val - pre_val > max_var_val) {
max_var_val = cur_val - pre_val;
max_cur_val = cur_val;
max_pre_val = pre_val;
}
pre_val = cur_val;
}
//
maxAnglePair.first = 0.5 * (max_cur_val + max_pre_val);
//
max_var_val = 0.0;
sIter = phi.begin();
pre_val = *sIter;
for (sIter++; sIter != phi.end(); sIter++) {
cur_val = *sIter;
if (cur_val - pre_val > max_var_val) {
max_var_val = cur_val - pre_val;
max_cur_val = cur_val;
max_pre_val = pre_val;
}
pre_val = cur_val;
}
maxAnglePair.second = 0.5 * (max_cur_val + max_pre_val);
//search the largest distance from these various existing points in the angle parametrization space
//std::cout << "max angle : " << maxAnglePair.first << " " << maxAnglePair.second << std::endl;
//calculate the direction according to the theta and phi parameter
_planeNormal[0] = cos(maxAnglePair.first) * sin(maxAnglePair.second);
_planeNormal[1] = sin(maxAnglePair.first) * sin(maxAnglePair.second);
_planeNormal[2] = cos(maxAnglePair.second);
//unitize(_planeNormal);
// calculate the lowest projection along the normal axis for each point in current XYZ-coordinate system
_ptOnPlane = Vector3(0., 0., 0.);//_planeNormal * (LowestProjectionDistance(_planeNormal, leftPlg, rightPlg) - 2.0);
//
//
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
Rotation_to_make_uvw_become_z_axis(_planeNormal[0], _planeNormal[1], _planeNormal[2],
leftPlg.vecPoints[i][0], leftPlg.vecPoints[i][1], leftPlg.vecPoints[i][2],
leftPlg.vecPoints[i]);
}
leftPlg.vecPoints.back() = leftPlg.vecPoints.front();
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
Rotation_to_make_uvw_become_z_axis(_planeNormal[0], _planeNormal[1], _planeNormal[2],
rightPlg.vecPoints[i][0], rightPlg.vecPoints[i][1], rightPlg.vecPoints[i][2],
rightPlg.vecPoints[i]);
}
rightPlg.vecPoints.back() = rightPlg.vecPoints.front();
//
/*Rotation_to_make_uvw_become_z_axis(_planeNormal[0], _planeNormal[1], _planeNormal[2],
_planeNormal[0], _planeNormal[1], _planeNormal[2],
_planeNormal);
std::cout << _planeNormal[0] << " " << _planeNormal[1] << " " << _planeNormal[2] << " "<< std::endl;*/
_planeNormal[0] = 0.;
_planeNormal[1] = 0.;
_planeNormal[2] = 1.;
_xAxis = Vector3(1., 0., 0.);
_yAxis = Vector3(0., 1., 0.);
//
return;
}
void LinkNumberPairPolygon::FindingProjectionPlaneWithoutDegeneratePointProjecting() {//
const int nSegmentNumber = leftPlg.vecPoints.size() - 1 + rightPlg.vecPoints.size() - 1;
Vector3 segment;
vector<double> theta;
vector<double> phi;
// process the left polygon
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = leftPlg.vecPoints[i + 1] - leftPlg.vecPoints[i];
theta.push_back(angle_between_projected_segment_and_X_axis_LinkNumber(segment));
//
if (norm2(segment) == 0.0)
phi.push_back(0.0);
else {
unitize(segment);
phi.push_back(MY_LOCAL_PI * 0.5 - std::min(acos(segment * Vector3(0.0, 0.0, 1.0)),
acos(segment * Vector3(0.0, 0.0, -1.0))));
}
}
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = rightPlg.vecPoints[i + 1] - rightPlg.vecPoints[i];
theta.push_back(angle_between_projected_segment_and_X_axis_LinkNumber(segment));
//
if (norm2(segment) == 0.0)
