// this code written by Forest Hale, on 2003-08-23, and placed into public domain
// this code deals with quadratic splines (minimum of 3 points), the same kind used in Quake3 maps.
-// LordHavoc's rant on misuse of the name 'bezier': many people seem to think that bezier is a generic term for splines, but it is not, it is a term for a specific type of spline (minimum of 4 control points, cubic spline).
+// LordHavoc's rant on misuse of the name 'bezier': many people seem to think that bezier is a generic term for splines, but it is not, it is a term for a specific type of bspline (4 control points, cubic bspline), bsplines are the generalization of the bezier spline to support dimensions other than just cubic.
+// this implements Quadratic BSpline surfaces
+#include <math.h>
#include "curves.h"
+#include "zone.h"
-void QuadraticSplineSubdivideFloat(int inpoints, int components, const float *in, int instride, float *out, int outstride)
+#if 0
+void QuadraticBSplineSubdivideFloat(int inpoints, int components, const float *in, int instride, float *out, int outstride)
{
int s;
// the input (control points) is read as a stream of points, and buffered
{
// more components can be handled, but slowly, by calling self multiple times...
for (c = 0;c < components;c++, in++, out++)
- QuadraticSplineSubdivideFloat(inpoints, 1, in, instride, out, outstride);
+ QuadraticBSplineSubdivideFloat(inpoints, 1, in, instride, out, outstride);
return;
}
for (c = 0;c < components;c++)
// note: out must have enough room!
// (see finalwidth/finalheight calcs below)
-void QuadraticSplinePatchSubdivideFloatBuffer(int cpwidth, int cpheight, int xlevel, int ylevel, int components, const float *in, float *out)
+void QuadraticBSplinePatchSubdivideFloatBuffer(int cpwidth, int cpheight, int xlevel, int ylevel, int components, const float *in, float *out)
{
int finalwidth, finalheight, xstep, ystep, x, y, c;
float *o;
if (xlevel == 1 && ylevel == 0)
{
for (y = 0;y < finalheight;y++)
- QuadraticSplineSubdivideFloat(cpwidth, components, in + y * cpwidth * components, sizeof(float) * components, out + y * finalwidth * components, sizeof(float) * components);
+ QuadraticBSplineSubdivideFloat(cpwidth, components, in + y * cpwidth * components, sizeof(float) * components, out + y * finalwidth * components, sizeof(float) * components);
return;
}
if (xlevel == 0 && ylevel == 1)
{
for (x = 0;x < finalwidth;x++)
- QuadraticSplineSubdivideFloat(cpheight, components, in + x * components, sizeof(float) * cpwidth * components, out + x * components, sizeof(float) * finalwidth * components);
+ QuadraticBSplineSubdivideFloat(cpheight, components, in + x * components, sizeof(float) * cpwidth * components, out + x * components, sizeof(float) * finalwidth * components);
return;
}
{
xstep >>= 1;
for (y = 0;y < finalheight;y += ystep)
- QuadraticSplineSubdivideFloat(cpwidth, components, out + y * finalwidth * components, sizeof(float) * xstep * 2 * components, out + y * finalwidth * components, sizeof(float) * xstep * components);
+ QuadraticBSplineSubdivideFloat(cpwidth, components, out + y * finalwidth * components, sizeof(float) * xstep * 2 * components, out + y * finalwidth * components, sizeof(float) * xstep * components);
