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// -*- C++ -*-
// -------------------------------------------------------------------
// MAdLib - Copyright (C) 2008-2009 Universite catholique de Louvain
//
// See the Copyright.txt and License.txt files for license information.
// You should have received a copy of these files along with MAdLib.
// If not, see <http://www.madlib.be/license/>
//
// Please report all bugs and problems to <contrib@madlib.be>
//
// Authors: Gaetan Compere, Jean-Francois Remacle
// -------------------------------------------------------------------
#include "MathUtils.h"
#include "MAdMessage.h"
#include "MAdDefines.h"
#include <stdio.h>
#include <math.h>
#ifdef _HAVE_GSL_
#include <gsl/gsl_math.h>
#include <gsl/gsl_eigen.h>
#endif
namespace MAd {
// -------------------------------------------------------------------
// VECTORS
// -------------------------------------------------------------------
// -------------------------------------------------------------------
void diffVec(const double v1[3], const double v0[3], double v01[3])
{
v01[0] = v1[0] - v0[0];
v01[1] = v1[1] - v0[1];
v01[2] = v1[2] - v0[2];
}
// -------------------------------------------------------------------
double dotProd(const double v1[3], const double v2[3])
{
return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}
// -------------------------------------------------------------------
void crossProd(const double v1[3], const double v2[3], double cp[3])
{
cp[0] = v1[1]*v2[2] - v1[2]*v2[1];
cp[1] = v1[2]*v2[0] - v1[0]*v2[2];
cp[2] = v1[0]*v2[1] - v1[1]*v2[0];
}
// -------------------------------------------------------------------
void normalizeVec(const double v[3], double nv[3])
{
double lSq = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
if ( lSq <= MAdTOLSQ ) {
MAdMsgSgl::instance().warning(__LINE__,__FILE__,
"Normalization called for a zero vector");
nv[0] = v[0];
nv[1] = v[1];
nv[2] = v[2];
}
double invNorm = 1. / sqrt( lSq );
nv[0] = v[0] * invNorm ;
nv[1] = v[1] * invNorm ;
nv[2] = v[2] * invNorm ;
}
// -------------------------------------------------------------------
void printVec(const double vec[3], const char * name)
{
printf("\nPrinting vector %s\n",name);
for (int i=0; i<3; i++) printf(" %g",vec[i]);
printf("\n\n");
}
// -------------------------------------------------------------------
bool isNanVec (const double vec[3])
{
if ( isnan(vec[0]) || isnan(vec[1]) || isnan(vec[2]) ) return true;
return false;
}
// -------------------------------------------------------------------
// -------------------------------------------------------------------
// MATRICES
// -------------------------------------------------------------------
// -------------------------------------------------------------------
void transpose(double mat[3][3])
{
double tmp;
tmp = mat[0][1]; mat[0][1] = mat[1][0]; mat[1][0] = tmp;
tmp = mat[0][2]; mat[0][2] = mat[2][0]; mat[2][0] = tmp;
tmp = mat[1][2]; mat[1][2] = mat[2][1]; mat[2][1] = tmp;
}
// -------------------------------------------------------------------
void transpMat(const double mat[3][3], double matT[3][3])
{
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
matT[i][j] = mat[j][i];
}
// -------------------------------------------------------------------
double detMat(const double mat[3][3])
{
return (mat[0][0] * (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1]) -
mat[0][1] * (mat[1][0] * mat[2][2] - mat[1][2] * mat[2][0]) +
mat[0][2] * (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]));