phi.push_back(0.0);
else {
unitize(segment);
phi.push_back(MY_LOCAL_PI * 0.5 - std::min(acos(segment * Vector3(0.0, 0.0, 1.0)),
acos(segment * Vector3(0.0, 0.0, -1.0))));
}
}
//search the largest distance from these various existing points in the angle parametrization space
const int sqrtSegNumber = int(sqrt(double(nSegmentNumber))) + 1;
std::cout << "sqrtSegNumber " << sqrtSegNumber << std::endl;
//
double delta_angle = MY_LOCAL_PI / (4.0 * sqrtSegNumber);
double max_angle_pair_dist = 0.0;
std::pair<double, double> maxAnglePair;
std::pair<double, double> anglePair;
anglePair.first = 0.0;
anglePair.second = 0.0;
//
maxAnglePair = anglePair;
//
for (int i = 0; i < 8 * sqrtSegNumber; i++) {
anglePair.first += delta_angle;
anglePair.second = 0.0;
for (int j = 0; j < 2 * sqrtSegNumber; j++) {
anglePair.second += delta_angle;
//
double max_dist_to_current_angle_pair = 0.0;
double current_dist = 0.0;
for (int k = 0; k < nSegmentNumber; k++) {
current_dist = std::min((anglePair.first - theta[k]) * (anglePair.first - theta[k]) +
(anglePair.second - phi[k]) * (anglePair.second - phi[k]),
(anglePair.first - theta[k] - 2 * MY_LOCAL_PI) *
(anglePair.first - theta[k] - 2 * MY_LOCAL_PI) +
(anglePair.second - phi[k]) * (anglePair.second - phi[k]));
if (current_dist > max_dist_to_current_angle_pair) {
max_dist_to_current_angle_pair = current_dist;
}
}
//
if (max_dist_to_current_angle_pair > max_angle_pair_dist) {
maxAnglePair = anglePair;
max_angle_pair_dist = max_dist_to_current_angle_pair;
}
}
}//
//calculate the direction according to the theta and phi parameter
_planeNormal[0] = cos(maxAnglePair.first);
_planeNormal[1] = sin(maxAnglePair.first);
_planeNormal[2] = cos(maxAnglePair.second);
unitize(_planeNormal);
// calculate the lowest projection along the normal axis for each point in current XYZ-coordinate system
_ptOnPlane = Vector3(0., 0., 0.);//_planeNormal * (LowestProjectionDistance(_planeNormal, leftPlg, rightPlg) - 2.0);
//
//
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
Rotation_to_make_uvw_become_z_axis(_planeNormal[0], _planeNormal[1], _planeNormal[2],
leftPlg.vecPoints[i][0], leftPlg.vecPoints[i][1], leftPlg.vecPoints[i][2],
leftPlg.vecPoints[i]);
}
leftPlg.vecPoints.back() = leftPlg.vecPoints.front();
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
Rotation_to_make_uvw_become_z_axis(_planeNormal[0], _planeNormal[1], _planeNormal[2],
rightPlg.vecPoints[i][0], rightPlg.vecPoints[i][1], rightPlg.vecPoints[i][2],
rightPlg.vecPoints[i]);
}
rightPlg.vecPoints.back() = rightPlg.vecPoints.front();
//
Rotation_to_make_uvw_become_z_axis(_planeNormal[0], _planeNormal[1], _planeNormal[2],
_planeNormal[0], _planeNormal[1], _planeNormal[2],
_planeNormal);
std::cout << _planeNormal[0] << " " << _planeNormal[1] << " " << _planeNormal[2] << " " << std::endl;
_planeNormal[0] = 0.;
_planeNormal[1] = 0.;
_planeNormal[2] = 1.;
_xAxis = Vector3(1., 0., 0.);
_yAxis = Vector3(0., 1., 0.);
return;
}
void LinkNumberPairPolygon::AvoidParallelOrthogonalToXYAxis() {
// preq: all points are rotated such that the plane normal is Z-axis