cpwidth = (cpwidth - 1) * 2 + 1;
}
if (ystep > 1)
{
ystep >>= 1;
for (x = 0;x < finalwidth;x += xstep)
- QuadraticSplineSubdivideFloat(cpheight, components, out + x * components, sizeof(float) * ystep * 2 * finalwidth * components, out + x * components, sizeof(float) * ystep * finalwidth * components);
+ QuadraticBSplineSubdivideFloat(cpheight, components, out + x * components, sizeof(float) * ystep * 2 * finalwidth * components, out + x * components, sizeof(float) * ystep * finalwidth * components);
cpheight = (cpheight - 1) * 2 + 1;
}
}
}
+#elif 1
+void QuadraticBSplinePatchSubdivideFloatBuffer(int cpwidth, int cpheight, int xlevel, int ylevel, int components, const float *in, float *out)
+{
+ int c, x, y, outwidth, outheight, halfstep, xstep, ystep;
+ float prev, curr, next;
+ xstep = 1 << xlevel;
+ ystep = 1 << ylevel;
+ outwidth = ((cpwidth - 1) * xstep) + 1;
+ outheight = ((cpheight - 1) * ystep) + 1;
+ for (y = 0;y < cpheight;y++)
+ for (x = 0;x < cpwidth;x++)
+ for (c = 0;c < components;c++)
+ out[(y * ystep * outwidth + x * xstep) * components + c] = in[(y * cpwidth + x) * components + c];
+ while (xstep > 1 || ystep > 1)
+ {
+ if (xstep >= ystep)
+ {
+ // subdivide on X
+ halfstep = xstep >> 1;
+ for (y = 0;y < outheight;y += ystep)
+ {
+ for (c = 0;c < components;c++)
+ {
+ x = xstep;
+ // fetch first two control points
+ prev = out[(y * outwidth + (x - xstep)) * components + c];
+ curr = out[(y * outwidth + x) * components + c];
+ // create first midpoint
+ out[(y * outwidth + (x - halfstep)) * components + c] = (curr + prev) * 0.5f;
+ for (;x < outwidth - xstep;x += xstep, prev = curr, curr = next)
+ {
+ // fetch next control point
+ next = out[(y * outwidth + (x + xstep)) * components + c];
+ // flatten central control point
+ out[(y * outwidth + x) * components + c] = (curr + (prev + next) * 0.5f) * 0.5f;
+ // create following midpoint
+ out[(y * outwidth + (x + halfstep)) * components + c] = (curr + next) * 0.5f;
+ }
+ }
+ }
+ xstep >>= 1;
+ }
+ else
+ {
+ // subdivide on Y
+ halfstep = ystep >> 1;
+ for (x = 0;x < outwidth;x += xstep)
+ {
+ for (c = 0;c < components;c++)
+ {
+ y = ystep;
+ // fetch first two control points
+ prev = out[((y - ystep) * outwidth + x) * components + c];
+ curr = out[(y * outwidth + x) * components + c];
+ // create first midpoint
+ out[((y - halfstep) * outwidth + x) * components + c] = (curr + prev) * 0.5f;
+ for (;y < outheight - ystep;y += ystep, prev = curr, curr = next)
+ {
+ // fetch next control point
+ next = out[((y + ystep) * outwidth + x) * components + c];
+ // flatten central control point
+ out[(y * outwidth + x) * components + c] = (curr + (prev + next) * 0.5f) * 0.5f;
+ // create following midpoint
+ out[((y + halfstep) * outwidth + x) * components + c] = (curr + next) * 0.5f;
+ }
+ }
+ }
+ ystep >>= 1;
+ }
+ }
+ // flatten control points on X
+ for (y = 0;y < outheight;y += ystep)
+ {
+ for (c = 0;c < components;c++)
+ {
+ x = xstep;
+ // fetch first two control points
+ prev = out[(y * outwidth + (x - xstep)) * components + c];