}
// -------------------------------------------------------------------
double traceMat(const double mat[3][3])
{
return mat[0][0] + mat[1][1] + mat[2][2];
}
// -------------------------------------------------------------------
double traceMatMat(const double mat[3][3])
{
double a00 = mat[0][0] * mat[0][0] + mat[1][0] * mat[0][1] + mat[2][0] * mat[0][2];
double a11 = mat[1][0] * mat[0][1] + mat[1][1] * mat[1][1] + mat[1][2] * mat[2][1];
double a22 = mat[2][0] * mat[0][2] + mat[2][1] * mat[1][2] + mat[2][2] * mat[2][2];
return a00 + a11 + a22;
}
// -------------------------------------------------------------------
void vecMat(const double vec[3], const double mat[3][3], double res[3])
{
res[0] = mat[0][0] * vec[0] + mat[1][0] * vec[1] + mat[2][0] * vec[2];
res[1] = mat[0][1] * vec[0] + mat[1][1] * vec[1] + mat[2][1] * vec[2];
res[2] = mat[0][2] * vec[0] + mat[1][2] * vec[1] + mat[2][2] * vec[2];
}
// -------------------------------------------------------------------
void matVec(const double mat[3][3], const double vec[3], double res[3])
{
res[0] = mat[0][0] * vec[0] + mat[0][1] * vec[1] + mat[0][2] * vec[2];
res[1] = mat[1][0] * vec[0] + mat[1][1] * vec[1] + mat[1][2] * vec[2];
res[2] = mat[2][0] * vec[0] + mat[2][1] * vec[1] + mat[2][2] * vec[2];
}
// -------------------------------------------------------------------
void matMat(const double mat1[3][3], const double mat2[3][3], double res[3][3])
{
res[0][0] = mat1[0][0] * mat2[0][0] + mat1[0][1] * mat2[1][0] + mat1[0][2] * mat2[2][0];
res[0][1] = mat1[0][0] * mat2[0][1] + mat1[0][1] * mat2[1][1] + mat1[0][2] * mat2[2][1];
res[0][2] = mat1[0][0] * mat2[0][2] + mat1[0][1] * mat2[1][2] + mat1[0][2] * mat2[2][2];
res[1][0] = mat1[1][0] * mat2[0][0] + mat1[1][1] * mat2[1][0] + mat1[1][2] * mat2[2][0];
res[1][1] = mat1[1][0] * mat2[0][1] + mat1[1][1] * mat2[1][1] + mat1[1][2] * mat2[2][1];
res[1][2] = mat1[1][0] * mat2[0][2] + mat1[1][1] * mat2[1][2] + mat1[1][2] * mat2[2][2];
res[2][0] = mat1[2][0] * mat2[0][0] + mat1[2][1] * mat2[1][0] + mat1[2][2] * mat2[2][0];
res[2][1] = mat1[2][0] * mat2[0][1] + mat1[2][1] * mat2[1][1] + mat1[2][2] * mat2[2][1];
res[2][2] = mat1[2][0] * mat2[0][2] + mat1[2][1] * mat2[1][2] + mat1[2][2] * mat2[2][2];
}
// -------------------------------------------------------------------
double vecMatVec(const double mat[3][3], const double vec[3])
{
double tmp[3];
matVec(mat,vec,tmp);
return dotProd(vec,tmp);
}
// -------------------------------------------------------------------
double inverseMat(const double mat[3][3], double inv[3][3])
{
double det = detMat(mat);
if(det) {
double idet = 1. / det;
inv[0][0] = (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1]) * idet;
inv[1][0] = -(mat[1][0] * mat[2][2] - mat[1][2] * mat[2][0]) * idet;
inv[2][0] = (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]) * idet;
inv[0][1] = -(mat[0][1] * mat[2][2] - mat[0][2] * mat[2][1]) * idet;
inv[1][1] = (mat[0][0] * mat[2][2] - mat[0][2] * mat[2][0]) * idet;
inv[2][1] = -(mat[0][0] * mat[2][1] - mat[0][1] * mat[2][0]) * idet;
inv[0][2] = (mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1]) * idet;
inv[1][2] = -(mat[0][0] * mat[1][2] - mat[0][2] * mat[1][0]) * idet;
inv[2][2] = (mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0]) * idet;
}
else{
MAdMsgSgl::instance().warning(__LINE__,__FILE__,"Singular matrix");
for(int i=0; i<3; i++) for(int j=0; j<3; j++) inv[i][j] = 0.;
}
return det;
}
// -------------------------------------------------------------------
