std::pair<gp_Pnt, bool> MathUtils::projectPointOnTriangle(
const gp_Pnt &p, const gp_Pnt &v0, const gp_Pnt &v1, const gp_Pnt &v2)
{
const gp_Vec e0(v0, v1);
const gp_Vec e1(v0, v2);
const gp_Vec D(p, v0);
const Standard_Real a = e0.Dot(e0);
const Standard_Real b = e0.Dot(e1);
const Standard_Real c = e1.Dot(e1);
const Standard_Real d = e0.Dot(D);
const Standard_Real e = e1.Dot(D);
const Standard_Real det = a * c - b * b;
Standard_Real s = b * e - c * d;
Standard_Real t = b * d - a * e;
int region = 0;
if (s + t <= det) {
if (s < 0.) {
if (t < 0.)
region = 4;
else
region = 3;
}
else if (t < 0.)
region = 5;
}
else {
if (s < 0.)
region = 2;
else if (t < 0.)
region = 6;
else
region = 1;
}
switch (region) {
case 0: {
const Standard_Real invDet = 1. / det;
s *= invDet;
t *= invDet;
break;
}
case 1: {
const Standard_Real numer = c + e - b - d;
if (numer <= 0.) {
s = 0.;
}
else {
const Standard_Real denom = a - 2. * b + c;
s = (numer >= denom ? 1. : numer / denom);
}
t = 1. - s;
break;
}
case 2: {
s = 0.;
t = 1.;
break;
}
case 3: {
s = 0.;
t = (e >= 0. ? 0. : (-e >= c ? 1. : -e / c));
break;
}
case 4: {
s = 0.;
t = 0.;
break;
}
case 5: {
t = 0.;
s = (d >= 0. ? 0. : (-d >= a ? 1. : -d / a));
break;
}
case 6: {
s = 1.;
t = 0.;
break;
}
} // end switch
return std::make_pair(
v0.Translated(e0 * s).Translated(e1 * t),
region == 0);
}
gp_Pnt MathUtils::projectPointOnPlane(const gp_Pnt &p, const gp_Vec &n)
{
const gp_Vec pVec(p.X(), p.Y(), p.Z());
const Standard_Real dotVN = pVec.Dot(n);
return p.Translated(-dotVN * n);
}
