Attachment 2996 Details for Bug 4188 – ok, fix the matrix transpose first

[patch] ok, fix the matrix transpose first

cairo-transpose.diff (text/plain), 2.61 KB, created by Bertram Felgenhauer on 2005-08-22 16:23:10 UTC

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Creator: Bertram Felgenhauer

Created: 2005-08-22 16:23:10 UTC

Size: 2.61 KB

patch

obsolete

>Index: ChangeLog
>===================================================================
>RCS file: /cvs/cairo/cairo/ChangeLog,v
>retrieving revision 1.942
>diff -u -r1.942 ChangeLog
>--- ChangeLog	22 Aug 2005 22:49:04 -0000	1.942
>+++ ChangeLog	22 Aug 2005 23:20:49 -0000
>@@ -1,3 +1,9 @@
>+2005-08-22  Bertram Felgenhauer  <int-e@gmx.de>
>+
>+	* src/cairo-pen.c (_cairo_pen_vertices_needed): use correctly
>+	transposed version of the matrix and fix up the comments above
>+	to use row vector notation.
>+
> 2005-08-22  Tor Lillqvist  <tml@novell.com>
> 
> 	* configure.in: Calculate LT_CURRENT_MINUS_AGE (which forms part
>Index: src/cairo-pen.c
>===================================================================
>RCS file: /cvs/cairo/cairo/src/cairo-pen.c,v
>retrieving revision 1.23
>diff -u -r1.23 cairo-pen.c
>--- src/cairo-pen.c	7 Apr 2005 17:01:49 -0000	1.23
>+++ src/cairo-pen.c	22 Aug 2005 23:20:49 -0000
>@@ -192,7 +192,7 @@
> 2.  The question has been posed:  What is the maximum expansion factor 
> achieved by the linear transformation
> 
>-X' = _R_ X
>+X' = X _R_
> 
> where _R_ is a real-valued 2x2 matrix with entries:
> 
>@@ -246,7 +246,9 @@
> 
> Thus 
> 
>-     X'(t) = (a*cos(t) + b*sin(t), c*cos(t) + d*sin(t)) .
>+     X'(t) = X(t) * _R_ = X(t) * [a b]
>+                                 [c d]
>+           = (a*cos(t) + c*sin(t), b*cos(t) + d*sin(t)).
> 
> Define 
> 
>@@ -254,22 +256,22 @@
> 
> Thus
> 
>-     r^2(t) = (a*cos(t) + b*sin(t))^2 + (c*cos(t) + d*sin(t))^2
>-            = (a^2 + c^2)*cos^2(t) + (b^2 + d^2)*sin^2(t) 
>-               + 2*(a*b + c*d)*cos(t)*sin(t) 
>+     r^2(t) = (a*cos(t) + c*sin(t))^2 + (b*cos(t) + d*sin(t))^2
>+            = (a^2 + b^2)*cos^2(t) + (c^2 + d^2)*sin^2(t) 
>+               + 2*(a*c + b*d)*cos(t)*sin(t) 
> 
> Now apply the double angle formulae (A) to (C) from above:
> 
>      r^2(t) = (a^2 + b^2 + c^2 + d^2)/2 
>-	  + (a^2 - b^2 + c^2 - d^2)*cos(2*t)/2
>-	  + (a*b + c*d)*sin(2*t)
>+	  + (a^2 + b^2 - c^2 - d^2)*cos(2*t)/2
>+	  + (a*c + b*d)*sin(2*t)
>             = f + g*cos(u) + h*sin(u)
> 
> Where
> 
>      f = (a^2 + b^2 + c^2 + d^2)/2
>-     g = (a^2 - b^2 + c^2 - d^2)/2
>-     h = (a*b + c*d)
>+     g = (a^2 + b^2 - c^2 - d^2)/2
>+     h = (a*c + b*d)
>      u = 2*t
> 
> It is clear that MAX[ |X'| ] = sqrt(MAX[ r^2 ]).  Here we determine MAX[ r^2 ]
>@@ -377,12 +379,12 @@
>     double  a = matrix->xx, b = matrix->yx;
>     double  c = matrix->xy, d = matrix->yy;
> 
>-    double  i = a*a + c*c;
>-    double  j = b*b + d*d;
>+    double  i = a*a + b*b;
>+    double  j = c*c + d*d;
> 
>     double  f = 0.5 * (i + j);
>     double  g = 0.5 * (i - j);
>-    double  h = a*b + c*d;
>+    double  h = a*c + b*d;
>     
>     /* 
>      * compute major and minor axes lengths for

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