From a0c4815433ccd57322f4f7703ca35e9ccfa59250 Mon Sep 17 00:00:00 2001
From: marha <marha@users.sourceforge.net>
Date: Thu, 8 Oct 2009 13:15:52 +0000
Subject: Added MesaLib-7.6

---
 mesalib/src/mesa/math/m_eval.h | 103 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 103 insertions(+)
 create mode 100644 mesalib/src/mesa/math/m_eval.h

(limited to 'mesalib/src/mesa/math/m_eval.h')

diff --git a/mesalib/src/mesa/math/m_eval.h b/mesalib/src/mesa/math/m_eval.h
new file mode 100644
index 000000000..d73ecaafb
--- /dev/null
+++ b/mesalib/src/mesa/math/m_eval.h
@@ -0,0 +1,103 @@
+
+/*
+ * Mesa 3-D graphics library
+ * Version:  3.5
+ *
+ * Copyright (C) 1999-2001  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.
+ */
+
+#ifndef _M_EVAL_H
+#define _M_EVAL_H
+
+#include "main/glheader.h"
+
+void _math_init_eval( void );
+
+
+/*
+ * 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);
+
+
+/*
+ * 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);
+
+
+/*
+ * 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);
+
+
+#endif
-- 
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