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.c | 501 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 501 insertions(+)
 create mode 100644 src/mesa/math/m_eval.c

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

diff --git a/src/mesa/math/m_eval.c b/src/mesa/math/m_eval.c
new file mode 100644
index 0000000000..a4ae0395ca
--- /dev/null
+++ b/src/mesa/math/m_eval.c
@@ -0,0 +1,501 @@
+/* $Id: m_eval.c,v 1.1 2000/12/26 05:09:31 keithw Exp $ */
+
+/*
+ * Mesa 3-D graphics library
+ * Version:  3.5
+ *
+ * Copyright (C) 1999-2000  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.
+ */
+
+
+/*
+ * eval.c was written by
+ * Bernd Barsuhn (bdbarsuh@cip.informatik.uni-erlangen.de) and
+ * Volker Weiss (vrweiss@cip.informatik.uni-erlangen.de).
+ *
+ * My original implementation of evaluators was simplistic and didn't
+ * compute surface normal vectors properly.  Bernd and Volker applied
+ * used more sophisticated methods to get better results.
+ *
+ * Thanks guys!
+ */
+
+
+#include "glheader.h"
+#include "config.h"
+#include "m_eval.h"
+
+static GLfloat inv_tab[MAX_EVAL_ORDER];
+
+
+
+/*
+ * 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)
+{
+   GLfloat s, powert;
+   GLuint i, k, bincoeff;
+
+   if(order >= 2)
+   {
+      bincoeff = order-1;
+      s = 1.0-t;
+
+      for(k=0; k<dim; k++)
+	 out[k] = s*cp[k] + bincoeff*t*cp[dim+k];
+
+      for(i=2, cp+=2*dim, powert=t*t; i<order; i++, powert*=t, cp +=dim)
+      {
+	 bincoeff *= order-i;
+	 bincoeff *= inv_tab[i];
+
+	 for(k=0; k<dim; k++)
+	    out[k] = s*out[k] + bincoeff*powert*cp[k];
+      }
+   }
+   else /* order=1 -> constant curve */
+   {
+      for(k=0; k<dim; k++)
+	 out[k] = cp[k];
+   }
+}
+
+/*
+ * 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)
+{
+   GLfloat *cp = cn + uorder*vorder*dim;
+   GLuint i, uinc = vorder*dim;
+
+   if(vorder > uorder)
+   {
+      if(uorder >= 2)
+      {
+	 GLfloat s, poweru;
+	 GLuint j, k, bincoeff;
+
+	 /* Compute the control polygon for the surface-curve in u-direction */
+	 for(j=0; j<vorder; j++)
+	 {
+	    GLfloat *ucp = &cn[j*dim];
+
+	    /* Each control point is the point for parameter u on a */
+	    /* curve defined by the control polygons in u-direction */
+	    bincoeff = uorder-1;
+	    s = 1.0-u;
+
+	    for(k=0; k<dim; k++)
+	       cp[j*dim+k] = s*ucp[k] + bincoeff*u*ucp[uinc+k];
+
+	    for(i=2, ucp+=2*uinc, poweru=u*u; i<uorder;
+		i++, poweru*=u, ucp +=uinc)
+	    {
+	       bincoeff *= uorder-i;
+	       bincoeff *= inv_tab[i];
+
+	       for(k=0; k<dim; k++)
+		  cp[j*dim+k] = s*cp[j*dim+k] + bincoeff*poweru*ucp[k];
+	    }
+	 }
+
+	 /* Evaluate curve point in v */
+	 _math_horner_bezier_curve(cp, out, v, dim, vorder);
+      }
+      else /* uorder=1 -> cn defines a curve in v */
+	 _math_horner_bezier_curve(cn, out, v, dim, vorder);
+   }
+   else /* vorder <= uorder */
+   {
+      if(vorder > 1)
+      {
+	 GLuint i;
+
+	 /* Compute the control polygon for the surface-curve in u-direction */
