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bool Geometry::doLinesIntersect2D(const Line& line1, const Line& line2) {
double x1 = line1.start.x;
double y1 = line1.start.y;
double z1 = line1.start.z;
double x2 = line1.end.x;
double y2 = line1.end.y;
double z2 = line1.end.z;
double x3 = line2.start.x;
double y3 = line2.start.y;
double z3 = line2.start.z;
double x4 = line2.end.x;
double y4 = line2.end.y;
double z4 = line2.end.z;
double ua = ((x4  x3) * (y1  y3)  (y4  y3) * (x1  x3)) / ((y4  y3) * (x2  x1)  (x4  x3) * (y2  y1));
double ub = ((x2  x1) * (y1  y3)  (y2  y1) * (x1  x3)) / ((y4  y3) * (x2  x1)  (x4  x3) * (y2  y1));
if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1) {
return true;
}
return false;
}
int Geometry::countIntersectingTriangles(Line& line) {
const double threshold = 1e7;
int count = 0;
for (const auto& triangle : triangles) {
Line edge1, edge2, edge3;
edge1.start = { triangle.x1, triangle.y1, triangle.z1 };
edge1.end = { triangle.x2, triangle.y2, triangle.z2 };
edge2.start = { triangle.x2, triangle.y2, triangle.z2 };
edge2.end = { triangle.x3, triangle.y3, triangle.z3 };
edge3.start = { triangle.x3, triangle.y3, triangle.z3 };
edge3.end = { triangle.x1, triangle.y1, triangle.z1 };
if (doLinesIntersect3D(line, edge1)  doLinesIntersect3D(line, edge2)  doLinesIntersect3D(line, edge3)) {
count++;
continue;
}
double px = line.start.x;
double py = line.start.y;
double pz = line.start.z;
double nx = triangle.nx;
double ny = triangle.ny;
double nz = triangle.nz;
double qx = triangle.x1;
double qy = triangle.y1;
double qz = triangle.z1;
double t = ((qx  px) * nx + (qy  py) * ny + (qz  pz) * nz)/
((line.end.x  line.start.x) * nx + (line.end.y  line.start.y) * ny + (line.end.z  line.start.z) * nz);
if (t >= 0 && t <= 1) {
double ix = px + t * (line.end.x  line.start.x);
double iy = py + t * (line.end.y  line.start.y);
double iz = pz + t * (line.end.z  line.start.z);
if (isPointInsideTriangle3D(ix, iy, iz, triangle) && t > threshold && t < 1  threshold) {
//if (isPointInsideTriangle2D(ix, iy, triangle) && t > threshold && t < 1  threshold) {
count++;
}
}
}
return count;
}
