From cab974cf6c2dbfbf5dd5d291e1aae0f8eeb34290 Mon Sep 17 00:00:00 2001
From: Keith Whitwell <keith@tungstengraphics.com>
Date: Tue, 26 Dec 2000 05:09:27 +0000
Subject: Major rework of tnl module New array_cache module Support 8 texture
 units in core mesa (now support 8 everywhere) Rework core mesa statechange
 operations to avoid flushing on many noop statechanges.

---
 src/mesa/math/m_eval.h | 79 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 79 insertions(+)
 create mode 100644 src/mesa/math/m_eval.h

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

diff --git a/src/mesa/math/m_eval.h b/src/mesa/math/m_eval.h
new file mode 100644
index 0000000000..b478b39351
--- /dev/null
+++ b/src/mesa/math/m_eval.h
@@ -0,0 +1,79 @@
+
+#ifndef _M_EVAL_H
+#define _M_EVAL_H
+
+#include "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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