+	 for(i=0; i<uorder; i++, cn += uinc)
+	 {
+	    /* For constant i all cn[i][j] (j=0..vorder) are located */
+	    /* on consecutive memory locations, so we can use        */
+	    /* horner_bezier_curve to compute the control points     */
+
+	    _math_horner_bezier_curve(cn, &cp[i*dim], v, dim, vorder);
+	 }
+
+	 /* Evaluate curve point in u */
+	 _math_horner_bezier_curve(cp, out, u, dim, uorder);
+      }
+      else  /* vorder=1 -> cn defines a curve in u */
+	 _math_horner_bezier_curve(cn, out, u, dim, uorder);
+   }
+}
+
+/*
+ * 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)
+{
+   GLfloat *dcn = cn + uorder*vorder*dim;
+   GLfloat us = 1.0-u, vs = 1.0-v;
+   GLuint h, i, j, k;
+   GLuint minorder = uorder < vorder ? uorder : vorder;
+   GLuint uinc = vorder*dim;
+   GLuint dcuinc = vorder;
+
+   /* Each component is evaluated separately to save buffer space  */
+   /* This does not drasticaly decrease the performance of the     */
+   /* algorithm. If additional storage for (uorder-1)*(vorder-1)   */
+   /* points would be available, the components could be accessed  */
+   /* in the innermost loop which could lead to less cache misses. */
+
+#define CN(I,J,K) cn[(I)*uinc+(J)*dim+(K)]
+#define DCN(I, J) dcn[(I)*dcuinc+(J)]
+   if(minorder < 3)
+   {
+      if(uorder==vorder)
+      {
+	 for(k=0; k<dim; k++)
+	 {
+	    /* Derivative direction in u */
+	    du[k] = vs*(CN(1,0,k) - CN(0,0,k)) +
+	       v*(CN(1,1,k) - CN(0,1,k));
+
+	    /* Derivative direction in v */
+	    dv[k] = us*(CN(0,1,k) - CN(0,0,k)) +
+	       u*(CN(1,1,k) - CN(1,0,k));
+
+	    /* bilinear de Casteljau step */
+	    out[k] =  us*(vs*CN(0,0,k) + v*CN(0,1,k)) +
+	       u*(vs*CN(1,0,k) + v*CN(1,1,k));
+	 }
+      }
+      else if(minorder == uorder)
+      {
+	 for(k=0; k<dim; k++)
+	 {
+	    /* bilinear de Casteljau step */
+	    DCN(1,0) =    CN(1,0,k) -   CN(0,0,k);
+	    DCN(0,0) = us*CN(0,0,k) + u*CN(1,0,k);
+
+	    for(j=0; j<vorder-1; j++)
+	    {
+	       /* for the derivative in u */
+	       DCN(1,j+1) =    CN(1,j+1,k) -   CN(0,j+1,k);
+	       DCN(1,j)   = vs*DCN(1,j)    + v*DCN(1,j+1);
+
+	       /* for the `point' */
+	       DCN(0,j+1) = us*CN(0,j+1,k) + u*CN(1,j+1,k);
+	       DCN(0,j)   = vs*DCN(0,j)    + v*DCN(0,j+1);
+	    }
+
+	    /* remaining linear de Casteljau steps until the second last step */
+	    for(h=minorder; h<vorder-1; h++)
+	       for(j=0; j<vorder-h; j++)
+	       {
+		  /* for the derivative in u */
+		  DCN(1,j) = vs*DCN(1,j) + v*DCN(1,j+1);
+
+		  /* for the `point' */
+		  DCN(0,j) = vs*DCN(0,j) + v*DCN(0,j+1);
+	       }
+
+	    /* derivative direction in v */
+	    dv[k] = DCN(0,1) - DCN(0,0);
+
+	    /* derivative direction in u */
+	    du[k] =   vs*DCN(1,0) + v*DCN(1,1);
+
+	    /* last linear de Casteljau step */
+	    out[k] =  vs*DCN(0,0) + v*DCN(0,1);
+	 }
+      }
+      else /* minorder == vorder */
+      {
+	 for(k=0; k<dim; k++)
+	 {
