-
/*
-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
#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)
// 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
{
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
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;
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)
+ {
+ // 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
{
- *elements++ = row0;
- *elements++ = row1;
- *elements++ = row0 + 1;
- *elements++ = row1;
- *elements++ = row1 + 1;
- *elements++ = row0 + 1;
- row0++;
- row1++;
+ 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++;
+ }
}
}
}
projects / xonotic / darkplaces.git / blobdiff