// the projection is only to take X, Y coordinate
//specify the XY axis in the projection plane first
if (leftPlg.vecPoints.size() < 2) {
std::cout << "NO ENOUGH POINTS" << std::endl;
return;
}
_xAxis = Vector3(1., 0., 0.);
_yAxis = Vector3(0., 1., 0.);
//
// computing the angle between the projected segment and its closest axis
Vector3 orgPt, dstPt;
std::vector<double> min_angle_to_axis;
// process the left polygon
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {
dstPt = leftPlg.vecPoints[i] - leftPlg.vecPoints[i + 1];
dstPt[2] = 0.0;
//
unitize(dstPt);
//
double cos_angle = acos(dstPt[0]);
//
min_angle_to_axis.push_back(cos_angle);
//
if (cos_angle > MY_LOCAL_PI * 0.5) {
min_angle_to_axis.push_back(cos_angle - MY_LOCAL_PI * 0.5);
} else {
min_angle_to_axis.push_back(cos_angle + MY_LOCAL_PI * 0.5);
}
}
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
dstPt = rightPlg.vecPoints[i] - rightPlg.vecPoints[i + 1];
dstPt[2] = 0.0;
//
unitize(dstPt);
//
double cos_angle = acos(dstPt * _xAxis);
//
min_angle_to_axis.push_back(cos_angle);
//
if (cos_angle > MY_LOCAL_PI * 0.5) {
min_angle_to_axis.push_back(cos_angle - MY_LOCAL_PI * 0.5);
} else {
min_angle_to_axis.push_back(cos_angle + MY_LOCAL_PI * 0.5);
}
}
//
min_angle_to_axis.push_back(0.0);
//min_angle_to_axis.push_back( MY_LOCAL_PI * 0.5);
min_angle_to_axis.push_back(MY_LOCAL_PI);
// sorting the angle
std::sort(min_angle_to_axis.begin(), min_angle_to_axis.end());
//scan the array to find the max-tempty interval
double maxIntervalBegin = 0.0;
double maxIntervalEnd = 0.0;
for (unsigned int i = 1; i < min_angle_to_axis.size(); i++) {
if (min_angle_to_axis[i] - min_angle_to_axis[i - 1] > maxIntervalEnd - maxIntervalBegin) {
maxIntervalBegin = min_angle_to_axis[i - 1];
maxIntervalEnd = min_angle_to_axis[i];
}
}
//
//
double rotAngle = -(maxIntervalBegin + maxIntervalEnd) * 0.5;
//
//std::cout << "rotAngle " << rotAngle << std::endl;
/*
//specify the XY axis in the projection plane first
if (leftPlg.vecPoints.size() < 2)
{
std::cout << "NO ENOUGH POINTS" << std::endl;
return;
}
ProjectingToPlane_LinkNumber(_ptOnPlane, _planeNormal, leftPlg.vecPoints[1], _xAxis);
ProjectingToPlane_LinkNumber(_ptOnPlane, _planeNormal, leftPlg.vecPoints[0], _yAxis);
_xAxis -= _yAxis;
unitize(_xAxis);
// taking the cross product
_yAxis = _xAxis^_planeNormal;
//
// computing the angle between the projected segment and its closest axis
Vector3 orgPt, dstPt;
std::vector<double> min_angle_to_axis;
// process the left polygon
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++)
{
ProjectingToPlane_LinkNumber(_ptOnPlane, _planeNormal,
leftPlg.vecPoints[i], orgPt);
ProjectingToPlane_LinkNumber(_ptOnPlane, _planeNormal,
leftPlg.vecPoints[i+1], dstPt);
dstPt -= orgPt;
//
unitize(dstPt);
//
double cos_angle = acos(dstPt * _xAxis);
min_angle_to_axis.push_back(cos_angle);
if (cos_angle > MY_LOCAL_PI * 0.5)
{
min_angle_to_axis.push_back(cos_angle - MY_LOCAL_PI * 0.5);
}
else
{
min_angle_to_axis.push_back(cos_angle - MY_LOCAL_PI * 0.5);
}
//if (abs(dstPt[0]) < 1e-10 || abs(dstPt[1]) < 1e-10)
//{
// min_angle_to_axis.push_back(0.0);
