reactos/dll/opengl/mesa/src/mesa/math/m_eval.h

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