#include "VolSurfUser.hxx"
#include "InterpKernelAutoPtr.hxx"
+#include "InterpolationUtils.hxx"
#include <cmath>
#include <limits>
return (x-pt[0])*(x-pt[0])+(y-pt[1])*(y-pt[1]);
}
+ /**
+ * See http://geomalgorithms.com/a02-_lines.html#Distance-to-Ray-or-Segment
+ */
+ double DistanceFromPtToSegInSpaceDim3(const double *pt, const double *pt0Seg2, const double *pt1Seg2)
+ {
+ double v[3], w[3];
+ for(int i=0; i < 3; i++) {
+ v[i]=pt1Seg2[i]-pt0Seg2[i];
+ w[i] = pt[i] - pt0Seg2[i];
+ }
+
+ double c1 = dotprod<3>(w,v);
+ if ( c1 <= 0 )
+ return norm<3>(w);
+ double c2 = dotprod<3>(v,v);
+ if ( c2 <= c1 )
+ {
+ for(int i=0; i < 3; i++)
+ w[i] = pt[i] - pt1Seg2[i];
+ return norm<3>(w);
+ }
+ double b = c1 / c2;
+ for(int i=0; i < 3; i++)
+ w[i] = pt0Seg2[i] + b * v[i] - pt[i];
+ return norm<3>(w);
+ }
+
+ /**
+ Helper for DistanceFromPtToTriInSpaceDim3
+ */
+ inline double _HelperDistancePtToTri3D_1(const double aXX, const double bX, const double c)
+ {
+ if (bX >= 0)
+ return c;
+ if (-bX >= aXX)
+ return aXX + 2*bX + c;
+ return bX*(-bX / aXX) + c;
+ }
+
+ /**
+ Helper for DistanceFromPtToTriInSpaceDim3
+ */
+ inline double _HelperDistancePtToTri3D_2(const double a01, const double aXX, const double aYY,
+ const double bX, const double bY, const double c)
+ {
+ double tmp0 = a01 + bX, tmp1 = aXX + bY;
+ if (tmp1 > tmp0) {
+ double numer = tmp1 - tmp0, denom = aXX - 2*a01 + aYY;
+ if (numer >= denom)
+ return aXX + 2*bX + c;
+ else {
+ double s, t;
+ s = numer / denom; t = 1 - s;
+ return s*(aXX*s + a01*t + 2*bX) + t*(a01*s + aYY*t + 2*bY) + c;
+ }
+ }
+ else
+ {
+ if (tmp1 <= 0) return aYY + 2*bY + c;
+ else {
+ if (bY >= 0) return c;
+ else return bY*(-bY / aYY) + c;
+ }
+ }
+ }
+
+ /**
+ * From https://www.geometrictools.com/Documentation/DistancePoint3Triangle3.pdf
+ */
double DistanceFromPtToTriInSpaceDim3(const double *pt, const double *pt0Tri3, const double *pt1Tri3, const double *pt2Tri3)
{
- double matrix[12];
- if(!ComputeRotTranslationMatrixToPut3PointsOnOXY(pt0Tri3,pt1Tri3,pt2Tri3,matrix))
- return std::numeric_limits<double>::max();
- double xy0[2],xy1[2],xy2[2],xy[2]; xy0[0]=0.; xy0[1]=0.;
- xy1[0]=matrix[0]*pt1Tri3[0]+matrix[1]*pt1Tri3[1]+matrix[2]*pt1Tri3[2]+matrix[3]; xy1[1]=0.;
- xy2[0]=matrix[0]*pt2Tri3[0]+matrix[1]*pt2Tri3[1]+matrix[2]*pt2Tri3[2]+matrix[3];
- xy2[1]=matrix[4]*pt2Tri3[0]+matrix[5]*pt2Tri3[1]+matrix[6]*pt2Tri3[2]+matrix[7];
- xy[0]=matrix[0]*pt[0]+matrix[1]*pt[1]+matrix[2]*pt[2]+matrix[3];
- xy[1]=matrix[4]*pt[0]+matrix[5]*pt[1]+matrix[6]*pt[2]+matrix[7];
- double z=matrix[8]*pt[0]+matrix[9]*pt[1]+matrix[10]*pt[2]+matrix[11];
- double ret=std::numeric_limits<double>::max();
- std::size_t nbOfHint=0;
- if(xy[0]>0. && xy[0]<xy1[0])
- { ret=std::min(ret,z*z+xy[1]*xy[1]); nbOfHint++; } //distance pt to edge [pt0Tri3,pt1Tri3]
- double tmp=SquareDistanceFromPtToSegInSpaceDim2(xy,xy1,xy2,nbOfHint); //distance pt to edge [pt1Tri3,pt2Tri3]
