Various coordinate transform corrections in overlap.c

- solidify/face.h (struct matrix), solidify/face.c (read_file): also record
  the face's center
- solidify/overlap.c (point): reference faces to the screen center
- solidify/overlap.c (point): use correct model coordinates for z0
  calculation

solidify/face.c

@@ -75,6 +75,9 @@ static struct face *read_file(const char *name)
 	f->sx = f->a->max_x-f->a->min_x+1;
 	f->sy = f->a->max_y-f->a->min_y+1;
 
+	f->cx = (f->a->min_x+f->a->max_x)/2;
+	f->cy = (f->a->min_y+f->a->max_y)/2;
+
 	h = make_histo(f->a);
 	f->z_ref = f->a->min_z+median(h);
 	free_histo(h);

solidify/face.h

@@ -32,6 +32,7 @@ struct matrix {
 struct face {
 	struct array *a;
 	int sx, sy;	/* size */
+	int cx, cy;	/* center */
 	int z_ref;
 	double fx, fy;	/* inclination factor */
 	struct matrix m;

solidify/overlap.c

@@ -83,20 +83,32 @@ static double zmix(struct face *f, double x, double y)
 }
 
 
+/*
+ * Coordinate transformations, on the example of the x coordinate:
+ *
+ * - the x coordinate runs from 0 to sx(s)-1
+ * - since we work relative to the screen center, this becomes x-sx(s)/2
+ *   This is what we perform the coordinate transform on.
+ * - our model runs from min_x to max_x. Its center is at cx.
+ */
+
 static void point(const struct solid *s, int x, int y, guchar *p)
 {
 	double za, zb, z;
-	int xa = x+s->a->a->min_x;
+	int xa, xb, ya, yb;
-	int ya = y+s->a->a->min_y;
+	double xaf, xbf, yaf, ybf;
-	int yb = sy(s)-1-y+s->a->a->min_y;
 
-	za = zmix(s->a,
+	xa = x-sx(s)/2;
-	    xa*s->a->m.a[0][0]+ya*s->a->m.a[0][1]+s->a->m.b[0],
+	ya = y-sy(s)/2;
-	    xa*s->a->m.a[1][0]+ya*s->a->m.a[1][1]+s->a->m.b[1]);
+	xaf = xa*s->a->m.a[0][0]+ya*s->a->m.a[0][1]+s->a->m.b[0]+s->a->cx;
+	yaf = xa*s->a->m.a[1][0]+ya*s->a->m.a[1][1]+s->a->m.b[1]+s->a->cy;
+	za = zmix(s->a, xaf, yaf);
 
-	zb = zmix(s->b,
+	xb = x-sx(s)/2;
-	    xa*s->b->m.a[0][0]+yb*s->b->m.a[0][1]+s->b->m.b[0],
+	yb = (sy(s)-1)/2-y;
-	    xa*s->b->m.a[1][0]+yb*s->b->m.a[1][1]+s->b->m.b[1]);
+	xbf = xb*s->b->m.a[0][0]+yb*s->b->m.a[0][1]+s->b->m.b[0]+s->b->cx;
+	ybf = xb*s->b->m.a[1][0]+yb*s->b->m.a[1][1]+s->b->m.b[1]+s->b->cy;
+	zb = zmix(s->b, xbf, ybf);
 
 	if (za == UNDEF_F && zb == UNDEF_F)
 		return;
@@ -125,8 +137,8 @@ static void point(const struct solid *s, int x, int y, guchar *p)
 	}
 
 	z = za;
-	za -= face_z0(s->a, xa, ya);
+	za -= face_z0(s->a, xaf, yaf);
-	zb -= face_z0(s->b, xa, yb);
+	zb -= face_z0(s->b, xbf, ybf);
 
 	if (za+zb < -s->dist) {
 		p[0] = 0;