X-Git-Url: https://git.xonotic.org/?a=blobdiff_plain;f=curves.c;h=154450de7cdd8b55e9493fbb065e10cc2795647a;hb=32c804dfbca9495b8d4bd40d07f289f8c890d813;hp=e4ef52ca1ca997c2ded8fe40953de196a756de8b;hpb=32e17a2898c22d871beb00b1e3a5d4a77d17088a;p=xonotic%2Fdarkplaces.git

diff --git a/curves.c b/curves.c
index e4ef52ca..154450de 100644
--- a/curves.c
+++ b/curves.c
@@ -1,6 +1,6 @@
 
 /*
-this code written by Forest Hale, on 2004-10-17, and placed into public domain
+this code written by Ashley Rose Hale (LadyHavoc), on 2004-10-17, and placed into public domain
 this implements Quadratic BSpline surfaces as seen in Quake3 by id Software
 
 a small rant on misuse of the name 'bezier': many people seem to think that
@@ -136,17 +136,18 @@ void Q3PatchTesselateFloat(int numcomponents, int outputstride, float *outputver
 #endif
 }
 
-static int Q3PatchTesselation(float bestsquareddeviation, float tolerance)
+static int Q3PatchTesselation(float largestsquared3xcurvearea, float tolerance)
 {
 	float f;
-	f = sqrt(bestsquareddeviation) / tolerance;
-	//if(f < 0.25) // REALLY flat patches
+	// f is actually a squared 2x curve area... so the formula had to be adjusted to give roughly the same subdivisions
+	f = pow(largestsquared3xcurvearea / 64.0f, 0.25f) / tolerance;
+	//if(f < 0.25) // VERY flat patches
 	if(f < 0.0001) // TOTALLY flat patches
 		return 0;
 	else if(f < 2)
 		return 1;
 	else
-		return (int) floor(log(f) / log(2)) + 1;
+		return (int) floor(log(f) / log(2.0f)) + 1;
 		// this is always at least 2
 		// maps [0.25..0.5[ to -1 (actually, 1 is returned)
 		// maps [0.5..1[ to 0 (actually, 1 is returned)
@@ -155,52 +156,117 @@ static int Q3PatchTesselation(float bestsquareddeviation, float tolerance)
 		// maps [4..8[ to 4
 }
 
+static float Squared3xCurveArea(const float *a, const float *control, const float *b, int components)
+{
+#if 0
+	// mimicing the old behaviour with the new code...
+
+	float deviation;
+	float quartercurvearea = 0;
+	int c;
+	for (c = 0;c < components;c++)
+	{
+		deviation = control[c] * 0.5f - a[c] * 0.25f - b[c] * 0.25f;
+		quartercurvearea += deviation*deviation;
+	}
+
+	// But as the new code now works on the squared 2x curve area, let's scale the value
+	return quartercurvearea * quartercurvearea * 64.0;
+
+#else
+	// ideally, we'd like the area between the spline a->control->b and the line a->b.
+	// but as this is hard to calculate, let's calculate an upper bound of it:
+	// the area of the triangle a->control->b->a.
+	//
+	// one can prove that the area of a quadratic spline = 2/3 * the area of
+	// the triangle of its control points!
+	// to do it, first prove it for the spline through (0,0), (1,1), (2,0)
+	// (which is a parabola) and then note that moving the control point
+	// left/right is just shearing and keeps the area of both the spline and
+	// the triangle invariant.
+	//
+	// why are we going for the spline area anyway?
+	// we know that:
+	//
+	//   the area between the spline and the line a->b is a measure of the
+	//   error of approximation of the spline by the line.
+	//
+	//   also, on circle-like or parabola-like curves, you easily get that the
+	//   double amount of line approximation segments reduces the error to its quarter
+	//   (also, easy to prove for splines by doing it for one specific one, and using
+	//   affine transforms to get all other splines)
+	//
+	// so...
+	//
+	// let's calculate the area! but we have to avoid the cross product, as
+	// components is not necessarily 3
+	//
+	// the area of a triangle spanned by vectors a and b is
+	//
+	// 0.5 * |a| |b| sin gamma
+	//
+	// now, cos gamma is
+	//
+	// a.b / (|a| |b|)
+	//
+	// so the area is
+	// 
+	// 0.5 * sqrt(|a|^2 |b|^2 - (a.b)^2)
+	int c;
+	float aa = 0, bb = 0, ab = 0;
+	for (c = 0;c < components;c++)
+	{
+		float xa = a[c] - control[c];
+		float xb = b[c] - control[c];
+		aa += xa * xa;
+		ab += xa * xb;
+		bb += xb * xb;
+	}
+	// area is 0.5 * sqrt(aa*bb - ab*ab)
+	// 2x TRIANGLE area is sqrt(aa*bb - ab*ab)
+	// 3x CURVE area is sqrt(aa*bb - ab*ab)
+	return aa * bb - ab * ab;
+#endif
+}
+
 // returns how much tesselation of each segment is needed to remain under tolerance
 int Q3PatchTesselationOnX(int patchwidth, int patchheight, int components, const float *in, float tolerance)
 {
-	int c, x, y;
+	int x, y;
 	const float *patch;
-	float deviation, squareddeviation, bestsquareddeviation;
-	bestsquareddeviation = 0;
+	float squared3xcurvearea, largestsquared3xcurvearea;
+	largestsquared3xcurvearea = 0;
 	for (y = 0;y < patchheight;y++)
 	{
 		for (x = 0;x < patchwidth-1;x += 2)
 		{
-			squareddeviation = 0;
-			for (c = 0, patch = in + ((y * patchwidth) + x) * components;c < components;c++, patch++)
-			{
-				deviation = patch[components] * 0.5f - patch[0] * 0.25f - patch[2*components] * 0.25f;
-				squareddeviation += deviation*deviation;
-			}
-			if (bestsquareddeviation < squareddeviation)
-				bestsquareddeviation = squareddeviation;
+			patch = in + ((y * patchwidth) + x) * components;
+			squared3xcurvearea = Squared3xCurveArea(&patch[0], &patch[components], &patch[2*components], components);
+			if (largestsquared3xcurvearea < squared3xcurvearea)
+				largestsquared3xcurvearea = squared3xcurvearea;
 		}
 	}
-	return Q3PatchTesselation(bestsquareddeviation, tolerance);
+	return Q3PatchTesselation(largestsquared3xcurvearea, tolerance);
 }
 
