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103 lines
3.5 KiB
C
103 lines
3.5 KiB
C
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/*
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* Mesa 3-D graphics library
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* Version: 3.5
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*
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* Copyright (C) 1999-2001 Brian Paul All Rights Reserved.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a
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* copy of this software and associated documentation files (the "Software"),
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* to deal in the Software without restriction, including without limitation
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* the rights to use, copy, modify, merge, publish, distribute, sublicense,
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* and/or sell copies of the Software, and to permit persons to whom the
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* Software is furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included
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* in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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* BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
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* AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*/
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#ifndef _M_EVAL_H
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#define _M_EVAL_H
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#include "main/glheader.h"
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void _math_init_eval( void );
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/*
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* Horner scheme for Bezier curves
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*
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* Bezier curves can be computed via a Horner scheme.
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* Horner is numerically less stable than the de Casteljau
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* algorithm, but it is faster. For curves of degree n
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* the complexity of Horner is O(n) and de Casteljau is O(n^2).
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* Since stability is not important for displaying curve
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* points I decided to use the Horner scheme.
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*
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* A cubic Bezier curve with control points b0, b1, b2, b3 can be
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* written as
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*
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* (([3] [3] ) [3] ) [3]
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* c(t) = (([0]*s*b0 + [1]*t*b1)*s + [2]*t^2*b2)*s + [3]*t^2*b3
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*
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* [n]
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* where s=1-t and the binomial coefficients [i]. These can
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* be computed iteratively using the identity:
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*
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* [n] [n ] [n]
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* [i] = (n-i+1)/i * [i-1] and [0] = 1
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*/
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void
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_math_horner_bezier_curve(const GLfloat *cp, GLfloat *out, GLfloat t,
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GLuint dim, GLuint order);
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/*
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* Tensor product Bezier surfaces
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*
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* Again the Horner scheme is used to compute a point on a
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* TP Bezier surface. First a control polygon for a curve
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* on the surface in one parameter direction is computed,
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* then the point on the curve for the other parameter
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* direction is evaluated.
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*
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* To store the curve control polygon additional storage
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* for max(uorder,vorder) points is needed in the
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* control net cn.
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*/
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void
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_math_horner_bezier_surf(GLfloat *cn, GLfloat *out, GLfloat u, GLfloat v,
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GLuint dim, GLuint uorder, GLuint vorder);
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/*
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* The direct de Casteljau algorithm is used when a point on the
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* surface and the tangent directions spanning the tangent plane
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* should be computed (this is needed to compute normals to the
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* surface). In this case the de Casteljau algorithm approach is
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* nicer because a point and the partial derivatives can be computed
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* at the same time. To get the correct tangent length du and dv
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* must be multiplied with the (u2-u1)/uorder-1 and (v2-v1)/vorder-1.
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* Since only the directions are needed, this scaling step is omitted.
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*
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* De Casteljau needs additional storage for uorder*vorder
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* values in the control net cn.
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*/
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void
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_math_de_casteljau_surf(GLfloat *cn, GLfloat *out, GLfloat *du, GLfloat *dv,
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GLfloat u, GLfloat v, GLuint dim,
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GLuint uorder, GLuint vorder);
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#endif
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