double inverseMat22 (const double mat[2][2], double inv[2][2])
{
double det = mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0];
if (det) {
double idet = 1. / det;
inv[0][0] = idet * mat[1][1];
inv[0][1] = -idet * mat[0][1];
inv[1][0] = -idet * mat[1][0];
inv[1][1] = idet * mat[0][0];
}
else{
MAdMsgSgl::instance().warning(__LINE__,__FILE__,"Singular matrix");
for(int i=0; i<2; i++) for(int j=0; j<2; j++) inv[i][j] = 0.;
}
return det;
}
// -------------------------------------------------------------------
double invertMat(double mat[3][3])
{
double inv[3][3];
double det = inverseMat(mat,inv);
for (int i=0; i<3; i++) {
for (int j=0; j<3; j++) {
mat[i][j] = inv[i][j];
}
}
return det;
}
// -------------------------------------------------------------------
bool system(const double A[3][3], const double b[3], double res[3], double * det)
{
*det = detMat(A);
if(*det == 0.0) {
res[0] = res[1] = res[2] = 0.0;
return false;
}
res[0] = b[0] * (A[1][1] * A[2][2] - A[1][2] * A[2][1]) -
A[0][1] * (b[1] * A[2][2] - A[1][2] * b[2]) +
A[0][2] * (b[1] * A[2][1] - A[1][1] * b[2]);
res[1] = A[0][0] * (b[1] * A[2][2] - A[1][2] * b[2]) -
b[0] * (A[1][0] * A[2][2] - A[1][2] * A[2][0]) +
A[0][2] * (A[1][0] * b[2] - b[1] * A[2][0]);
res[2] = A[0][0] * (A[1][1] * b[2] - b[1] * A[2][1]) -
A[0][1] * (A[1][0] * b[2] - b[1] * A[2][0]) +
b[0] * (A[1][0] * A[2][1] - A[1][1] * A[2][0]);
double idet = 1. / (*det);
for(int i=0; i<3; i++) res[i] *= idet;
return true;
}
// -------------------------------------------------------------------
void printMat(const double mat[3][3], const char * name)
{
printf("\nPrinting matrix %s\n",name);
for (int i=0; i<3; i++) {
for (int j=0; j<3; j++) {
printf(" %g",mat[i][j]);
}
printf("\n");
}
printf("\n");
}
// -------------------------------------------------------------------
void meanRow33(const double mat[3][3], double mean[3])
{
mean[0] = MAdTHIRD * ( mat[0][0] + mat[1][0] + mat[2][0] );
mean[1] = MAdTHIRD * ( mat[0][1] + mat[1][1] + mat[2][1] );
mean[2] = MAdTHIRD * ( mat[0][2] + mat[1][2] + mat[2][2] );
}
// -------------------------------------------------------------------
void meanRow43(const double mat[4][3], double mean[3])
{
mean[0] = 0.25 * ( mat[0][0] + mat[1][0] + mat[2][0] + mat[3][0] );
mean[1] = 0.25 * ( mat[0][1] + mat[1][1] + mat[2][1] + mat[3][1] );
mean[2] = 0.25 * ( mat[0][2] + mat[1][2] + mat[2][2] + mat[3][2] );
}
// -------------------------------------------------------------------
bool isNanMat (const double mat[3][3])
{
if ( isNanVec(mat[0]) || isNanVec(mat[1]) || isNanVec(mat[2]) ) return true;
return false;
}
// -------------------------------------------------------------------
// Miscellaneous
// -------------------------------------------------------------------
// -------------------------------------------------------------------
void sort(double lst[3])
{
for (int i=0; i<3; i++) {
int k = i;
double mx = lst[i];
for (int j=i+1; j<3; j++) if (lst[j] >= mx) { mx = lst[j]; k = j; }
if (k != i) { lst[k] = lst[i]; lst[i] = mx; }
}
}
// -------------------------------------------------------------------
void cubicRoots(const double coef[4], double real[3], double imag[3]) // GCTODO: to be rewritten
{
double a = coef[3];
double b = coef[2];
double c = coef[1];
double d = coef[0];
if(!a || !d){
printf("Error: Degenerate cubic: use a second degree solver!\n");
return;
}
b /= a;
c /= a;
d /= a;
double q = (3.0*c - (b*b))/9.0;
double r = -(27.0*d) + b*(9.0*c - 2.0*(b*b));
r /= 54.0;
double discrim = q*q*q + r*r;
imag[0] = 0.0; // The first root is always real.
