bool inBox(const Vec3r& inter, const Vec3r& box_min, const Vec3r& box_max){
if(((inter.x()>=box_min.x()) && (inter.x() <box_max.x()))
&& ((inter.y()>=box_min.y()) && (inter.y() <box_max.y()))
&& ((inter.z()>=box_min.z()) && (inter.z() <box_max.z()))
){
return true;
}
return false;
}
// precondition1: P is inside the sphere
// precondition2: P,V points to the outside of the sphere (i.e. OP.V > 0)
static bool sphere_clip_vector(const Vec3r& O, real r, const Vec3r& P, Vec3r& V)
{
Vec3r W = P - O;
real a = V.squareNorm();
real b = 2.0 * V * W;
real c = W.squareNorm() - r * r;
real delta = b * b - 4 * a * c;
if (delta < 0) {
// Should not happen, but happens sometimes (numerical precision)
return true;
}
real t = - b + ::sqrt(delta) / (2.0 * a);
if (t < 0.0) {
// Should not happen, but happens sometimes (numerical precision)
return true;
}
if (t >= 1.0) {
// Inside the sphere
return false;
}
V[0] = (t * V.x());
V[1] = (t * V.y());
V[2] = (t * V.z());
return true;
}
real CurvePoint::curvature2d_as_angle() const
{
#if 0
Vec3r edgeA = (_FEdges[0])->orientation2d();
Vec3r edgeB = (_FEdges[1])->orientation2d();
Vec2d N1(-edgeA.y(), edgeA.x());
N1.normalize();
Vec2d N2(-edgeB.y(), edgeB.x());
N2.normalize();
return acos((N1 * N2));
#endif
if (__A == 0)
return __B->curvature2d_as_angle();
if (__B == 0)
return __A->curvature2d_as_angle();
return ((1 - _t2d) * __A->curvature2d_as_angle() + _t2d * __B->curvature2d_as_angle());
}
// assume the point is inside the triangle
Vec3r ComputeBarycentricCoords(const Vec3r A,const Vec3r B,const Vec3r C,const Vec3r P)
{
Vec3r BA = B-A;
Vec3r CA = C-A;
Vec3r N = BA^CA;
Vec3r PA = A-P;
Vec3r PB = B-P;
Vec3r PC = C-P;
double areaA = (PB^PC) * N;
double areaB = (PC^PA) * N;
double areaC = (PA^PB) * N;
#if 0
// checking
printf("Barycentric debug: ----------------------------------\n");
printf("A = [%f %f %f], B = [%f %f %f], C = [%f %f %f]\n",
A.x(), A.y(), A.z(), B.x(), B.y(), B.z(), C.x(), C.y(), C.z());
printf("P = [%f %f %f]\n", P.x(), P.y(), P.z());
printf("areas = [%f %f %f]\n", areaA, areaB, areaC);
printf("plot3([%f %f %f %f],[%f %f %f %f],[%f %f %f %f],'r-');\n",
A.x(), B.x(), C.x(), A.x(),
A.y(), B.y(), C.y(), A.y(),
A.z(), B.z(), C.z(), A.z());
printf("hold on; plot3(%f,%f,%f,'bo');\n",
P.x(),P.y(),P.z());
#endif
assert(areaA > -0.1 && areaB > -0.1 && areaC > -0.1);
if (areaA < 0)
areaA = 0;
if (areaB < 0)
areaB = 0;
if (areaC < 0)
areaC = 0;
double totalArea = areaA + areaB + areaC;
double a = areaA / totalArea;
double b = areaB / totalArea;
double c = areaC / totalArea;
// printf("c = [%f %f %f]\n", a,b,c);
Vec3r result(a,b,c);
return result;
}
bool intersectRayBBox(const Vec3r& orig, const Vec3r& dir, // ray origin and direction
const Vec3r& boxMin, const Vec3r& boxMax, // the bbox
real t0, real t1,
real& tmin, real& tmax, // I0=orig+tmin*dir is the first intersection, I1=orig+tmax*dir is the second intersection
real epsilon){
float tymin, tymax, tzmin, tzmax;
Vec3r inv_direction(1.0/dir[0], 1.0/dir[1], 1.0/dir[2]);
int sign[3];
sign[0] = (inv_direction.x() < 0);
sign[1] = (inv_direction.y() < 0);
sign[2] = (inv_direction.z() < 0);
Vec3r bounds[2];
bounds[0] = boxMin;
bounds[1] = boxMax;
tmin = (bounds[sign[0]].x() - orig.x()) * inv_direction.x();
tmax = (bounds[1-sign[0]].x() - orig.x()) * inv_direction.x();
tymin = (bounds[sign[1]].y() - orig.y()) * inv_direction.y();
tymax = (bounds[1-sign[1]].y() - orig.y()) * inv_direction.y();
if ( (tmin > tymax) || (tymin > tmax) )
return false;
if (tymin > tmin)
tmin = tymin;
if (tymax < tmax)
tmax = tymax;
tzmin = (bounds[sign[2]].z() - orig.z()) * inv_direction.z();
tzmax = (bounds[1-sign[2]].z() - orig.z()) * inv_direction.z();
if ( (tmin > tzmax) || (tzmin > tmax) )
return false;
if (tzmin > tmin)
tmin = tzmin;
if (tzmax < tmax)
tmax = tzmax;
return ( (tmin < t1) && (tmax > t0) );
}
Vec2r SilhouetteGeomEngine::WorldToImage2(const Vec3r & M)
{
Vec3r newPoint = WorldToImage(M);
return Vec2r(newPoint.x(), newPoint.y());
}