+ curr = out[(y * outwidth + x) * components + c];
+ for (;x < outwidth - xstep;x += xstep, prev = curr, curr = next)
+ {
+ // fetch next control point
+ next = out[(y * outwidth + (x + xstep)) * components + c];
+ // flatten central control point
+ out[(y * outwidth + x) * components + c] = (curr + (prev + next) * 0.5f) * 0.5f;
+ }
+ }
+ }
+ // flatten control points on Y
+ for (x = 0;x < outwidth;x += xstep)
+ {
+ for (c = 0;c < components;c++)
+ {
+ y = ystep;
+ // fetch first two control points
+ prev = out[((y - ystep) * outwidth + x) * components + c];
+ curr = out[(y * outwidth + x) * components + c];
+ for (;y < outheight - ystep;y += ystep, prev = curr, curr = next)
+ {
+ // fetch next control point
+ next = out[((y + ystep) * outwidth + x) * components + c];
+ // flatten central control point
+ out[(y * outwidth + x) * components + c] = (curr + (prev + next) * 0.5f) * 0.5f;
+ }
+ }
+ }
+
+ /*
+ for (y = ystep;y < outheight - ystep;y += ystep)
+ {
+ for (c = 0;c < components;c++)
+ {
+ for (x = xstep, outp = out + (y * outwidth + x) * components + c, prev = outp[-xstep * components], curr = outp[0], next = outp[xstep * components];x < outwidth;x += xstep, outp += ystep * outwidth * components, prev = curr, curr = next, next = outp[xstep * components])
+ {
+ // midpoint
+ outp[-halfstep * components] = (prev + curr) * 0.5f;
+ // flatten control point
+ outp[0] = (curr + (prev + next) * 0.5f) * 0.5f;
+ // next midpoint (only needed for end segment)
+ outp[halfstep * components] = (next + curr) * 0.5f;
+ }
+ }
+ }
+ */
+}
+#else
+// unfinished code
+void QuadraticBSplinePatchSubdivideFloatBuffer(int cpwidth, int cpheight, int xlevel, int ylevel, int components, const float *in, float *out)
+{
+ int outwidth, outheight;
+ outwidth = ((cpwidth - 1) << xlevel) + 1;
+ outheight = ((cpheight - 1) << ylevel) + 1;
+ for (y = 0;y < cpheight;y++)
+ {
+ for (x = 0;x < cpwidth;x++)
+ {
+ for (c = 0;c < components;c++)
+ {
+ inp = in + (y * cpwidth + x) * components + c;
+ outp = out + ((y<<ylevel) * outwidth + (x<<xlevel)) * components + c;
+ for (sy = 0;sy < expandy;sy++)
+ {
+ for (sx = 0;sx < expandx;sx++)
+ {
+ d = a + (b - a) * 2 * t + (a - b + c - b) * t * t;
+ }
+ }
+ }
+ }
+ }
+}
+#endif
+
+/*
+0.00000 ?.????? ?.????? ?.????? ?.????? ?.????? ?.????? ?.????? 1.00000 ?.????? ?.????? ?.????? ?.????? ?.????? ?.????? ?.????? 0.00000 deviation: 0.5
+0.00000 ?.????? ?.????? ?.????? 0.50000 ?.????? ?.????? ?.????? 0.50000 ?.????? ?.????? ?.????? 0.50000 ?.????? ?.????? ?.????? 0.00000 deviation: 0.125
+0.00000 ?.????? 0.25000 ?.????? 0.37500 ?.????? 0.50000 ?.????? 0.50000 ?.????? 0.50000 ?.????? 0.37500 ?.????? 0.25000 ?.????? 0.00000 deviation: 0.03125
+0.00000 0.12500 0.21875 0.31250 0.37500 0.43750 0.46875 0.50000 0.50000 0.50000 0.46875 0.43750 0.37500 0.31250 0.21875 0.12500 0.00000 deviation: not available
+*/
+
+float QuadraticBSplinePatchLargestDeviationOnX(int cpwidth, int cpheight, int components, const float *in)
+{
+ int c, x, y;
+ const float *cp;
+ float deviation, squareddeviation, bestsquareddeviation;
+ bestsquareddeviation = 0;
+ for (y = 0;y < cpheight;y++)
+ {
+ for (x = 1;x < cpwidth-1;x++)
