SGI SI GLU library

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diff --git a/src/glu/sgi/libnurbs/interface/bezierEval.cc b/src/glu/sgi/libnurbs/interface/bezierEval.cc
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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.
+**
+** $Date: 2001/03/17 00:25:40 $ $Revision: 1.1 $
+*/
+/*
+** $Header: /home/krh/git/sync/mesa-cvs-repo/Mesa/src/glu/sgi/libnurbs/interface/bezierEval.cc,v 1.1 2001/03/17 00:25:40 brianp Exp $
+*/
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <assert.h>
+#include <math.h>
+#include "bezierEval.h"
+
+#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]);
+static void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retpoint[]);
+
+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 = 1.0-uprime;
+  float XPower = 1.0;
+
+  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;
+    }
+  }
+}
+
+      
+
+/*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];
+}
+
+
+
+/*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,j,k;
+  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 = 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];
+
+}
+