double term1 = (b/3.0);
if (discrim > 0) { // one root is real, two are complex
double s = r + sqrt(discrim);
s = ((s < 0) ? -pow(-s, (1.0/3.0)) : pow(s, (1.0/3.0)));
double t = r - sqrt(discrim);
t = ((t < 0) ? -pow(-t, (1.0/3.0)) : pow(t, (1.0/3.0)));
real[0] = -term1 + s + t;
term1 += (s + t)/2.0;
real[1] = real[2] = -term1;
term1 = sqrt(3.0)*(-t + s)/2;
imag[1] = term1;
imag[2] = -term1;
return;
}
// The remaining options are all real
imag[1] = imag[2] = 0.0;
double r13;
if (discrim == 0){ // All roots real, at least two are equal.
r13 = ((r < 0) ? -pow(-r,(1.0/3.0)) : pow(r,(1.0/3.0)));
real[0] = -term1 + 2.0*r13;
real[1] = real[2] = -(r13 + term1);
return;
}
// Only option left is that all roots are real and unequal (to get
// here, q < 0)
q = -q;
double dum1 = q*q*q;
dum1 = acos(r/sqrt(dum1));
r13 = 2.0*sqrt(q);
real[0] = -term1 + r13*cos(dum1/3.0);
real[1] = -term1 + r13*cos((dum1 + 2.0*M_PI)/3.0);
real[2] = -term1 + r13*cos((dum1 + 4.0*M_PI)/3.0);
}
// -------------------------------------------------------------------
// solve x^2 + b x + c = 0
// x[2] is always set to be zero
// long FindQuadraticRoots(const double b, const double c, double x[3]) // GCTODO: to be rewritten
// {
// // printf("Quadratic roots\n");
// x[2]=0.0;
// double delt=b*b-4.*c;
// if( delt >=0 ) {
// delt=sqrt(delt);
// x[0]=(-b+delt)/2.0;
// x[1]=(-b-delt)/2.0;
// return 3;
// }
// printf("Imaginary roots, impossible, delt=%f\n",delt);
// return 1;
// }
// -------------------------------------------------------------------
// solve x^3 + a1 x^2 + a2 x + a3 = 0
// long FindCubicRoots(const double coeff[4], double x[3]) // GCTODO: to be rewritten
// {
// double a1 = coeff[2] / coeff[3];
// double a2 = coeff[1] / coeff[3];
// double a3 = coeff[0] / coeff[3];
// if( fabs(a3)<1.0e-8 )
// return FindQuadraticRoots(a1,a2,x);
// double Q = (a1 * a1 - 3 * a2) / 9.;
// double R = (2. * a1 * a1 * a1 - 9. * a1 * a2 + 27. * a3) / 54.;
// double Qcubed = Q * Q * Q;
// double d = Qcubed - R * R;
// // printf ("d = %22.15e Q = %12.5E R = %12.5E Qcubed %12.5E\n",d,Q,R,Qcubed);
// /// three roots, 2 equal
// if(Qcubed == 0.0 || fabs ( Qcubed - R * R ) < 1.e-8 * (fabs ( Qcubed) + fabs( R * R)) )
// {
// double theta;
// if (Qcubed <= 0.0)theta = acos(1.0);
// else if (R / sqrt(Qcubed) > 1.0)theta = acos(1.0);
// else if (R / sqrt(Qcubed) < -1.0)theta = acos(-1.0);
// else theta = acos(R / sqrt(Qcubed));
// double sqrtQ = sqrt(Q);
// // printf("sqrtQ = %12.5E teta=%12.5E a1=%12.5E\n",sqrt(Q),theta,a1);
// x[0] = -2 * sqrtQ * cos( theta / 3) - a1 / 3;
// x[1] = -2 * sqrtQ * cos((theta + 2 * M_PI) / 3) - a1 / 3;
// x[2] = -2 * sqrtQ * cos((theta + 4 * M_PI) / 3) - a1 / 3;
// return (3);
// }
// // Three real roots
// if (d >= 0.0) {
// double theta = acos(R / sqrt(Qcubed));