+	    /* bilinear de Casteljau step */
+	    DCN(0,1) =    CN(0,1,k) -   CN(0,0,k);
+	    DCN(0,0) = vs*CN(0,0,k) + v*CN(0,1,k);
+	    for(i=0; i<uorder-1; i++)
+	    {
+	       /* for the derivative in v */
+	       DCN(i+1,1) =    CN(i+1,1,k) -   CN(i+1,0,k);
+	       DCN(i,1)   = us*DCN(i,1)    + u*DCN(i+1,1);
+
+	       /* for the `point' */
+	       DCN(i+1,0) = vs*CN(i+1,0,k) + v*CN(i+1,1,k);
+	       DCN(i,0)   = us*DCN(i,0)    + u*DCN(i+1,0);
+	    }
+
+	    /* remaining linear de Casteljau steps until the second last step */
+	    for(h=minorder; h<uorder-1; h++)
+	       for(i=0; i<uorder-h; i++)
+	       {
+		  /* for the derivative in v */
+		  DCN(i,1) = us*DCN(i,1) + u*DCN(i+1,1);
+
+		  /* for the `point' */
+		  DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0);
+	       }
+
+	    /* derivative direction in u */
+	    du[k] = DCN(1,0) - DCN(0,0);
+
+	    /* derivative direction in v */
+	    dv[k] =   us*DCN(0,1) + u*DCN(1,1);
+
+	    /* last linear de Casteljau step */
+	    out[k] =  us*DCN(0,0) + u*DCN(1,0);
+	 }
+      }
+   }
+   else if(uorder == vorder)
+   {
+      for(k=0; k<dim; k++)
+      {
+	 /* first bilinear de Casteljau step */
+	 for(i=0; i<uorder-1; i++)
+	 {
+	    DCN(i,0) = us*CN(i,0,k) + u*CN(i+1,0,k);
+	    for(j=0; j<vorder-1; j++)
+	    {
+	       DCN(i,j+1) = us*CN(i,j+1,k) + u*CN(i+1,j+1,k);
+	       DCN(i,j)   = vs*DCN(i,j)    + v*DCN(i,j+1);
+	    }
+	 }
+
+	 /* remaining bilinear de Casteljau steps until the second last step */
+	 for(h=2; h<minorder-1; h++)
+	    for(i=0; i<uorder-h; i++)
+	    {
+	       DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0);
+	       for(j=0; j<vorder-h; j++)
+	       {
+		  DCN(i,j+1) = us*DCN(i,j+1) + u*DCN(i+1,j+1);
+		  DCN(i,j)   = vs*DCN(i,j)   + v*DCN(i,j+1);
+	       }
+	    }
+
+	 /* derivative direction in u */
+	 du[k] = vs*(DCN(1,0) - DCN(0,0)) +
+	    v*(DCN(1,1) - DCN(0,1));
+
+	 /* derivative direction in v */
+	 dv[k] = us*(DCN(0,1) - DCN(0,0)) +
+	    u*(DCN(1,1) - DCN(1,0));
+
+	 /* last bilinear de Casteljau step */
+	 out[k] =  us*(vs*DCN(0,0) + v*DCN(0,1)) +
+	    u*(vs*DCN(1,0) + v*DCN(1,1));
+      }
+   }
+   else if(minorder == uorder)
+   {
+      for(k=0; k<dim; k++)
+      {
+	 /* first bilinear de Casteljau step */
+	 for(i=0; i<uorder-1; i++)
+	 {
+	    DCN(i,0) = us*CN(i,0,k) + u*CN(i+1,0,k);
+	    for(j=0; j<vorder-1; j++)
+	    {
+	       DCN(i,j+1) = us*CN(i,j+1,k) + u*CN(i+1,j+1,k);
+	       DCN(i,j)   = vs*DCN(i,j)    + v*DCN(i,j+1);
+	    }
+	 }
+
+	 /* remaining bilinear de Casteljau steps until the second last step */
+	 for(h=2; h<minorder-1; h++)
+	    for(i=0; i<uorder-h; i++)
+	    {
+	       DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0);
+	       for(j=0; j<vorder-h; j++)
+	       {
+		  DCN(i,j+1) = us*DCN(i,j+1) + u*DCN(i+1,j+1);
+		  DCN(i,j)   = vs*DCN(i,j)   + v*DCN(i,j+1);
+	       }
+	    }
+
+	 /* last bilinear de Casteljau step */
+	 DCN(2,0) =    DCN(1,0) -   DCN(0,0);