 // returns how much tesselation of each segment is needed to remain under tolerance
 int Q3PatchTesselationOnY(int patchwidth, int patchheight, int components, const float *in, float tolerance)
 {
-	int c, x, y;
+	int x, y;
 	const float *patch;
-	float deviation, squareddeviation, bestsquareddeviation;
-	bestsquareddeviation = 0;
+	float squared3xcurvearea, largestsquared3xcurvearea;
+	largestsquared3xcurvearea = 0;
 	for (y = 0;y < patchheight-1;y += 2)
 	{
 		for (x = 0;x < patchwidth;x++)
 		{
-			squareddeviation = 0;
-			for (c = 0, patch = in + ((y * patchwidth) + x) * components;c < components;c++, patch++)
-			{
-				deviation = patch[patchwidth*components] * 0.5f - patch[0] * 0.25f - patch[2*patchwidth*components] * 0.25f;
-				squareddeviation += deviation*deviation;
-			}
-			if (bestsquareddeviation < squareddeviation)
-				bestsquareddeviation = squareddeviation;
+			patch = in + ((y * patchwidth) + x) * components;
+			squared3xcurvearea = Squared3xCurveArea(&patch[0], &patch[patchwidth*components], &patch[2*patchwidth*components], components);
+			if (largestsquared3xcurvearea < squared3xcurvearea)
+				largestsquared3xcurvearea = squared3xcurvearea;
 		}
 	}
-	return Q3PatchTesselation(bestsquareddeviation, tolerance);
+	return Q3PatchTesselation(largestsquared3xcurvearea, tolerance);
 }
 
 // Find an equal vertex in array. Check only vertices with odd X and Y
@@ -211,7 +277,7 @@ static int FindEqualOddVertexInArray(int numcomponents, float *vertex, float *ve
 	{
 		for (x=0; x<width; x+=2)
 		{
-			qboolean found = true;
+			qbool found = true;
 			for (j=0; j<numcomponents; j++)
 				if (fabs(*(vertex+j) - *(vertices+j)) > 0.05)
 				// div0: this is notably smaller than the smallest radiant grid
@@ -270,8 +336,8 @@ int Q3PatchAdjustTesselation(int numcomponents, patchinfo_t *patch1, float *patc
 
 	struct {int id1,id2;} commonverts[8];
 	int i, j, k, side1, side2, *tess1, *tess2;
-	int dist1, dist2;
-	qboolean modified = false;
+	int dist1 = 0, dist2 = 0;
+	qbool modified = false;
 
 	// Potential paired vertices (corners of the first patch)
 	commonverts[0].id1 = 0;
@@ -336,18 +402,38 @@ void Q3PatchTriangleElements(int *elements, int width, int height, int firstvert
 	int x, y, row0, row1;
 	for (y = 0;y < height - 1;y++)
 	{
-		row0 = firstvertex + (y + 0) * width;
-		row1 = firstvertex + (y + 1) * width;
-		for (x = 0;x < width - 1;x++)
+		if(y % 2)
 		{
-			*elements++ = row0;
-			*elements++ = row1;
-			*elements++ = row0 + 1;
-			*elements++ = row1;
-			*elements++ = row1 + 1;
-			*elements++ = row0 + 1;
-			row0++;
-			row1++;
+			// swap the triangle order in odd rows as optimization for collision stride
+			row0 = firstvertex + (y + 0) * width + width - 2;
+			row1 = firstvertex + (y + 1) * width + width - 2;
+			for (x = 0;x < width - 1;x++)
+			{
+				*elements++ = row1;
+				*elements++ = row1 + 1;
+				*elements++ = row0 + 1;
+				*elements++ = row0;
+				*elements++ = row1;
+				*elements++ = row0 + 1;
+				row0--;
+				row1--;
+			}
+		}
+		else
+		{
+			row0 = firstvertex + (y + 0) * width;
+			row1 = firstvertex + (y + 1) * width;
+			for (x = 0;x < width - 1;x++)
+			{
+				*elements++ = row0;
+				*elements++ = row1;
+				*elements++ = row0 + 1;
+				*elements++ = row1;
+				*elements++ = row1 + 1;
+				*elements++ = row0 + 1;
+				row0++;
+				row1++;
+			}
 		}
 	}
 }