// double sqrtQ = sqrt(Q);
// x[0] = -2 * sqrtQ * cos( theta / 3) - a1 / 3;
// x[1] = -2 * sqrtQ * cos((theta + 2 * M_PI) / 3) - a1 / 3;
// x[2] = -2 * sqrtQ * cos((theta + 4 * M_PI) / 3) - a1 / 3;
// return (3);
// }
// // One real root
// else {
// printf("IMPOSSIBLE !!!\n");
// double e = pow(sqrt(-d) + fabs(R), 1. / 3.);
// if (R > 0)
// e = -e;
// x[0] = (e + Q / e) - a1 / 3.;
// return (1);
// }
// }
// -------------------------------------------------------------------
int indexOfMin(double v0, double v1, double v2)
{
double minV = v0;
int index = 0;
if ( v1 < minV ) { minV = v1; index = 1; }
if ( v2 < minV ) { minV = v2; index = 2; }
return index;
}
// -------------------------------------------------------------------
int indexOfMax(double v0, double v1, double v2)
{
double maxV = v0;
int index = 0;
if ( v1 > maxV ) { maxV = v1; index = 1; }
if ( v2 > maxV ) { maxV = v2; index = 2; }
return index;
}
// -------------------------------------------------------------------
double Tri_area(const double xyz[3][3])
{
double e0[3], e1[3];
diffVec(xyz[1],xyz[0],e0);
diffVec(xyz[2],xyz[0],e1);
double nor[3];
crossProd(e0,e1,nor);
return ( 0.5 * dotProd(nor,nor) );
}
// -------------------------------------------------------------------
double distToLineSq(const double p0[3], const double p1[3],
const double xyz[3], double proj2pt[3], bool * onSegment)
{
double v01[3]; diffVec(p1,p0,v01);
double v0x[3]; diffVec(xyz,p0,v0x);
double t = dotProd(v01,v0x) / dotProd(v01,v01);
if ( onSegment ) {
*onSegment = false;
if ( t >= 0. && t <= 1. ) *onSegment = true;
}
for (int i=0; i<3; i++) {
proj2pt[i] = xyz[i] - ( (1.-t) * p0[i] + t * p1[i] );
}
return dotProd(proj2pt,proj2pt);
}
// -------------------------------------------------------------------
// double distToLineSq(const double p0[3], const double p1[3],
// const double xyz[3], bool * onSegment)
// {
// double v01[3]; diffVec(p1,p0,v01);
// double vx0[3]; diffVec(p0,xyz,vx0);
// double d01Sq = dotProd(v01,v01);
// double dx0Sq = dotProd(vx0,vx0);
// double prod = dotProd(vx0,v01);
// if ( onSegment ) {
// *onSegment = false;
// double vx1[3]; diffVec(p1,xyz,vx1);
// if ( prod <= 0. && dotProd(vx1,v01) >= 0. ) *onSegment = true;
// }
// return std::max( ( dx0Sq * d01Sq - prod * prod ) / d01Sq, 0. );
// }
// -------------------------------------------------------------------
//! Returns the coordinates (u,v) of the point in the parent element
void Tri_linearParams(const double tri[3][3], const double xyz[3],
double res[2])
{
double v0X[3], v01[3], v02[3];
diffVec(xyz,tri[0],v0X);
diffVec(tri[1],tri[0],v01);
diffVec(tri[2],tri[0],v02);
double n[3], nTmp[3];
crossProd(v01,v02,n);
double ASqInv = 1. / dotProd(n,n);
crossProd(v0X,v02,nTmp);
double A0X2Sq = dotProd(nTmp,nTmp);
