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authormarha <marha@users.sourceforge.net>2009-10-08 13:15:52 +0000
committermarha <marha@users.sourceforge.net>2009-10-08 13:15:52 +0000
commita0c4815433ccd57322f4f7703ca35e9ccfa59250 (patch)
treef5213802ec12adb86ec3136001c1c29fe5343700 /mesalib/src/glu/sgi/libnurbs/interface/bezierEval.cc
parentc73dc01b6de45612b24dc2dd34fba24d81ebf46c (diff)
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Added MesaLib-7.6
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+/*
+** License Applicability. Except to the extent portions of this file are
+** made subject to an alternative license as permitted in the SGI Free
+** Software License B, Version 1.1 (the "License"), the contents of this
+** file are subject only to the provisions of the License. You may not use
+** this file except in compliance with the License. You may obtain a copy
+** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
+** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
+**
+** http://oss.sgi.com/projects/FreeB
+**
+** Note that, as provided in the License, the Software is distributed on an
+** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
+** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
+** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
+** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
+**
+** Original Code. The Original Code is: OpenGL Sample Implementation,
+** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
+** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
+** Copyright in any portions created by third parties is as indicated
+** elsewhere herein. All Rights Reserved.
+**
+** Additional Notice Provisions: The application programming interfaces
+** established by SGI in conjunction with the Original Code are The
+** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
+** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
+** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
+** Window System(R) (Version 1.3), released October 19, 1998. This software
+** was created using the OpenGL(R) version 1.2.1 Sample Implementation
+** published by SGI, but has not been independently verified as being
+** compliant with the OpenGL(R) version 1.2.1 Specification.
+**
+*/
+/*
+*/
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <assert.h>
+#include <math.h>
+#include "bezierEval.h"
+
+#ifdef __WATCOMC__
+#pragma warning 14 10
+#endif
+
+#define TOLERANCE 0.0001
+
+#ifndef MAX_ORDER
+#define MAX_ORDER 16
+#endif
+
+#ifndef MAX_DIMENSION
+#define MAX_DIMENSION 4
+#endif
+
+static void normalize(float vec[3]);
+static void crossProduct(float x[3], float y[3], float ret[3]);
+#if 0 // UNUSED
+static void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[]);
+#endif
+
+static float binomialCoefficients[8][8] = {
+ {1,0,0,0,0,0,0,0},
+ {1,1,0,0,0,0,0,0},
+ {1,2,1,0,0,0,0,0},
+ {1,3,3,1,0,0,0,0},
+ {1,4,6,4,1,0,0,0},
+ {1,5,10,10,5,1,0,0},
+ {1,6,15,20,15,6,1,0},
+ {1,7,21,35,35,21,7,1}
+};
+
+void bezierCurveEval(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[])
+{
+ float uprime = (u-u0)/(u1-u0);
+ float *ctlptr = ctlpoints;
+ float oneMinusX = 1.0f-uprime;
+ float XPower = 1.0f;
+
+ int i,k;
+ for(k=0; k<dimension; k++)
+ retpoint[k] = (*(ctlptr + k));
+
+ for(i=1; i<order; i++){
+ ctlptr += stride;
+ XPower *= uprime;
+ for(k=0; k<dimension; k++) {
+ retpoint[k] = retpoint[k]*oneMinusX + ctlptr[k]* binomialCoefficients[order-1][i] * XPower;
+ }
+ }
+}
+
+
+#if 0 // UNUSED
+/*order = degree +1 >=1.
+ */
+void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[])
+{
+ float uprime = (u-u0)/(u1-u0);
+ float buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];
+ float* ctlptr = ctlpoints;
+ int r, i,j;
+ for(i=0; i<order; i++) {
+ for(j=0; j<dimension; j++)
+ buf[0][i][j] = ctlptr[j];
+ ctlptr += stride;
+ }
+ for(r=1; r<order; r++){
+ for(i=0; i<order-r; i++) {
+ for(j=0; j<dimension; j++)
+ buf[r][i][j] = (1-uprime)*buf[r-1][i][j] + uprime*buf[r-1][i+1][j];
+ }
+ }
+
+ for(j=0; j<dimension; j++)
+ retpoint[j] = buf[order-1][0][j];
+}
+#endif
+
+
+/*order = degree +1 >=1.
