cameo: detect and adjust handedness

- cameo/path.h, cameo/path.c (offset_point, path_offset): added "left"
  argument to indicate the handedness
- cameo/path.h, cameo/path.c (path_tool_is_left): new function to determine
  which way the path turns
- cameo/cameo.c: auto-detect handedness and instruct path_offset accordingly

cameo/cameo.c

@@ -32,6 +32,7 @@ int main(int argc, char **argv)
 	char *in = NULL, *out = NULL;
 	double r;
 	struct path *paths;
+	int left;
 
 	switch (argc) {
 	case 4:
@@ -50,14 +51,13 @@ int main(int argc, char **argv)
 
 /*
  * To do:
- * - auto-detect orientation
  * - handle multiple paths
- * - instead of reversing the path, reverse the handedness
  */
 	paths = gnuplot_read(in, r);
 	assert(!paths->next); /* we don't handle this yet */
-	paths = path_reverse(paths);
-	paths = path_offset(paths, 1);
+//	paths = path_reverse(paths);
+	left = path_tool_is_left(paths);
+	paths = path_offset(paths, left, 1);
 	gnuplot_write(out, paths);
 	return 0;
 }

cameo/path.c

@@ -99,7 +99,7 @@ struct path *path_reverse(const struct path *path)
 
 
 static struct point *offset_point(const struct point *a, const struct point *b,
-    const struct point *c, double off)
+    const struct point *c, double off, int left)
 {
 	double ax, ay, bx, by;
 	double aa, bb;
@@ -113,8 +113,13 @@ static struct point *offset_point(const struct point *a, const struct point *b,
 
 	aa = hypot(ax, ay);
 	bb = hypot(bx, by);
-	nx = -(ay/aa+by/bb);
-	ny = ax/aa+bx/bb;
+	if (left) {
+		nx = -(ay/aa+by/bb);
+		ny = ax/aa+bx/bb;
+	} else {
+		nx = ay/aa+by/bb;
+		ny = -(ax/aa+bx/bb);
+	}
 
 	nx *= off;
 	ny *= off;
@@ -143,6 +148,53 @@ static int left_turn(const struct point *a, const struct point *b,
 }
 
 
+/*
+ * Angle in counter-clockwise direction to turn at point B when coming from A
+ * in order to face towards C.
+ */
+
+static double angle(const struct point *a, const struct point *b,
+    const struct point *c)
+{
+	double ax, ay, bx, by;
+	double aa, bb;
+	double angle;
+
+	ax = b->x-a->x;
+	ay = b->y-a->y;
+	bx = c->x-b->x;
+	by = c->y-b->y;
+
+	aa = hypot(ax, ay);
+	bb = hypot(bx, by);
+
+	angle = acos((ax*bx+ay*by)/aa/bb)/M_PI*180.0;
+
+	return (ax*by-ay*bx) >= 0 ? angle : -angle;
+}
+
+
+/*
+ * If we predominantly turn to the right, then the tool must be on the
+ * left-hand side. Otherwise, it's on the right.
+ */
+
+int path_tool_is_left(const struct path *path)
+{
+	const struct point *prev, *p, *next;
+	double a = 0;
+
+	assert(path_is_closed(path));
+	prev = path->first;
+	for (p = path->first->next; p; p = p->next) {
+		next = p->next ? p->next : path->first->next;
+		a += angle(prev, p, next);
+		prev = p;
+	}
+	return a < 0;
+}
+
+
 /*
  * http://www.makecnc.com/bones.jpg
  */
@@ -176,7 +228,7 @@ static struct point *dog_point(const struct point *edge,
  * 6 o'clock to 12 o'clock, the tool would be at 9 o'clock.
  */
 
-struct path *path_offset(const struct path *path, int notch)
+struct path *path_offset(const struct path *path, int left, int notch)
 {
 	struct path *new;
 	const struct point *prev, *p, *next;
@@ -188,8 +240,8 @@ struct path *path_offset(const struct path *path, int notch)
 	prev = path->first;
 	for (p = path->first->next; p; p = p->next) {
 		next = p->next ? p->next : path->first->next;
-		n = offset_point(prev, p, next, path->r_tool);
-		dog = notch && left_turn(prev, p, next);
+		n = offset_point(prev, p, next, path->r_tool, left);
+		dog = notch && left_turn(prev, p, next) == left;
 		if (dog)
 			n2 = clone_point(n);
 		path_add_point(new, n);

cameo/path.h

@@ -30,7 +30,9 @@ struct path {
 struct path *path_new(double r_tool);
 void path_add(struct path *path, double x, double y, double z);
 struct path *path_reverse(const struct path *path);
-struct path *path_offset(const struct path *path, int notch);
+int path_direction(const struct path *path);
+int path_tool_is_left(const struct path *path);
+struct path *path_offset(const struct path *path, int left, int notch);
 void path_free(struct path *path);
 
 #endif /* !PATH_H */