res[0] = sqrt( A0X2Sq * ASqInv );
if ( dotProd(n,nTmp) < 0. ) res[0] = -res[0];
crossProd(v01,v0X,nTmp);
double A01XSq = dotProd(nTmp,nTmp);
res[1] = sqrt( A01XSq * ASqInv );
if ( dotProd(n,nTmp) < 0. ) res[1] = -res[1];
// double n[3];
// crossProd(v01,v02,n);
// double A = sqrt ( dotProd(n,n) );
// crossProd(v0X,v02,n);
// double A1 = sqrt ( dotProd(n,n) );
// crossProd(v01,v0X,n);
// double A2 = sqrt ( dotProd(n,n) );
// res[0] = A1/A;
// res[1] = A2/A;
}
// -------------------------------------------------------------------
//! Gets the projection of a point on a plane defined by 3 points
//! and a bit representing the zone of the plane on wich the projection
//! falls given by:
//!
//! 010=2 | 011=3 / 001=1
//! | /
//! ------------+--e2--+-----------
//! v0| /v2
//! | 7 /
//! 110=6 e0 e1
//! | /
//! | / 101=5
//! |/
//! v1+
//! /|
//! / |
//! 4
//!
//! and 8, 9 or 10 if it falls on v0, v1 or v2 (respectively)
//!
//! Computes the square area of the faces of the tetrahedron defined by the
//! triangle and the point, projected on the plane of the triangle,
//! with the triangle being the first, and then
//! the 3 faces being ordered the same way as the edges e0, e1, e2 in
//! the triangle.
//!
void pointToTriangle(const double tri[3][3],
const double xyz[3],
double proj[3],
int * bit,
double area[4])
{
pointToPlane(tri,xyz,proj);
// find if the projection coincides with any of the 3 points
for(int i=0; i<3; i++) {
if( distanceSq(proj,tri[i]) < MAdTOL ) {
*bit=8+i;
// area[0] = triArea(tri);
// area[1] = area[2] = area[3] = 0.;
//#warning "implement this"
return;
}
}
// find normal to the triangle
double v01[3], v02[3], norm[3];
diffVec(tri[1],tri[0],v01);
diffVec(tri[2],tri[0],v02);
crossProd(v01,v02,norm);
double ri[3], rj[3], rk[3];
diffVec(proj,tri[0],ri);
diffVec(proj,tri[1],rj);
diffVec(proj,tri[2],rk);
// determine on which side of the edges does the point lie.
// First get normal vectors
double temp[3];
double normi[3], normj[3], normk[3];
crossProd(v01,ri,normi);
diffVec(tri[2],tri[1],temp);
crossProd(temp,rj,normj);
diffVec(tri[0],tri[2],temp);
crossProd(temp,rk,normk);
double mag[3];
mag[0] = dotProd(normi,norm);
mag[1] = dotProd(normj,norm);
mag[2] = dotProd(normk,norm);
if (area) {
area[0] = 0.5 * dotProd(norm,norm);
area[1] = 0.5 * dotProd(normi,normi);
area[2] = 0.5 * dotProd(normj,normj);
area[3] = 0.5 * dotProd(normk,normk);
}
int filter[] = {1,2,4};
*bit=0;
for(int i=0; i<3; i++){
if( mag[i] > 0. ) {
*bit = *bit | filter[i];
}
}
}
// -------------------------------------------------------------------
//! Gets the distance from a point to a triangle. Consider the
//! projection of the point to the plane of the triangle and a bit
//! taking the following values according to the zone in which the
//! projection falls:
//!