+	 DCN(0,0) = us*DCN(0,0) + u*DCN(1,0);
+	 for(j=0; j<vorder-1; j++)
+	 {
+	    /* for the derivative in u */
+	    DCN(2,j+1) =    DCN(1,j+1) -    DCN(0,j+1);
+	    DCN(2,j)   = vs*DCN(2,j)    + v*DCN(2,j+1);
+	
+	    /* for the `point' */
+	    DCN(0,j+1) = us*DCN(0,j+1 ) + u*DCN(1,j+1);
+	    DCN(0,j)   = vs*DCN(0,j)    + v*DCN(0,j+1);
+	 }
+
+	 /* remaining linear de Casteljau steps until the second last step */
+	 for(h=minorder; h<vorder-1; h++)
+	    for(j=0; j<vorder-h; j++)
+	    {
+	       /* for the derivative in u */
+	       DCN(2,j) = vs*DCN(2,j) + v*DCN(2,j+1);
+	
+	       /* for the `point' */
+	       DCN(0,j) = vs*DCN(0,j) + v*DCN(0,j+1);
+	    }
+
+	 /* derivative direction in v */
+	 dv[k] = DCN(0,1) - DCN(0,0);
+
+	 /* derivative direction in u */
+	 du[k] =   vs*DCN(2,0) + v*DCN(2,1);
+
+	 /* last linear de Casteljau step */
+	 out[k] =  vs*DCN(0,0) + v*DCN(0,1);
+      }
+   }
+   else /* minorder == vorder */
+   {
+      for(k=0; k<dim; k++)
+      {
+	 /* first bilinear de Casteljau step */
+	 for(i=0; i<uorder-1; i++)
+	 {
+	    DCN(i,0) = us*CN(i,0,k) + u*CN(i+1,0,k);
+	    for(j=0; j<vorder-1; j++)
+	    {
+	       DCN(i,j+1) = us*CN(i,j+1,k) + u*CN(i+1,j+1,k);
+	       DCN(i,j)   = vs*DCN(i,j)    + v*DCN(i,j+1);
+	    }
+	 }
+
+	 /* remaining bilinear de Casteljau steps until the second last step */
+	 for(h=2; h<minorder-1; h++)
+	    for(i=0; i<uorder-h; i++)
+	    {
+	       DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0);
+	       for(j=0; j<vorder-h; j++)
+	       {
+		  DCN(i,j+1) = us*DCN(i,j+1) + u*DCN(i+1,j+1);
+		  DCN(i,j)   = vs*DCN(i,j)   + v*DCN(i,j+1);
+	       }
+	    }
+
+	 /* last bilinear de Casteljau step */
+	 DCN(0,2) =    DCN(0,1) -   DCN(0,0);
+	 DCN(0,0) = vs*DCN(0,0) + v*DCN(0,1);
+	 for(i=0; i<uorder-1; i++)
+	 {
+	    /* for the derivative in v */
+	    DCN(i+1,2) =    DCN(i+1,1)  -   DCN(i+1,0);
+	    DCN(i,2)   = us*DCN(i,2)    + u*DCN(i+1,2);
+	
+	    /* for the `point' */
+	    DCN(i+1,0) = vs*DCN(i+1,0)  + v*DCN(i+1,1);
+	    DCN(i,0)   = us*DCN(i,0)    + u*DCN(i+1,0);
+	 }
+
+	 /* remaining linear de Casteljau steps until the second last step */
+	 for(h=minorder; h<uorder-1; h++)
+	    for(i=0; i<uorder-h; i++)
+	    {
+	       /* for the derivative in v */
+	       DCN(i,2) = us*DCN(i,2) + u*DCN(i+1,2);
+	
+	       /* for the `point' */
+	       DCN(i,0) = us*DCN(i,0) + u*DCN(i+1,0);
+	    }
+
+	 /* derivative direction in u */
+	 du[k] = DCN(1,0) - DCN(0,0);
+
+	 /* derivative direction in v */
+	 dv[k] =   us*DCN(0,2) + u*DCN(1,2);
+
+	 /* last linear de Casteljau step */
+	 out[k] =  us*DCN(0,0) + u*DCN(1,0);
+      }
+   }
+#undef DCN
+#undef CN
+}
+
+
+/*
+ * Do one-time initialization for evaluators.
+ */
+void _math_init_eval( void )
+{
+   GLuint i;
+
+   /* KW: precompute 1/x for useful x.
+    */
+   for (i = 1 ; i < MAX_EVAL_ORDER ; i++)
+      inv_tab[i] = 1.0 / i;
+}
+
-- 
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