//}
//else
//{
// double initAngle = atan(dstPt[1] / dstPt[0]);
// initAngle += MY_LOCAL_PI;
// if (initAngle >= MY_LOCAL_PI)
// initAngle -= MY_LOCAL_PI;
// else
// {
// if (initAngle >= MY_LOCAL_PI * 0.5)
// {
// initAngle -= 0.5 * MY_LOCAL_PI;
// }
// }
// min_angle_to_axis.push_back(initAngle);
//}
//
//min_angle_to_axis.push_back(std::max( std::max(dstPt * _xAxis, dstPt * _yAxis),
// std::max(dstPt * (-_xAxis), dstPt * (-_yAxis)) )
// );
}
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++)
{// project the segment onto the XY-plane
ProjectingToPlane_LinkNumber(_ptOnPlane, _planeNormal,
rightPlg.vecPoints[i], orgPt);
ProjectingToPlane_LinkNumber(_ptOnPlane, _planeNormal,
rightPlg.vecPoints[i+1], dstPt);
dstPt -= orgPt;
//
unitize(dstPt);
//
double cos_angle = acos(dstPt * _xAxis);
min_angle_to_axis.push_back(cos_angle);
if (cos_angle > MY_LOCAL_PI * 0.5)
{
min_angle_to_axis.push_back(cos_angle - MY_LOCAL_PI * 0.5);
}
else
{
min_angle_to_axis.push_back(cos_angle - MY_LOCAL_PI * 0.5);
}
//if (abs(dstPt[0]) < 1e-10 || abs(dstPt[1]) < 1e-10)
//{
// min_angle_to_axis.push_back(0.0);
//}
//else
//{
// double initAngle = atan(dstPt[1] / dstPt[0]);
// initAngle += MY_LOCAL_PI;
// if (initAngle >= MY_LOCAL_PI)
// initAngle -= MY_LOCAL_PI;
// else
// {
// if (initAngle >= MY_LOCAL_PI * 0.5)
// {
// initAngle -= 0.5 * MY_LOCAL_PI;
// }
// }
// min_angle_to_axis.push_back(initAngle);
//}
//min_angle_to_axis.push_back(std::max( std::max(dstPt * _xAxis, dstPt * _yAxis),
// std::max(dstPt * (-_xAxis), dstPt * (-_yAxis)) )
// );
}
//
min_angle_to_axis.push_back(0.0);
min_angle_to_axis.push_back(MY_LOCAL_PI);
// sorting the angle
std::sort(min_angle_to_axis.begin(), min_angle_to_axis.end());
//scan the array to find the max-tempty interval
double maxIntervalBegin = 0.0;
double maxIntervalEnd = 0.0;
for (unsigned int i = 1; i < min_angle_to_axis.size(); i++)
{
if (min_angle_to_axis[i] - min_angle_to_axis[i-1] > maxIntervalEnd - maxIntervalBegin)
{
maxIntervalBegin = min_angle_to_axis[i - 1];
maxIntervalEnd = min_angle_to_axis[i];
}
}
//
double rotAngle = (maxIntervalBegin + maxIntervalEnd) * 0.5;
std::cout << "rotAngle " << rotAngle << std::endl;
*/
// rotate all points
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {
RotateAlongAxis_LinkNumber(_planeNormal[0], _planeNormal[1], _planeNormal[2],
leftPlg.vecPoints[i][0], leftPlg.vecPoints[i][1], leftPlg.vecPoints[i][2],
rotAngle,
leftPlg.vecPoints[i]);
}
leftPlg.vecPoints[leftPlg.vecPoints.size() - 1] = leftPlg.vecPoints[0];
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
RotateAlongAxis_LinkNumber(_planeNormal[0], _planeNormal[1], _planeNormal[2],
rightPlg.vecPoints[i][0], rightPlg.vecPoints[i][1], rightPlg.vecPoints[i][2],
rotAngle,
rightPlg.vecPoints[i]);
}
rightPlg.vecPoints[rightPlg.vecPoints.size() - 1] = rightPlg.vecPoints[0];
//std::cout << _xAxis * _yAxis << std::endl;
/**/
return;
}
void LinkNumberPairPolygon::AvoidOverlapping() {
//
// calculating the intersection angle delta
std::vector<double> delta_angle;
// process the left polygon
Vector3 segment;
