How to Handle Corners in Segment Intersection Checks - c++

Question

I am creating a ray-casting simulation that uses ray-segment intersection checks. On the corners where two segments meet the code determines there is no intersection.
I have tried extending the segments a small distance but this causes other issues with the simulation. What can I do in this situation?
The code for the intersection check:
struct Point {
double x, y;
}
std::unique_ptr<Point> Ray::cast(const Boundary& wall) const {
const double x1 = wall.a.x;
const double y1 = wall.a.y;
const double x2 = wall.b.x;
const double y2 = wall.b.y;
const double x3 = pos.x;
const double y3 = pos.y;
const double x4 = pos.x + dir.x;
const double y4 = pos.y + dir.y;
const double den = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
if (den == 0) {
return nullptr;
}
const double t = ((x1 - x3) * (y3 - y4) - (y1 - y3) * (x3 - x4)) / den;
const double u = -((x1 - x2) * (y1 - y3) - (y1 - y2) * (x1 - x3)) / den;
if ((t > 0.0f && t < 1.0f) && u > 0.0f) {
return std::make_unique<Point>(x1 + t * (x2 - x1), y1 + t * (y2 - y1));
}
else {
return nullptr;
}
}
Intersection Failure:

Answer 1

You need to include equal to check for when the float is zero:
if ((t >= 0.0f && t <= 1.0f) && u >= 0.0f) {

Answer 2

One standard answer is to define the question in terms of points’ relationship to the ray being cast. It is known how to partition the plane into non-overlapping regions that are “left of”, “right of”, and optionally “on” a line. (The last is optional because you can arbitrarily include it in one of the other two.) Then a ray hits a line segment if the two endpoints are in different regions.