Recast: implement intersection test for convex hulls

Similar to the intersection test for cylindric volumes. The old convex hull intersection test in the raycast algorithm is inaccurate and also doesn't calculate the hit time, which prevents the editor from placing the cursor at the intersection. Raycast algorithm is pending a refactor and its convex hull isect test will be replaced with this.

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

@@ -486,6 +486,10 @@ bool rdIntersectSegmentCylinder(const float* sp, const float* sq, const float* p
 								const float radius, const float height,
 								float& tmin, float& tmax);
 
+bool rdIntersectSegmentConvexHull(const float* sp, const float* sq, const float* verts,
+								  int nverts, float hmin, float hmax,
+								  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

@@ -282,6 +282,48 @@ bool rdIntersectSegmentCylinder(const float* sp, const float* sq, const float* p
 	return true;
 }
 
+bool rdIntersectSegmentConvexHull(const float* sp, const float* sq,
+								  const float* verts, const int nverts,
+								  const float hmin, const float hmax,
+								  float& tmin, float& tmax)
+{
+	int segMin, segMax;
+	if (!rdIntersectSegmentPoly2D(sp, sq, verts, nverts, tmin, tmax, segMin, segMax))
+		return false; // No intersection with the polygon base
+
+	tmin = rdMax(0.0f, tmin);
+	tmax = rdMin(1.0f, tmax);
+
+	if (tmin > tmax)
+		return false; // No valid intersection range
+
+	// Vertical (z-axis) intersection test
+	const float dz = sq[2]-sp[2];
+
+	if (dz != 0.0f)
+	{
+		float tCapMin = (hmin-sp[2]) / dz;
+		float tCapMax = (hmax-sp[2]) / dz;
+
+		if (tCapMin > tCapMax) rdSwap(tCapMin, tCapMax);
+
+		// Update tmin and tmax for cap intersections
+		tmin = rdMax(tmin, tCapMin);
+		tmax = rdMin(tmax, tCapMax);
+
+		if (tmin > tmax)
+			return false;
+	}
+
+	const float z0 = sp[2] + tmin*dz;
+	const float z1 = sp[2] + tmax*dz;
+
+	if ((z0 < hmin && z1 < hmin) || (z0 > hmax && z1 > hmax))
+		return false; // No intersection within the vertical bounds
+
+	return true;
+}
+
 float rdDistancePtSegSqr2D(const float* pt, const float* p, const float* q, float& t)
 {
 	float pqx = q[0] - p[0];