src/mesa/math/m_eval.h

   1 /* $Id: m_eval.h,v 1.2 2001/03/12 00:48:41 gareth Exp $ */
   2
   3 /*
   4  * Mesa 3-D graphics library
   5  * Version:  3.5
   6  *
   7  * Copyright (C) 1999-2001  Brian Paul   All Rights Reserved.
   8  *
   9  * Permission is hereby granted, free of charge, to any person obtaining a
  10  * copy of this software and associated documentation files (the "Software"),
  11  * to deal in the Software without restriction, including without limitation
  12  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
  13  * and/or sell copies of the Software, and to permit persons to whom the
  14  * Software is furnished to do so, subject to the following conditions:
  15  *
  16  * The above copyright notice and this permission notice shall be included
  17  * in all copies or substantial portions of the Software.
  18  *
  19  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  20  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  21  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
  22  * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
  23  * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
  24  * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  25  */
  26
  27 #ifndef _M_EVAL_H
  28 #define _M_EVAL_H
  29
  30 #include "glheader.h"
  31
  32 void _math_init_eval( void );
  33
  34
  35 /*
  36  * Horner scheme for Bezier curves
  37  *
  38  * Bezier curves can be computed via a Horner scheme.
  39  * Horner is numerically less stable than the de Casteljau
  40  * algorithm, but it is faster. For curves of degree n
  41  * the complexity of Horner is O(n) and de Casteljau is O(n^2).
  42  * Since stability is not important for displaying curve
  43  * points I decided to use the Horner scheme.
  44  *
  45  * A cubic Bezier curve with control points b0, b1, b2, b3 can be
  46  * written as
  47  *
  48  *        (([3]        [3]     )     [3]       )     [3]
  49  * c(t) = (([0]*s*b0 + [1]*t*b1)*s + [2]*t^2*b2)*s + [3]*t^2*b3
  50  *
  51  *                                           [n]
  52  * where s=1-t and the binomial coefficients [i]. These can
  53  * be computed iteratively using the identity:
  54  *
  55  * [n]               [n  ]             [n]
  56  * [i] = (n-i+1)/i * [i-1]     and     [0] = 1
  57  */
  58
  59
  60 void
  61 _math_horner_bezier_curve(const GLfloat *cp, GLfloat *out, GLfloat t,
  62                           GLuint dim, GLuint order);
  63
  64
  65 /*
  66  * Tensor product Bezier surfaces
  67  *
  68  * Again the Horner scheme is used to compute a point on a
  69  * TP Bezier surface. First a control polygon for a curve
  70  * on the surface in one parameter direction is computed,
  71  * then the point on the curve for the other parameter
  72  * direction is evaluated.
  73  *
  74  * To store the curve control polygon additional storage
  75  * for max(uorder,vorder) points is needed in the
  76  * control net cn.
  77  */
  78
  79 void
  80 _math_horner_bezier_surf(GLfloat *cn, GLfloat *out, GLfloat u, GLfloat v,
  81                          GLuint dim, GLuint uorder, GLuint vorder);
  82
  83
  84 /*
  85  * The direct de Casteljau algorithm is used when a point on the
  86  * surface and the tangent directions spanning the tangent plane
  87  * should be computed (this is needed to compute normals to the
  88  * surface). In this case the de Casteljau algorithm approach is
  89  * nicer because a point and the partial derivatives can be computed
  90  * at the same time. To get the correct tangent length du and dv
  91  * must be multiplied with the (u2-u1)/uorder-1 and (v2-v1)/vorder-1.
  92  * Since only the directions are needed, this scaling step is omitted.
  93  *
  94  * De Casteljau needs additional storage for uorder*vorder
  95  * values in the control net cn.
  96  */
  97
  98 void
  99 _math_de_casteljau_surf(GLfloat *cn, GLfloat *out, GLfloat *du, GLfloat *dv,
 100                         GLfloat u, GLfloat v, GLuint dim,
 101                         GLuint uorder, GLuint vorder);
 102
 103
 104 #endif