- ret=std::min(ret,z*z+tmp);
- tmp=SquareDistanceFromPtToSegInSpaceDim2(xy,xy2,xy0,nbOfHint);//distance pt to edge [pt2Tri3,pt0Tri3]
- ret=std::min(ret,z*z+tmp);
- if(nbOfHint==3)
- ret=std::min(ret,z*z);
- return sqrt(ret);
+ double diff[3], edge0[3], edge1[3];
+ for(int i=0; i < 3; i++) diff[i]=pt0Tri3[i]-pt[i];
+ for(int i=0; i < 3; i++) edge0[i]=pt1Tri3[i]-pt0Tri3[i];
+ for(int i=0; i < 3; i++) edge1[i]=pt2Tri3[i]-pt0Tri3[i];
+
+ double a00=dotprod<3>(edge0, edge0), a01=dotprod<3>(edge0,edge1), a11=dotprod<3>(edge1,edge1);
+ double b0=dotprod<3>(diff, edge0), b1=dotprod<3>(diff, edge1), c=dotprod<3>(diff, diff);
+ double det = fabs(a00*a11 - a01*a01);
+ double s = a01*b1 - a11*b0, t = a01*b0 - a00*b1;
+ double sDist;
+
+ if (s + t <= det)
+ {
+ if (s < 0) {
+ if (t < 0) { // region 4
+ if (b0 < 0) {
+ if (-b0 >= a00) sDist = a00 + 2*b0 + c;
+ else sDist = b0*(-b0 / a00) + c;
+ }
+ else
+ sDist = _HelperDistancePtToTri3D_1(a11, b1, c);
+ }
+ else // region 3
+ sDist = _HelperDistancePtToTri3D_1(a11, b1, c);
+ }
+ else {
+ if (t < 0) // region 5
+ sDist = _HelperDistancePtToTri3D_1(a00, b0, c);
+ else // region 0
+ {
+ // minimum at interior point
+ if (fabs(det) < 1.0e-12)
+ {
+ // points are colinear (degenerated triangle)
+ // => Compute distance between segments
+ double distance = std::min(DistanceFromPtToSegInSpaceDim3(pt, pt0Tri3, pt1Tri3),
+ DistanceFromPtToSegInSpaceDim3(pt, pt1Tri3, pt2Tri3));
+ return distance;
+ }
+
+ // else we can divide by non-zero
+ double invDet = 1 / det;
+ s *= invDet; t *= invDet;
+ sDist = s*(a00*s + a01*t + 2*b0) + t*(a01*s + a11*t + 2*b1) + c;
+ }
+ }
+ }
+ else // s+t > det
+ {
+ if (s < 0.0) // region 2
+ sDist = _HelperDistancePtToTri3D_2(a01, a00, a11, b0, b1, c);
+ else {
+ if (t < 0.0) // region 6
+ sDist = _HelperDistancePtToTri3D_2(a01, a11, a00, b1, b0, c);
+ else { // region 1
+ double numer = a11 + b1 - a01 - b0;
+ if (numer <= 0.0)
+ sDist = a11 + 2*b1 + c;
+ else {
+ double denom = a00 - 2*a01 + a11;
+ if (numer >= denom)
+ sDist = a00 + 2*b0 + c;
+ else {
+ s = numer / denom; t = 1 - s;
+ sDist = s*(a00*s + a01*t + 2*b0) + t*(a01*s + a11*t + 2*b1) + c;
+ }
+ }
+ }
+ }
+ }
+ // Account for numerical round-off error.
+ if (sDist < 0)
+ sDist = 0.0;
+
+ return sqrt(sDist);
}
double DistanceFromPtToPolygonInSpaceDim3(const double *pt, const int *connOfPolygonBg, const int *connOfPolygonEnd, const double *coords)
}
/*!
- * \param [out] matrix contain a dense matrix of size 12 with 3 rows containing each 4 colums. This matrix is the reduction of 4x4 matrix but the last
+ * \param [out] matrix contain a dense matrix of size 12 with 3 rows containing each 4 columns. This matrix is the reduction of 4x4 matrix but the last
* line containing [0,0,0,1] is omitted.
*/
bool ComputeRotTranslationMatrixToPut3PointsOnOXY(const double *p0, const double *p1, const double *p2, double *matrix)