Vector3 intersectLineVec;
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++) {
segment = leftPlg.vecPoints[i + 1] - leftPlg.vecPoints[i];
unitize(segment);
if (abs(segment[2]) < 1e-10) {
delta_angle.push_back(0.0);
} else {
delta_angle.push_back(atan(-segment[0] / segment[2]));
}
}
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++) {// project the segment onto the XY-plane
segment = rightPlg.vecPoints[i + 1] - rightPlg.vecPoints[i];
unitize(segment);
if (abs(segment[2]) < 1e-10) {
delta_angle.push_back(0.0);
} else {
delta_angle.push_back(atan(-segment[0] / segment[2]));
}
}
//
//
delta_angle.push_back(MY_LOCAL_PI * 0.5);
delta_angle.push_back(MY_LOCAL_PI * (-0.5));
// sorting the angle
std::sort(delta_angle.begin(), delta_angle.end());
//scan the array to find the max-tempty interval
double maxIntervalBegin = 0.0;
double maxIntervalEnd = 0.0;
for (unsigned int i = 1; i < delta_angle.size(); i++) {
if (delta_angle[i] - delta_angle[i - 1] > maxIntervalEnd - maxIntervalBegin) {
maxIntervalBegin = delta_angle[i - 1];
maxIntervalEnd = delta_angle[i];
}
}
//
double rotAngle = (maxIntervalBegin + maxIntervalEnd) * 0.5;
//
if (rotAngle < 0.0) {
rotAngle = -rotAngle;
} else {//
rotAngle = 0.5 * MY_LOCAL_PI - rotAngle;
rotAngle = -rotAngle;
}
// rotate all points
for (unsigned int i = 0;
i < leftPlg.vecPoints.size() - 1; i++) {// rotate the points to make the new direction become Z-axis
RotateAlongAxis_LinkNumber(_yAxis[0], _yAxis[1], _yAxis[2],
leftPlg.vecPoints[i][0], leftPlg.vecPoints[i][1], leftPlg.vecPoints[i][2],
rotAngle,
leftPlg.vecPoints[i]);
}
leftPlg.vecPoints[leftPlg.vecPoints.size() - 1] = leftPlg.vecPoints[0];
// process the right polygon
for (unsigned int i = 0;
i < rightPlg.vecPoints.size() - 1; i++) {// rotate the points to make the new direction become Z-axis
RotateAlongAxis_LinkNumber(_yAxis[0], _yAxis[1], _yAxis[2],
rightPlg.vecPoints[i][0], rightPlg.vecPoints[i][1], rightPlg.vecPoints[i][2],
rotAngle,
rightPlg.vecPoints[i]);
}
rightPlg.vecPoints[rightPlg.vecPoints.size() - 1] = rightPlg.vecPoints[0];
//
/*
// calculating the intersection angle delta
std::vector<double> delta_angle;
// process the left polygon
Vector3 segment;
Vector3 intersectLineVec;
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++)
{
segment = leftPlg.vecPoints[i + 1] - leftPlg.vecPoints[i];
unitize(segment);
//
if (abs(segment[2]) < 1e-10)
{
delta_angle.push_back(0.0);
}
else
{
delta_angle.push_back(atan(-segment[0]/segment[2]));
//double denominator = segment[0] * _xAxis[2] - segment[2] * _xAxis[0];
//denominator = 1.0 / denominator;
//intersectLineVec[0] = denominator * (segment[1] * _xAxis[2] - segment[2] * _xAxis[1]);
//intersectLineVec[2] = denominator * (segment[1] * _xAxis[0] - segment[0] * _xAxis[1]);
//intersectLineVec[1] = -1;
}
//
//unitize(intersectLineVec);
//
//delta_angle.push_back(acos(_yAxis * intersectLineVec));
//delta_angle.push_back(acos(_yAxis * (-intersectLineVec)));
}
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++)
{// project the segment onto the XY-plane
segment = rightPlg.vecPoints[i + 1] - rightPlg.vecPoints[i];
