Recast: add cylindric and AABB intersection functions

'rdIntersectSegmentCylinder' is a new function that will be used for intersection tests on cylindric clip volumes.
'rdIntersectSegmentAABB' was already present in the library, but used and reimplemented across multiple source files (pending deduplication).

src/thirdparty/recast/Shared/Include/SharedCommon.h

@@ -478,6 +478,14 @@ bool rdIntersectSegmentPoly2D(const float* p0, const float* p1,
 							  float& tmin, float& tmax,
 							  int& segMin, int& segMax);
 
+bool rdIntersectSegmentAABB(const float* sp, const float* sq,
+						 const float* amin, const float* amax,
+						 float& tmin, float& tmax);
+
+bool rdIntersectSegmentCylinder(const float* sp, const float* sq, const float* position,
+								const float radius, const float height,
+								float& tmin, float& tmax);
+
 bool rdIntersectSegSeg2D(const float* ap, const float* aq,
 						 const float* bp, const float* bq,
 						 float& s, float& t);

src/thirdparty/recast/Shared/Source/SharedCommon.cpp

@@ -180,6 +180,91 @@ bool rdIntersectSegmentPoly2D(const float* p0, const float* p1,
 	return true;
 }
 
+bool rdIntersectSegmentAABB(const float* sp, const float* sq,
+						 const float* amin, const float* amax,
+						 float& tmin, float& tmax)
+{
+	float d[3];
+	rdVsub(d, sq, sp);
+	tmin = 0;  // set to -FLT_MAX to get first hit on line
+	tmax = FLT_MAX;		// set to max distance ray can travel (for segment)
+	
+	// For all three slabs
+	for (int i = 0; i < 3; i++)
+	{
+		if (rdMathFabsf(d[i]) < RD_EPS)
+		{
+			// Ray is parallel to slab. No hit if origin not within slab
+			if (sp[i] < amin[i] || sp[i] > amax[i])
+				return false;
+		}
+		else
+		{
+			// Compute intersection t value of ray with near and far plane of slab
+			const float ood = 1.0f / d[i];
+			float t1 = (amin[i]-sp[i]) * ood;
+			float t2 = (amax[i]-sp[i]) * ood;
+			// Make t1 be intersection with near plane, t2 with far plane
+			if (t1 > t2) rdSwap(t1, t2);
+			// Compute the intersection of slab intersections intervals
+			if (t1 > tmin) tmin = t1;
+			if (t2 < tmax) tmax = t2;
+			// Exit with no collision as soon as slab intersection becomes empty
+			if (tmin > tmax) return false;
+		}
+	}
+	
+	return true;
+}
+
+bool rdIntersectSegmentCylinder(const float* sp, const float* sq, const float* position,
+								const float radius, const float height,
+								float& tmin, float& tmax)
+{
+	const float cx = position[0];
+	const float cy = position[1];
+	const float cz = position[2];
+	const float topZ = cz + height;
+
+	// Horizontal (x-y plane) intersection test with infinite cylinder
+	const float dx = sq[0]-sp[0];
+	const float dy = sq[1]-sp[1];
+
+	const float px = sp[0]-cx;
+	const float py = sp[1]-cy;
+
+	const float a = dx*dx + dy*dy;
+	const float b = 2.0f * (px*dx + py*dy);
+	const float c = px*px + py*py - radius*radius;
+	
+	// Discriminant for solving quadratic equation
+	float disc = b*b - 4.0f * a*c;
+
+	if (disc < 0.0f)
+		return false; // No intersection in the horizontal plane
+
+	disc = rdMathSqrtf(disc);
+	float t0 = (-b-disc) / (2.0f*a);
+	float t1 = (-b+disc) / (2.0f*a);
+
+	if (t0 > t1) rdSwap(t0, t1);
+
+	tmin = rdMax(0.0f, t0);
+	tmax = rdMin(1.0f, t1);
+
+	if (tmin > tmax)
+		return false; // No intersection in the [tmin, tmax] range
+
+	// Vertical (z-axis) intersection test
+	const float z0 = sp[2] + tmin * (sq[2]-sp[2]);
+	const float z1 = sp[2] + tmax * (sq[2]-sp[2]);
+
+	if ((z0 < cz && z1 < cz) || (z0 > topZ && z1 > topZ))
+		return false; // No intersection with the vertical height of the cylinder
+
+	return true;
+}
+
 float rdDistancePtSegSqr2D(const float* pt, const float* p, const float* q, float& t)
 {
 	float pqx = q[0] - p[0];