| /* |
| ** 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]; |
| |
| } |
| |