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Diffstat (limited to 'src/mesa/math/m_eval.c')
| -rw-r--r-- | src/mesa/math/m_eval.c | 501 |
1 files changed, 501 insertions, 0 deletions
diff --git a/src/mesa/math/m_eval.c b/src/mesa/math/m_eval.c new file mode 100644 index 00000000000..a4ae0395cad --- /dev/null +++ b/src/mesa/math/m_eval.c @@ -0,0 +1,501 @@ +/* $Id: m_eval.c,v 1.1 2000/12/26 05:09:31 keithw Exp $ */ + +/* + * Mesa 3-D graphics library + * Version: 3.5 + * + * Copyright (C) 1999-2000 Brian Paul All Rights Reserved. + * + * Permission is hereby granted, free of charge, to any person obtaining a + * copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN + * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN + * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + */ + + +/* + * eval.c was written by + * Bernd Barsuhn ([email protected]) and + * Volker Weiss ([email protected]). + * + * My original implementation of evaluators was simplistic and didn't + * compute surface normal vectors properly. Bernd and Volker applied + * used more sophisticated methods to get better results. + * + * Thanks guys! + */ + + +#include "glheader.h" +#include "config.h" +#include "m_eval.h" + +static GLfloat inv_tab[MAX_EVAL_ORDER]; + + + +/* + * Horner scheme for Bezier curves + * + * Bezier curves can be computed via a Horner scheme. + * Horner is numerically less stable than the de Casteljau + * algorithm, but it is faster. For curves of degree n + * the complexity of Horner is O(n) and de Casteljau is O(n^2). + * Since stability is not important for displaying curve + * points I decided to use the Horner scheme. + * + * A cubic Bezier curve with control points b0, b1, b2, b3 can be + * written as + * + * (([3] [3] ) [3] ) [3] + * c(t) = (([0]*s*b0 + [1]*t*b1)*s + [2]*t^2*b2)*s + [3]*t^2*b3 + * + * [n] + * where s=1-t and the binomial coefficients [i]. These can + * be computed iteratively using the identity: + * + * [n] [n ] [n] + * [i] = (n-i+1)/i * [i-1] and [0] = 1 + */ + + +void +_math_horner_bezier_curve(const GLfloat *cp, GLfloat *out, GLfloat t, + GLuint dim, GLuint order) +{ + GLfloat s, powert; + GLuint i, k, bincoeff; + + if(order >= 2) + { + bincoeff = order-1; + s = 1.0-t; + + for(k=0; k<dim; k++) + out[k] = s*cp[k] + bincoeff*t*cp[dim+k]; + + for(i=2, cp+=2*dim, powert=t*t; i<order; i++, powert*=t, cp +=dim) + { + bincoeff *= order-i; + bincoeff *= inv_tab[i]; + + for(k=0; k<dim; k++) + out[k] = s*out[k] + bincoeff*powert*cp[k]; + } + } + else /* order=1 -> constant curve */ + { + for(k=0; k<dim; k++) + out[k] = cp[k]; + } +} + +/* + * Tensor product Bezier surfaces + * + * Again the Horner scheme is used to compute a point on a + * TP Bezier surface. First a control polygon for a curve + * on the surface in one parameter direction is computed, + * then the point on the curve for the other parameter + * direction is evaluated. + * + * To store the curve control polygon additional storage + * for max(uorder,vorder) points is needed in the + * control net cn. + */ + +void +_math_horner_bezier_surf(GLfloat *cn, GLfloat *out, GLfloat u, GLfloat v, + GLuint dim, GLuint uorder, GLuint vorder) +{ + GLfloat *cp = cn + uorder*vorder*dim; + GLuint i, uinc = vorder*dim; + + if(vorder > uorder) + { + if(uorder >= 2) + { + GLfloat s, poweru; + GLuint j, k, bincoeff; + + /* Compute the control polygon for the surface-curve in u-direction */ + for(j=0; j<vorder; j++) + { + GLfloat *ucp = &cn[j*dim]; + + /* Each control point is the point for parameter u on a */ + /* curve defined by the control polygons in u-direction */ + bincoeff = uorder-1; + s = 1.0-u; + + for(k=0; k<dim; k++) + cp[j*dim+k] = s*ucp[k] + bincoeff*u*ucp[uinc+k]; + + for(i=2, ucp+=2*uinc, poweru=u*u; i<uorder; + i++, poweru*=u, ucp +=uinc) + { + bincoeff *= uorder-i; + bincoeff *= inv_tab[i]; + + for(k=0; k<dim; k++) + cp[j*dim+k] = s*cp[j*dim+k] + bincoeff*poweru*ucp[k]; + } + } + + /* Evaluate curve point in v */ + _math_horner_bezier_curve(cp, out, v, dim, vorder); + } + else /* uorder=1 -> cn defines a curve in v */ + _math_horner_bezier_curve(cn, out, v, dim, vorder); + } + else /* vorder <= uorder */ + { + if(vorder > 1) + { + GLuint i; + + /* Compute the control polygon for the surface-curve in u-direction */ + for(i=0; i<uorder; i++, cn += uinc) + { + /* For constant i all cn[i][j] (j=0..vorder) are located */ + /* on consecutive memory locations, so we can use */ + /* horner_bezier_curve to compute the control points */ + + _math_horner_bezier_curve(cn, &cp[i*dim], v, dim, vorder); + } + + /* Evaluate curve point in u */ + _math_horner_bezier_curve(cp, out, u, dim, uorder); + } + else /* vorder=1 -> cn defines a curve in u */ + _math_horner_bezier_curve(cn, out, u, dim, uorder); + } +} + +/* + * The direct de Casteljau algorithm is used when a point on the + * surface and the tangent directions spanning the tangent plane + * should be computed (this is needed to compute normals to the + * surface). In this case the de Casteljau algorithm approach is + * nicer because a point and the partial derivatives can be computed + * at the same time. To get the correct tangent length du and dv + * must be multiplied with the (u2-u1)/uorder-1 and (v2-v1)/vorder-1. + * Since only the directions are needed, this scaling step is omitted. + * + * De Casteljau needs additional storage for uorder*vorder + * values in the control net cn. + */ + +void +_math_de_casteljau_surf(GLfloat *cn, GLfloat *out, GLfloat *du, GLfloat *dv, + GLfloat u, GLfloat v, GLuint dim, + GLuint uorder, GLuint vorder) +{ + GLfloat *dcn = cn + uorder*vorder*dim; + GLfloat us = 1.0-u, vs = 1.0-v; + GLuint h, i, j, k; + GLuint minorder = uorder < vorder ? uorder : vorder; + GLuint uinc = vorder*dim; + GLuint dcuinc = vorder; + + /* Each component is evaluated separately to save buffer space */ + /* This does not drasticaly decrease the performance of the */ + /* algorithm. If additional storage for (uorder-1)*(vorder-1) */ + /* points would be available, the components could be accessed */ + /* in the innermost loop which could lead to less cache misses. */ + +#define CN(I,J,K) cn[(I)*uinc+(J)*dim+(K)] +#define DCN(I, J) dcn[(I)*dcuinc+(J)] + if(minorder < 3) + { + if(uorder==vorder) + { + for(k=0; k<dim; k++) + { + /* Derivative direction in u */ + du[k] = vs*(CN(1,0,k) - CN(0,0,k)) + + v*(CN(1,1,k) - CN(0,1,k)); + + /* Derivative direction in v */ + dv[k] = us*(CN(0,1,k) - CN(0,0,k)) + + u*(CN(1,1,k) - CN(1,0,k)); + + /* bilinear de Casteljau step */ + out[k] = us*(vs*CN(0,0,k) + v*CN(0,1,k)) + + u*(vs*CN(1,0,k) + v*CN(1,1,k)); + } + } + else if(minorder == uorder) + { + for(k=0; k<dim; k++) + { + /* bilinear de Casteljau step */ + DCN(1,0) = CN(1,0,k) - CN(0,0,k); + DCN(0,0) = us*CN(0,0,k) + u*CN(1,0,k); + + for(j=0; j<vorder-1; j++) + { + /* for the derivative in u */ + DCN(1,j+1) = CN(1,j+1,k) - CN(0,j+1,k); + DCN(1,j) = vs*DCN(1,j) + v*DCN(1,j+1); + + /* for the `point' */ + DCN(0,j+1) = us*CN(0,j+1,k) + u*CN(1,j+1,k); + DCN(0,j) = vs*DCN(0,j) + v*DCN(0,j+1); + } + + /* remaining linear de Casteljau steps until the second last step */ + for(h=minorder; h<vorder-1; h++) + for(j=0; j<vorder-h; j++) + { + /* for the derivative in u */ + DCN(1,j) = vs*DCN(1,j) + v*DCN(1,j+1); + + /* for the `point' */ + DCN(0,j) = vs*DCN(0,j) + v*DCN(0,j+1); + } + + /* derivative direction in v */ + dv[k] = DCN(0,1) - DCN(0,0); + + /* derivative direction in u */ + du[k] = vs*DCN(1,0) + v*DCN(1,1); + + /* last linear de Casteljau step */ + out[k] = vs*DCN(0,0) + v*DCN(0,1); + } + } + else /* minorder == vorder */ + { + for(k=0; k<dim; k++) + { + /* bilinear de Casteljau step */ + DCN(0,1) = CN(0,1,k) - CN(0,0,k); + DCN(0,0) = vs*CN(0,0,k) + v*CN(0,1,k); + for(i=0; i<uorder-1; i++) + { + /* for the derivative in v */ + DCN(i+1,1) = CN(i+1,1,k) - CN(i+1,0,k); + DCN(i,1) = us*DCN(i,1) + u*DCN(i+1,1); + + /* for the `point' */ + DCN(i+1,0) = vs*CN(i+1,0,k) + v*CN(i+1,1,k); + DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0); + } + + /* remaining linear de Casteljau steps until the second last step */ + for(h=minorder; h<uorder-1; h++) + for(i=0; i<uorder-h; i++) + { + /* for the derivative in v */ + DCN(i,1) = us*DCN(i,1) + u*DCN(i+1,1); + + /* for the `point' */ + DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0); + } + + /* derivative direction in u */ + du[k] = DCN(1,0) - DCN(0,0); + + /* derivative direction in v */ + dv[k] = us*DCN(0,1) + u*DCN(1,1); + + /* last linear de Casteljau step */ + out[k] = us*DCN(0,0) + u*DCN(1,0); + } + } + } + else if(uorder == vorder) + { + for(k=0; k<dim; k++) + { + /* first bilinear de Casteljau step */ + for(i=0; i<uorder-1; i++) + { + DCN(i,0) = us*CN(i,0,k) + u*CN(i+1,0,k); + for(j=0; j<vorder-1; j++) + { + DCN(i,j+1) = us*CN(i,j+1,k) + u*CN(i+1,j+1,k); + DCN(i,j) = vs*DCN(i,j) + v*DCN(i,j+1); + } + } + + /* remaining bilinear de Casteljau steps until the second last step */ + for(h=2; h<minorder-1; h++) + for(i=0; i<uorder-h; i++) + { + DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0); + for(j=0; j<vorder-h; j++) + { + DCN(i,j+1) = us*DCN(i,j+1) + u*DCN(i+1,j+1); + DCN(i,j) = vs*DCN(i,j) + v*DCN(i,j+1); + } + } + + /* derivative direction in u */ + du[k] = vs*(DCN(1,0) - DCN(0,0)) + + v*(DCN(1,1) - DCN(0,1)); + + /* derivative direction in v */ + dv[k] = us*(DCN(0,1) - DCN(0,0)) + + u*(DCN(1,1) - DCN(1,0)); + + /* last bilinear de Casteljau step */ + out[k] = us*(vs*DCN(0,0) + v*DCN(0,1)) + + u*(vs*DCN(1,0) + v*DCN(1,1)); + } + } + else if(minorder == uorder) + { + for(k=0; k<dim; k++) + { + /* first bilinear de Casteljau step */ + for(i=0; i<uorder-1; i++) + { + DCN(i,0) = us*CN(i,0,k) + u*CN(i+1,0,k); + for(j=0; j<vorder-1; j++) + { + DCN(i,j+1) = us*CN(i,j+1,k) + u*CN(i+1,j+1,k); + DCN(i,j) = vs*DCN(i,j) + v*DCN(i,j+1); + } + } + + /* remaining bilinear de Casteljau steps until the second last step */ + for(h=2; h<minorder-1; h++) + for(i=0; i<uorder-h; i++) + { + DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0); + for(j=0; j<vorder-h; j++) + { + DCN(i,j+1) = us*DCN(i,j+1) + u*DCN(i+1,j+1); + DCN(i,j) = vs*DCN(i,j) + v*DCN(i,j+1); + } + } + + /* last bilinear de Casteljau step */ + DCN(2,0) = DCN(1,0) - DCN(0,0); + DCN(0,0) = us*DCN(0,0) + u*DCN(1,0); + for(j=0; j<vorder-1; j++) + { + /* for the derivative in u */ + DCN(2,j+1) = DCN(1,j+1) - DCN(0,j+1); + DCN(2,j) = vs*DCN(2,j) + v*DCN(2,j+1); + + /* for the `point' */ + DCN(0,j+1) = us*DCN(0,j+1 ) + u*DCN(1,j+1); + DCN(0,j) = vs*DCN(0,j) + v*DCN(0,j+1); + } + + /* remaining linear de Casteljau steps until the second last step */ + for(h=minorder; h<vorder-1; h++) + for(j=0; j<vorder-h; j++) + { + /* for the derivative in u */ + DCN(2,j) = vs*DCN(2,j) + v*DCN(2,j+1); + + /* for the `point' */ + DCN(0,j) = vs*DCN(0,j) + v*DCN(0,j+1); + } + + /* derivative direction in v */ + dv[k] = DCN(0,1) - DCN(0,0); + + /* derivative direction in u */ + du[k] = vs*DCN(2,0) + v*DCN(2,1); + + /* last linear de Casteljau step */ + out[k] = vs*DCN(0,0) + v*DCN(0,1); + } + } + else /* minorder == vorder */ + { + for(k=0; k<dim; k++) + { + /* first bilinear de Casteljau step */ + for(i=0; i<uorder-1; i++) + { + DCN(i,0) = us*CN(i,0,k) + u*CN(i+1,0,k); + for(j=0; j<vorder-1; j++) + { + DCN(i,j+1) = us*CN(i,j+1,k) + u*CN(i+1,j+1,k); + DCN(i,j) = vs*DCN(i,j) + v*DCN(i,j+1); + } + } + + /* remaining bilinear de Casteljau steps until the second last step */ + for(h=2; h<minorder-1; h++) + for(i=0; i<uorder-h; i++) + { + DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0); + for(j=0; j<vorder-h; j++) + { + DCN(i,j+1) = us*DCN(i,j+1) + u*DCN(i+1,j+1); + DCN(i,j) = vs*DCN(i,j) + v*DCN(i,j+1); + } + } + + /* last bilinear de Casteljau step */ + DCN(0,2) = DCN(0,1) - DCN(0,0); + DCN(0,0) = vs*DCN(0,0) + v*DCN(0,1); + for(i=0; i<uorder-1; i++) + { + /* for the derivative in v */ + DCN(i+1,2) = DCN(i+1,1) - DCN(i+1,0); + DCN(i,2) = us*DCN(i,2) + u*DCN(i+1,2); + + /* for the `point' */ + DCN(i+1,0) = vs*DCN(i+1,0) + v*DCN(i+1,1); + DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0); + } + + /* remaining linear de Casteljau steps until the second last step */ + for(h=minorder; h<uorder-1; h++) + for(i=0; i<uorder-h; i++) + { + /* for the derivative in v */ + DCN(i,2) = us*DCN(i,2) + u*DCN(i+1,2); + + /* for the `point' */ + DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0); + } + + /* derivative direction in u */ + du[k] = DCN(1,0) - DCN(0,0); + + /* derivative direction in v */ + dv[k] = us*DCN(0,2) + u*DCN(1,2); + + /* last linear de Casteljau step */ + out[k] = us*DCN(0,0) + u*DCN(1,0); + } + } +#undef DCN +#undef CN +} + + +/* + * Do one-time initialization for evaluators. + */ +void _math_init_eval( void ) +{ + GLuint i; + + /* KW: precompute 1/x for useful x. + */ + for (i = 1 ; i < MAX_EVAL_ORDER ; i++) + inv_tab[i] = 1.0 / i; +} + |