ptrude/: cleanup and addition of comments (WIP)

- arc.fig: corrected formula for 2t
- path.c (corner): cleanup and added comments

ptrude/arc.fig

@@ -60,7 +60,7 @@ Single
 4 1 0 50 -1 18 18 0.0000 4 195 240 8505 7380 2t\001
 4 0 0 50 -1 18 18 0.0000 4 270 2085 9405 7200 (r-d)^2+u^2=r^2\001
 4 0 0 50 -1 18 18 0.0000 4 270 2610 9405 7650 (r-d)^2+v^2=(r+d)^2\001
-4 0 0 50 -1 18 18 0.0000 4 270 1530 9405 8100 2t = 2p+n*q\001
+4 0 0 50 -1 18 18 0.0000 4 270 2400 9405 8100 2t = 2*(p+(n+1)*q)\001
 4 0 0 50 -1 18 18 0.0000 4 210 915 4410 3105 ...+q+p\001
 4 1 0 50 -1 18 18 0.0000 4 210 180 4950 3555 q\001
 4 1 0 50 -1 18 18 0.0000 4 210 180 4635 3870 q\001

ptrude/path.c

@@ -95,20 +95,38 @@ static const struct vertex *add_vertex(struct path *path, double x, double y,
 static const struct vertex *corner(struct path *path, const struct vertex *a,
     const struct vertex *b, const struct vertex *c, double r, double d)
 {
+	/* points to vectors */
 	double ax = b->x-a->x;
 	double ay = b->y-a->y;
 	double bx = c->x-b->x;
 	double by = c->y-b->y;
+
+	/* vector length */
 	double aa = hypot(ax, ay);
 	double bb = hypot(bx, by);
+
+	/* dot and cross product */
 	double dp = ax*bx+ay*by; /* a * b = a*b*cos 2t */
 	double cp = ax*by-ay*bx; /* |a x b| = a*b*sin 2t */
-	double dd; /* "d" of the given vectors */
+	double dir = copysign(1, cp);
-	double tt, s;
+
-	double t2, p, q, ang;
+	/* see corner.fig */
-	double u, v;
+	double dd;	/* "d" of the given vectors */
-	double f, x, y;
+	double tt;	/* tan t */
-	int n, i;
+	double s;	/* distance between start of arc and corner */
+	double t2;	/* angle, t*2 */
+
+	/* see arc.fig */
+	double p;	/* half-angle of border side of border segment */
+	double q;	/* half-angle of connecting segment */
+	double u;	/* length of border side of border segment */
+	double v;	/* half-length of connecting segment */
+	int n;		/* number of connecting segments (0 if none) */
+
+	double f;	/* scale factor; various uses */
+	double ang;	/* current angle, for iteration */
+	double x, y;	/* current position; for iteration */
+	int i;		/* segment; for iteration */
 
 	/*
 	 * http://en.wikipedia.org/wiki/Dot_product
@@ -212,24 +230,18 @@ static const struct vertex *corner(struct path *path, const struct vertex *a,
 		n = (int) ceil((t2-2*(p+q))/(2*q));
 
 		/*
-		 * @@@ We should evenly distribute the slack, but that seems
+		 * @@@ We should evenly distribute the slack and try to pick a
-		 * difficult. For now, we just center the polygon.
+		 * smaller value for d, but that seems difficult.
+		 *
+		 * For now, we just center the polygon.
 		 */
 		q = (t2/2-p)/(n+1);
 
-		double dir = copysign(1, cp);
-#if 0
-		if (cp < 0) {
-//			t2 = -t2;
-			q = -q;
-			p = -p;
-		}
-#endif
-
 		if (n)
 			ang = p+q;
 		else
 			ang = t2/2;
+
 		u = tan(p)*(r-d);
 		v = tan(q)*(r-d);
 		f = (u+v)/aa;