+ */
+void bezierCurveEvalDer(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retDer[])
+{
+ int i,k;
+ float width = u1-u0;
+ float *ctlptr = ctlpoints;
+
+ float buf[MAX_ORDER][MAX_DIMENSION];
+ if(order == 1){
+ for(k=0; k<dimension; k++)
+ retDer[k]=0;
+ }
+ for(i=0; i<order-1; i++){
+ for(k=0; k<dimension; k++) {
+ buf[i][k] = (ctlptr[stride+k] - ctlptr[k])*(order-1)/width;
+ }
+ ctlptr += stride;
+ }
+
+ bezierCurveEval(u0, u1, order-1, (float*) buf, MAX_DIMENSION, dimension, u, retDer);
+}
+
+void bezierCurveEvalDerGen(int der, float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retDer[])
+{
+ int i,k,r;
+ float *ctlptr = ctlpoints;
+ float width=u1-u0;
+ float buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];
+ if(der<0) der=0;
+ for(i=0; i<order; i++){
+ for(k=0; k<dimension; k++){
+ buf[0][i][k] = ctlptr[k];
+ }
+ ctlptr += stride;
+ }
+
+
+ for(r=1; r<=der; r++){
+ for(i=0; i<order-r; i++){
+ for(k=0; k<dimension; k++){
+ buf[r][i][k] = (buf[r-1][i+1][k] - buf[r-1][i][k])*(order-r)/width;
+ }
+ }
+ }
+
+ bezierCurveEval(u0, u1, order-der, (float *) (buf[der]), MAX_DIMENSION, dimension, u, retDer);
+}
+
+/*the Bezier bivarite polynomial is:
+ * sum[i:0,uorder-1][j:0,vorder-1] { ctlpoints[i*ustride+j*vstride] * B(i)*B(j)
+ * where B(i) and B(j) are basis functions
+ */
+void bezierSurfEvalDerGen(int uder, int vder, float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float ret[])
+{
+ int i;
+ float newPoints[MAX_ORDER][MAX_DIMENSION];
+
+ for(i=0; i<uorder; i++){
+
+ bezierCurveEvalDerGen(vder, v0, v1, vorder, ctlpoints+ustride*i, vstride, dimension, v, newPoints[i]);
+
+ }
+
+ bezierCurveEvalDerGen(uder, u0, u1, uorder, (float *) newPoints, MAX_DIMENSION, dimension, u, ret);
+}
+
+
+/*division by w is performed*/
+void bezierSurfEval(float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float ret[])
+{
+ bezierSurfEvalDerGen(0, 0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, ret);
+ if(dimension == 4) /*homogeneous*/{
+ ret[0] /= ret[3];
+ ret[1] /= ret[3];
+ ret[2] /= ret[3];
+ }
+}
+
+void bezierSurfEvalNormal(float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float retNormal[])
+{
+ float partialU[4];
+ float partialV[4];
+ assert(dimension>=3 && dimension <=4);
+ bezierSurfEvalDerGen(1,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, partialU);
+ bezierSurfEvalDerGen(0,1, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, partialV);
+
+ if(dimension == 3){/*inhomogeneous*/
+ crossProduct(partialU, partialV, retNormal);
+
+ normalize(retNormal);
+
+ return;
+ }
+ else { /*homogeneous*/
+ float val[4]; /*the point coordinates (without derivative)*/
+ float newPartialU[MAX_DIMENSION];
+ float newPartialV[MAX_DIMENSION];
+ int i;
+ bezierSurfEvalDerGen(0,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, val);
+
+ for(i=0; i<=2; i++){
+ newPartialU[i] = partialU[i] * val[3] - val[i] * partialU[3];
+ newPartialV[i] = partialV[i] * val[3] - val[i] * partialV[3];
+ }
+ crossProduct(newPartialU, newPartialV, retNormal);
+ normalize(retNormal);
+ }
+}
+
+/*if size is 0, then nothing is done*/
+static void normalize(float vec[3])
+{
+ float size = (float)sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]);
+
+ if(size < TOLERANCE)
+ {
+#ifdef DEBUG
+ fprintf(stderr, "Warning: in oglBSpline.c normal is 0\n");
+#endif
+ return;
+ }
+ else {
+ vec[0] = vec[0]/size;
+ vec[1] = vec[1]/size;
+ vec[2] = vec[2]/size;
+ }
+}
+
+
+static void crossProduct(float x[3], float y[3], float ret[3])
+{
+ ret[0] = x[1]*y[2] - y[1]*x[2];
+ ret[1] = x[2]*y[0] - y[2]*x[0];
+ ret[2] = x[0]*y[1] - y[0]*x[1];
+
+}
+