fixed the rframe xforms.HEADmaster

also brought in the manpage.

1 files changed, 72 insertions, 16 deletions

diff --git a/rframe.c b/rframe.c
index 2f7c682..aee3c03 100644
--- a/rframe.c
+++ b/rframe.c
@@ -2,50 +2,106 @@
 #include <libc.h>
 #include <geometry.h>
 
+/*
+ * implicit identity origin rframes
+ *
+ * 	static RFrame IRF2 = {
+ * 		.p  = {0,0,1},
+ * 		.bx = {1,0,0},
+ * 		.by = {0,1,0},
+ * 	};
+ * 	
+ * 	static RFrame3 IRF3 = {
+ * 		.p  = {0,0,0,1},
+ * 		.bx = {1,0,0,0},
+ * 		.by = {0,1,0,0},
+ * 		.bz = {0,0,1,0},
+ * 	};
+ *
+ * these rframes are used on every xform to keep the points in the
+ * correct plane (i.e. with proper w values); they are written here as a
+ * reference for future changes. the bases are ignored since they turn
+ * into an unnecessary identity xform.
+ *
+ * the implicitness comes from the fact that using the _irf* filters
+ * makes the rframexform equivalent to:
+ * 	rframexform(invrframexform(p, IRF), rf);
+ * and the invrframexform to:
+ * 	rframexform(invrframexform(p, rf), IRF);
+ */
+
+static Point2
+_irfxform(Point2 p)
+{
+	p.w--;
+	return p;
+}
+
+static Point2
+_irfxform⁻¹(Point2 p)
+{
+	p.w++;
+	return p;
+}
+
+static Point3
+_irfxform3(Point3 p)
+{
+	p.w--;
+	return p;
+}
+
+static Point3
+_irfxform3⁻¹(Point3 p)
+{
+	p.w++;
+	return p;
+}
+
 Point2
 rframexform(Point2 p, RFrame rf)
 {
 	Matrix m = {
-		rf.bx.x, rf.bx.y, -dotvec2(rf.bx, rf.p),
-		rf.by.x, rf.by.y, -dotvec2(rf.by, rf.p),
+		rf.bx.x, rf.by.x, 0,
+		rf.bx.y, rf.by.y, 0,
 		0, 0, 1,
 	};
-	return xform(p, m);
+	invm(m);
+	return xform(subpt2(_irfxform⁻¹(p), rf.p), m);
 }
 
 Point3
 rframexform3(Point3 p, RFrame3 rf)
 {
 	Matrix3 m = {
-		rf.bx.x, rf.bx.y, rf.bx.z, -dotvec3(rf.bx, rf.p),
-		rf.by.x, rf.by.y, rf.by.z, -dotvec3(rf.by, rf.p),
-		rf.bz.x, rf.bz.y, rf.bz.z, -dotvec3(rf.bz, rf.p),
+		rf.bx.x, rf.by.x, rf.bz.x, 0,
+		rf.bx.y, rf.by.y, rf.bz.y, 0,
+		rf.bx.z, rf.by.z, rf.bz.z, 0,
 		0, 0, 0, 1,
 	};
-	return xform3(p, m);
+	invm3(m);
+	return xform3(subpt3(_irfxform3⁻¹(p), rf.p), m);
 }
 
 Point2
 invrframexform(Point2 p, RFrame rf)
 {
 	Matrix m = {
-		rf.bx.x, rf.bx.y, -dotvec2(rf.bx, rf.p),
-		rf.by.x, rf.by.y, -dotvec2(rf.by, rf.p),
+		rf.bx.x, rf.by.x, 0,
+		rf.bx.y, rf.by.y, 0,
 		0, 0, 1,
 	};
-	invm(m);
-	return xform(p, m);
+	return _irfxform(addpt2(xform(p, m), rf.p));
 }
 
 Point3
 invrframexform3(Point3 p, RFrame3 rf)
 {
 	Matrix3 m = {
-		rf.bx.x, rf.bx.y, rf.bx.z, -dotvec3(rf.bx, rf.p),
-		rf.by.x, rf.by.y, rf.by.z, -dotvec3(rf.by, rf.p),
-		rf.bz.x, rf.bz.y, rf.bz.z, -dotvec3(rf.bz, rf.p),
+		rf.bx.x, rf.by.x, rf.bz.x, 0,
+		rf.bx.y, rf.by.y, rf.bz.y, 0,
+		rf.bx.z, rf.by.z, rf.bz.z, 0,
 		0, 0, 0, 1,
 	};
-	invm3(m);
-	return xform3(p, m);
+	return _irfxform3(addpt3(xform3(p, m), rf.p));
 }