X-Git-Url: http://de.git.xonotic.org/?p=xonotic%2Fdarkplaces.git;a=blobdiff_plain;f=curves.c;h=910201ad791444b8ce77e503df6026a39e193be2;hp=ea18cf47fed03d8aee60a5f3a1f93e15a3b34178;hb=9e10334c3d85c0ff3630fe015f40b5c5a227668a;hpb=d5a75020f55315a6b3abd3d218e61398e4708b8e

diff --git a/curves.c b/curves.c
index ea18cf47..910201ad 100644
--- a/curves.c
+++ b/curves.c
@@ -136,11 +136,11 @@ void Q3PatchTesselateFloat(int numcomponents, int outputstride, float *outputver
 #endif
 }
 
-static int Q3PatchTesselation(float largestsquared2xcurvearea, float tolerance)
+static int Q3PatchTesselation(float largestsquared3xcurvearea, float tolerance)
 {
 	float f;
 	// f is actually a squared 2x curve area... so the formula had to be adjusted to give roughly the same subdivisions
-	f = pow(largestsquared2xcurvearea / 64.0, 0.25) / tolerance;
+	f = pow(largestsquared3xcurvearea / 64.0, 0.25) / tolerance;
 	//if(f < 0.25) // VERY flat patches
 	if(f < 0.0001) // TOTALLY flat patches
 		return 0;
@@ -156,7 +156,7 @@ static int Q3PatchTesselation(float largestsquared2xcurvearea, float tolerance)
 		// maps [4..8[ to 4
 }
 
-float Squared2xCurveArea(const float *a, const float *control, const float *b, int components)
+float Squared3xCurveArea(const float *a, const float *control, const float *b, int components)
 {
 #if 0
 	// mimicing the old behaviour with the new code...
@@ -178,6 +178,13 @@ float Squared2xCurveArea(const float *a, const float *control, const float *b, i
 	// 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:
 	//
@@ -186,6 +193,8 @@ float Squared2xCurveArea(const float *a, const float *control, const float *b, i
 	//
 	//   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...
 	//
@@ -214,7 +223,8 @@ float Squared2xCurveArea(const float *a, const float *control, const float *b, i
 		bb += xb * xb;
 	}
 	// area is 0.5 * sqrt(aa*bb - ab*ab)
-	// 2x area is 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
 }
@@ -224,19 +234,19 @@ int Q3PatchTesselationOnX(int patchwidth, int patchheight, int components, const
 {
 	int x, y;
 	const float *patch;
-	float squared2xcurvearea, largestsquared2xcurvearea;
-	largestsquared2xcurvearea = 0;
+	float squared3xcurvearea, largestsquared3xcurvearea;
+	largestsquared3xcurvearea = 0;
 	for (y = 0;y < patchheight;y++)
 	{
 		for (x = 0;x < patchwidth-1;x += 2)
 		{
 			patch = in + ((y * patchwidth) + x) * components;
-			squared2xcurvearea = Squared2xCurveArea(&patch[0], &patch[components], &patch[2*components], components);
-			if (largestsquared2xcurvearea < squared2xcurvearea)
-				largestsquared2xcurvearea = squared2xcurvearea;
+			squared3xcurvearea = Squared3xCurveArea(&patch[0], &patch[components], &patch[2*components], components);
+			if (largestsquared3xcurvearea < squared3xcurvearea)
+				largestsquared3xcurvearea = squared3xcurvearea;
 		}
 	}
-	return Q3PatchTesselation(largestsquared2xcurvearea, tolerance);
+	return Q3PatchTesselation(largestsquared3xcurvearea, tolerance);
 }
 
 // returns how much tesselation of each segment is needed to remain under tolerance
@@ -244,19 +254,19 @@ int Q3PatchTesselationOnY(int patchwidth, int patchheight, int components, const
 {
 	int x, y;
 	const float *patch;
-	float squared2xcurvearea, largestsquared2xcurvearea;
-	largestsquared2xcurvearea = 0;
+	float squared3xcurvearea, largestsquared3xcurvearea;
+	largestsquared3xcurvearea = 0;
 	for (y = 0;y < patchheight-1;y += 2)
 	{
 		for (x = 0;x < patchwidth;x++)
 		{
 			patch = in + ((y * patchwidth) + x) * components;
-			squared2xcurvearea = Squared2xCurveArea(&patch[0], &patch[patchwidth*components], &patch[2*patchwidth*components], components);
-			if (largestsquared2xcurvearea < squared2xcurvearea)
-				largestsquared2xcurvearea = squared2xcurvearea;
+			squared3xcurvearea = Squared3xCurveArea(&patch[0], &patch[patchwidth*components], &patch[2*patchwidth*components], components);
+			if (largestsquared3xcurvearea < squared3xcurvearea)
+				largestsquared3xcurvearea = squared3xcurvearea;
 		}
 	}
-	return Q3PatchTesselation(largestsquared2xcurvearea, tolerance);
+	return Q3PatchTesselation(largestsquared3xcurvearea, tolerance);
 }
 
 // Find an equal vertex in array. Check only vertices with odd X and Y