//! 010=2 | 011=3|
//! | | 001=1
//! ------------+--e2--+v2
//! v0| / `
//! | 7 / `
//! 110=6 e0 e1 `
//! | / `
//! | / 101=5
//! v1|/
//! ------------+
//! `
//! 100=4 `
//! `
//!
//! and 8, 9 or 10 if it falls on v0, v1 or v2 (respectively).
//! The distance will be
//! * the distance to v0, v1, v2 if the bit = 2,4,1 resp.,
//! * the distance to e0, e1, e2 if the bit = 6,5,3 resp.,
//! * the distance to the projection point if the bit >= 7
//!
//! Computes the vector from the closest point on the tri to 'xyz'.
//!
//! GC note: returning the square distance only allows to find the
//! distance with a precision of the square of the machine precision.
//! It could be a problem when computing Laplacian of the distance for
//! the curvature on highly anisotropic elements.
double distToTriangleSq(const double tri[3][3],
const double xyz[3],
double vec[3])
{
double distSq = MAdBIG;
double proj[3];
pointToPlane(tri,xyz,proj);
double par[2];
Tri_linearParams(tri,proj,par);
// -- see if the closest point is inside the triangle ---
if ( par[0] >= 0. && par[1] >= 0. &&
par[0] + par[1] <= 1. )
{
diffVec(xyz,proj,vec);
distSq = dotProd(vec,vec);
}
// --- else ---
else
{
// --- see if the closest point is on an edge of the triangle ---
bool onSeg=false, onSegTest;
double testD;
double testVec[3];
for (int iE=0; iE<3; iE++) {
testD = distToLineSq(tri[iE],tri[(iE+1)%3],xyz,testVec,&onSegTest);
if ( onSegTest ) {
if ( testD < distSq ) {
distSq = testD;
vec[0] = testVec[0]; vec[1] = testVec[1]; vec[2] = testVec[2];
}
onSeg = true;
}
}
// --- otherwise it is a summit of the triangle
if ( !onSeg ) {
for (int iV=0; iV<3; iV++) {
diffVec(xyz,tri[iV],testVec);
testD = dotProd(testVec,testVec);
if ( testD < distSq ) {
distSq = testD;
vec[0] = testVec[0]; vec[1] = testVec[1]; vec[2] = testVec[2];
}
}
}
}
return distSq;
}
// -------------------------------------------------------------------
//! Gets the projection of a point on a plane defined by 3 points
void pointToPlane(const double plane[3][3],
const double xyz[3],
double proj[3])
{
double v01[3], v02[3];
diffVec(plane[1],plane[0],v01);
diffVec(plane[2],plane[0],v02);
double normal[3];
crossProd(v01,v02,normal);
double areaSq = dotProd(normal,normal);
double v0X[3];
diffVec(xyz,plane[0],v0X);
double ASqX = dotProd(v0X,normal);
double ratio = ASqX / areaSq;
for (int i=0; i<3; i++) proj[i] = xyz[i] - ratio * normal[i];
}
// -------------------------------------------------------------------
double distanceSq(const double xyz0[3], const double xyz1[3])
{
return ( ( xyz1[0] - xyz0[0] ) * ( xyz1[0] - xyz0[0] ) +
( xyz1[1] - xyz0[1] ) * ( xyz1[1] - xyz0[1] ) +
( xyz1[2] - xyz0[2] ) * ( xyz1[2] - xyz0[2] ) );
}
// -------------------------------------------------------------------
} // End of namespace MAd
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