//Checks if the provided lines intersect
//Derived from https://blogs.sas.com/content/iml/2018/07/09/intersection-line-segments.html
private static bool Intersects(VecLine a, VecLine b)
{
//Convert the lines to 4 points
MFG.Vector3 p1 = a.p;
MFG.Vector3 p2 = a.p + a.v;
MFG.Vector3 q1 = b.p;
MFG.Vector3 q2 = b.p + b.v;
//Form a matrix from the vector differences between the points
MFG.Matrix3 A = new MFG.Matrix3((p2 - p1).x, (p2 - p1).y, 0, (q1 - q2).x, (q1 - q2).y, 0, 0, 0, 1);
//Form a vector from the differences between the start points
MFG.Vector3 B = q1 - p1;
//Then
//A*t = b
//t = A^-1 * b
//Get the inverted matrix as required by the previous maths
MFG.Matrix3 inverted = A.GetInverted();
if (inverted != null) //If it is invertible, they don't share a slope. The lines will intersect.
{
MFG.Vector3 solution = inverted * B; //Solve the equation
return((solution.x >= 0 && solution.x <= 1) && (solution.y >= 0 && solution.y <= 1)); //If the solution falls in the unit square, valid collision, else not.
}
else //Otherwise, if they share a slope,
{ //Check for overlaps
if (IsBetween(p1, p2, q1)) //Is q1 between p1 and p2?
{
return(true); //They collide!
}
if (IsBetween(p1, p2, q2)) //Is q2 between p1 and p2?
{
return(true); //They collide!
}
if (IsBetween(q1, q2, p1)) //Is p11 between q1 and q2?
{
return(true); //They collide!
}
return(false); //If there were no overlaps, they don't collide!
}
}
/*
* Narrow phase collision detection considers each line of the bounding box of object A vs each line in the bounding box of object B.
* If slopes match+not collinear, it escapes as false.
* It then checks for collisions by representing each line as a parametric linear equation point+t*vector, then checks for where their (x,y) match.
* If the lines collide such that both parametric variables are between 0 and 1, there is a collision between the line segments.
*/
private static bool Collides(BoundingBox a, BoundingBox b)
{
var origin = new MFG.Vector3(0, 0, 1);
int aLen = a.vertices.Length;
int bLen = b.vertices.Length;
for (int i = 0; i < aLen; i++) //For each vertex comprising the bounding box of the first object
{
var lineA = new VecLine(a.vertices[i], a.vertices[(i + 1) % aLen]); //Create a line to the next vertex
for (int j = 0; j < bLen; j++) //For each vertex comprising the bounding box of the first object
{
var lineB = new VecLine(b.vertices[j], b.vertices[(j + 1) % bLen]); //Create a line to the next vertex
if (Intersects(lineA, lineB)) //Do the line segments intersect?
{
return(true); //Yes! So the boxes collide!
}
}
}
return(false); //No, none do, so the boxes don't collide.
}