unitize(segment);
// set up the intersection directions
if (abs(segment[2]) < 1e-10)
{
delta_angle.push_back(0.0);
}
else
{
delta_angle.push_back(atan(-segment[0]/segment[2]));
//double denominator = segment[0] * _xAxis[2] - segment[2] * _xAxis[0];
//denominator = 1.0 / denominator;
//intersectLineVec[0] = denominator * (segment[1] * _xAxis[2] - segment[2] * _xAxis[1]);
//intersectLineVec[2] = denominator * (segment[1] * _xAxis[0] - segment[0] * _xAxis[1]);
//intersectLineVec[1] = -1;
}
//double denominator = segment[0] * _xAxis[2] - segment[2] * _xAxis[0];
//denominator = 1.0 / denominator;
//intersectLineVec[0] = denominator * (segment[1] * _xAxis[2] - segment[2] * _xAxis[1]);
//intersectLineVec[2] = denominator * (segment[1] * _xAxis[0] - segment[0] * _xAxis[1]);
//intersectLineVec[1] = -1;
////
//unitize(intersectLineVec);
////
//delta_angle.push_back(acos(_yAxis * intersectLineVec));
//delta_angle.push_back(acos(_yAxis * (-intersectLineVec)));
}
//
//
//delta_angle.push_back(0.0);
//delta_angle.push_back(MY_LOCAL_PI);
delta_angle.push_back(MY_LOCAL_PI * (-0.5));
delta_angle.push_back(MY_LOCAL_PI * 0.5);
// sorting the angle
std::sort(delta_angle.begin(), delta_angle.end());
//scan the array to find the max-tempty interval
double maxIntervalBegin = 0.0;
double maxIntervalEnd = 0.0;
for (unsigned int i = 1; i < delta_angle.size(); i++)
{
if (delta_angle[i] - delta_angle[i-1] > maxIntervalEnd - maxIntervalBegin)
{
maxIntervalBegin = delta_angle[i - 1];
maxIntervalEnd = delta_angle[i];
}
}
//
double rotAngle = (maxIntervalBegin + maxIntervalEnd) * 0.5;
//
rotAngle = 0.5 * MY_LOCAL_PI - rotAngle ;
// rotate all points
for (unsigned int i = 0; i < leftPlg.vecPoints.size() - 1; i++)
{
RotateAlongAxis_LinkNumber(_yAxis[0], _yAxis[1], _yAxis[2],
leftPlg.vecPoints[i][0], leftPlg.vecPoints[i][1], leftPlg.vecPoints[i][2],
rotAngle,
leftPlg.vecPoints[i]);
angle_between_projected_segment_and_X_axis_LinkNumber(_planeNormal[0], _planeNormal[1], _planeNormal[2],
leftPlg.vecPoints[i][0], leftPlg.vecPoints[i][1], leftPlg.vecPoints[i][2],
leftPlg.vecPoints[i]);
}
leftPlg.vecPoints[leftPlg.vecPoints.size() - 1] = leftPlg.vecPoints[0];
// process the right polygon
for (unsigned int i = 0; i < rightPlg.vecPoints.size() - 1; i++)
{// project the segment onto the XY-plane
RotateAlongAxis_LinkNumber(_yAxis[0], _yAxis[1], _yAxis[2],
rightPlg.vecPoints[i][0], rightPlg.vecPoints[i][1], rightPlg.vecPoints[i][2],
rotAngle,
rightPlg.vecPoints[i]);
angle_between_projected_segment_and_X_axis_LinkNumber (_planeNormal[0], _planeNormal[1], _planeNormal[2],
rightPlg.vecPoints[i][0], rightPlg.vecPoints[i][1], rightPlg.vecPoints[i][2],
rightPlg.vecPoints[i]);
}
rightPlg.vecPoints[rightPlg.vecPoints.size() - 1] = rightPlg.vecPoints[0];
//std::cout << _xAxis * _yAxis << std::endl;
angle_between_projected_segment_and_X_axis_LinkNumber(_planeNormal[0], _planeNormal[1], _planeNormal[2],
_yAxis[0], _yAxis[1], _yAxis[2],
_yAxis);
angle_between_projected_segment_and_X_axis_LinkNumber(_planeNormal[0], _planeNormal[1], _planeNormal[2],
_xAxis[0], _xAxis[1], _xAxis[2],