From 5c9e7d5e5207be46a12601981f8acf0a5c1a7596 Mon Sep 17 00:00:00 2001
From: Werner Almesberger <werner@openmoko.org>
Date: Mon, 1 Nov 2010 16:42:32 -0300
Subject: [PATCH] Corrected math for offsets to work also for angles different
 from 90 degrees.

- cameo/path.c (offset_point): calculation assumed the normals were
  linearly independent. Replaced it with corrected version.
---
 cameo/path.c | 13 +++++++++++--
 1 file changed, 11 insertions(+), 2 deletions(-)

diff --git a/cameo/path.c b/cameo/path.c
index 88f4289..65d5294 100644
--- a/cameo/path.c
+++ b/cameo/path.c
@@ -104,6 +104,7 @@ static struct point *offset_point(const struct point *a, const struct point *b,
 	double ax, ay, bx, by;
 	double aa, bb;
 	double nx, ny;
+	double angle, f;
 	struct point *p;
 
 	ax = b->x-a->x;
@@ -113,6 +114,7 @@ static struct point *offset_point(const struct point *a, const struct point *b,
 
 	aa = hypot(ax, ay);
 	bb = hypot(bx, by);
+
 	if (left) {
 		nx = -(ay/aa+by/bb);
 		ny = ax/aa+bx/bb;
@@ -121,8 +123,15 @@ static struct point *offset_point(const struct point *a, const struct point *b,
 		ny = -(ax/aa+bx/bb);
 	}
 
-	nx *= off;
-	ny *= off;
+	/* angle between AB and BC */
+	angle = acos(-(ax*bx+ay*by)/aa/bb);
+
+	/* multiplier for combination of normal vectors */
+	f = off/sin(angle/2);
+	f /= hypot(nx, ny);
+
+	nx *= f;
+	ny *= f;
 
 	p = alloc_type(struct point);
 	p->x = b->x+nx;