+ {
+ squareddeviation = 0;
+ for (c = 0, cp = in + ((y * cpwidth) + x) * components;c < components;c++, cp++)
+ {
+ deviation = cp[0] * 0.5f - cp[-components] * 0.25f - cp[components] * 0.25f;
+ squareddeviation += deviation*deviation;
+ }
+ if (bestsquareddeviation < squareddeviation)
+ bestsquareddeviation = squareddeviation;
+ }
+ }
+ return (float)sqrt(bestsquareddeviation);
+}
+
+float QuadraticBSplinePatchLargestDeviationOnY(int cpwidth, int cpheight, int components, const float *in)
+{
+ int c, x, y;
+ const float *cp;
+ float deviation, squareddeviation, bestsquareddeviation;
+ bestsquareddeviation = 0;
+ for (y = 1;y < cpheight-1;y++)
+ {
+ for (x = 0;x < cpwidth;x++)
+ {
+ squareddeviation = 0;
+ for (c = 0, cp = in + ((y * cpwidth) + x) * components;c < components;c++, cp++)
+ {
+ deviation = cp[0] * 0.5f - cp[-cpwidth * components] * 0.25f - cp[cpwidth * components] * 0.25f;
+ squareddeviation += deviation*deviation;
+ }
+ if (bestsquareddeviation < squareddeviation)
+ bestsquareddeviation = squareddeviation;
+ }
+ }
+ return (float)sqrt(bestsquareddeviation);
+}
+int QuadraticBSplinePatchSubdivisionLevelForDeviation(float deviation, float level1tolerance, int levellimit)
+{
+ int level;
+ // count the automatic flatten step which reduces deviation by 50%
+ deviation *= 0.5f;
+ // count the levels to subdivide to come under the tolerance
+ for (level = 0;level < levellimit && deviation > level1tolerance;level++)
+ deviation *= 0.25f;
+ return level;
+}
+
+int QuadraticBSplinePatchSubdivisionLevelOnX(int cpwidth, int cpheight, int components, const float *in, float level1tolerance, int levellimit)
+{
+ return QuadraticBSplinePatchSubdivisionLevelForDeviation(QuadraticBSplinePatchLargestDeviationOnX(cpwidth, cpheight, components, in), level1tolerance, levellimit);
+}
+
+int QuadraticBSplinePatchSubdivisionLevelOnY(int cpwidth, int cpheight, int components, const float *in, float level1tolerance, int levellimit)
+{
+ return QuadraticBSplinePatchSubdivisionLevelForDeviation(QuadraticBSplinePatchLargestDeviationOnY(cpwidth, cpheight, components, in), level1tolerance, levellimit);
+}
+
+/*
+ // 1: flat (0th dimension)
+ o = a
+ // 2: linear (1st dimension)
+ o = a * (1 - t) + b * t
+ // 3: quadratic bspline (2nd dimension)
+ o = a * (1 - t) * (1 - t) + 2 * b * (1 - t) * t + c * t * t
+ // 4: cubic (bezier) bspline (3rd dimension)
+ o = a * (1 - t) * (1 - t) * (1 - t) + 3 * b * (1 - t) * (1 - t) * t + 3 * c * (1 - t) * t * t + d * t * t * t
+ // 5: quartic bspline (4th dimension)
+ o = a * (1 - t) * (1 - t) * (1 - t) * (1 - t) + 4 * b * (1 - t) * (1 - t) * (1 - t) * t + 6 * c * (1 - t) * (1 - t) * t * t + 4 * d * (1 - t) * t * t * t + e * t * t * t * t
+
+ // n: arbitrary dimension bspline
+double factorial(int n)
+{
+ int i;
+ double f;
+ f = 1;
+ for (i = 1;i < n;i++)
+ f = f * i;
+ return f;
+}
+double bsplinesample(int dimensions, double t, double *param)
+{
+ double o = 0;
+ for (i = 0;i < dimensions + 1;i++)
+ o += param[i] * factorial(dimensions)/(factorial(i)*factorial(dimensions-i)) * pow(t, i) * pow(1 - t, dimensions - i);
+}
+*/
projects / xonotic / darkplaces.git / blobdiff