# [cairo-commit] cairo/src cairo_pen.c,1.18,1.19

Carl Worth commit at pdx.freedesktop.org
Tue Oct 12 14:09:39 PDT 2004

```Committed by: cworth

Update of /cvs/cairo/cairo/src
In directory gabe:/tmp/cvs-serv8321/src

Modified Files:
cairo_pen.c
Log Message:

* src/cairo_pen.c: Fix a few typos in pen vertex math description.

Index: cairo_pen.c
===================================================================
RCS file: /cvs/cairo/cairo/src/cairo_pen.c,v
retrieving revision 1.18
retrieving revision 1.19
diff -u -d -r1.18 -r1.19
--- cairo_pen.c	12 Oct 2004 19:29:30 -0000	1.18
+++ cairo_pen.c	12 Oct 2004 21:09:37 -0000	1.19
@@ -231,7 +231,7 @@

Thus the maximum value is

-     MAX[a*cos(t) + b*sin(t)] = (a*a + b*b)/sqrt(a^2 + b^2)
+     MAX[a*cos(t) + b*sin(t)] = (a^2 + b^2)/sqrt(a^2 + b^2)
= sqrt(a^2 + b^2)

@@ -253,7 +253,7 @@
Thus

r^2(t) = (a*cos(t) + b*sin(t))^2 + (c*cos(t) + d*sin(t))^2
-            = (a^2 + c^2)*cos(t) + (b^2 + d^2)*sin(t)
+            = (a^2 + c^2)*cos^2(t) + (b^2 + d^2)*sin^2(t)
+ 2*(a*b + c*d)*cos(t)*sin(t)

Now apply the double angle formulae (A) to (C) from above:
@@ -333,7 +333,7 @@

Find the extremum by differentiation wrt t and setting that to zero

-âˆ‚(EÂ²)/âˆ‚(t) = (1-cos(d))Â² (MÂ² - mÂ²) (-2 cos(t) sin(t))
+âˆ‚(EÂ²)/âˆ‚(t) = (1-cos(âˆ†))Â² (MÂ² - mÂ²) (-2 cos(t) sin(t))

0 = 2 cos (t) sin (t)
0 = sin (2t)

```