[gatest] Implement and use multi-vector reverse

This gives the resultant point the correct sign.  Though the projective
divide would take care of the sign, this makes reading the point a
little less confusing (still need to sort out automatic blade reversals
for the likes of e31).

ruamoko/gatest/main.r

@@ -89,7 +89,7 @@ main ()
 	MultiVector *origin = [alg group:3 values:origin_vals];
 
 	MultiVector *line = [plane1 wedge:plane2];
-	MultiVector *point = [[line dot:origin] product:line];
+	MultiVector *point = [[line dot:origin] product:[line reverse]];
 	printf ("plane1:%@\nplane2:%@\nline:%@\norigin:%@\n", plane1, plane2, line, origin);
 	printf ("point:%@\n", point);
 

ruamoko/gatest/multivector.h

@@ -23,6 +23,7 @@
 -(MultiVector *) wedge:(MultiVector *) rhs;
 -(MultiVector *) dot:(MultiVector *) rhs;
 -(MultiVector *) dual;
+-(MultiVector *) reverse;
 @end
 
 #endif//__multivector_h

ruamoko/gatest/multivector.r

@@ -198,4 +198,22 @@ static MultiVector *new_mv (Algebra *algebra, BasisLayout *layout)
 	}
 	return dual;
 }
+
+-(MultiVector *) reverse
+{
+	MultiVector *reverse = new_mv (algebra, nil);
+	for (int i = 0; i < num_components; i++) {
+		if (!components[i]) {
+			continue;
+		}
+		double c = components[i];
+		BasisBlade *b = [layout bladeAt:i];
+		int         g = [b grade];
+		unsigned    mask = [b mask];
+		double s = g & 2 ? -1 : 1;//FIXME do in BasisBlade?
+		int ind = [layout bladeIndex:mask];
+		reverse.components[ind] += s * c;
+	}
+	return reverse;
+}
 @end