void test12D() {
Point2D pt(1.0, 2.0);
Transform2D trans;
trans.TransformPoint(pt);
CHECK_INVARIANT(abs(pt.x - 1.0) < 1.e-8, "");
CHECK_INVARIANT(abs(pt.y - 2.0) < 1.e-8, "");
Point2D ref1(randNum(), randNum());
Point2D ref2(randNum(), randNum());
std::cout << "ref1: " << ref1 << " ref2: " << ref2 << "\n";
Point2D pt1(randNum(), randNum());
Point2D pt2(randNum(), randNum());
Point2D pt1o = pt1;
Point2D pt2o = pt2;
std::cout << "pt1: " << pt1 << " pt2: " << pt2 << "\n";
Transform2D t2d;
t2d.SetTransform(ref1, ref2, pt1, pt2);
t2d.TransformPoint(pt1);
t2d.TransformPoint(pt2);
// make sure pt1 overlaps ref1
Point2D dif1 = pt1 - ref1;
CHECK_INVARIANT(abs(dif1.x) < 1.e-8, "");
CHECK_INVARIANT(abs(dif1.y) < 1.e-8, "");
// now check that the angle between the two vectors (ref2 - ref1) and
// (pt2 - pt1) is zero
Point2D rvec = ref2 - ref1;
Point2D pvec = pt2 - pt1;
rvec.normalize();
pvec.normalize();
double pdot = rvec.dotProduct(pvec);
CHECK_INVARIANT(abs(pdot - 1.0) < 1.e-8, "");
// compute the reverse transform and make sure we are basically getting the
// identity
Transform2D tdi;
tdi.SetTransform(pt1o, pt2o, pt1, pt2);
tdi.TransformPoint(pt1);
tdi.TransformPoint(pt2);
CHECK_INVARIANT(ptEq(pt1, pt1o), "");
CHECK_INVARIANT(ptEq(pt2, pt2o), "");
// the following product should result in an identity matrix
tdi *= t2d;
tdi.TransformPoint(pt1);
tdi.TransformPoint(pt2);
CHECK_INVARIANT(ptEq(pt1, pt1o), "");
CHECK_INVARIANT(ptEq(pt2, pt2o), "");
Point2D npt1(1.0, 0.0);
Point2D npt2(5.0, 0.0);
Point2D opt1 = npt1;
Point2D opt2(1.0, 4.0);
Transform2D ntd;
ntd.SetTransform(npt1, M_PI / 2);
ntd.TransformPoint(npt1);
ntd.TransformPoint(npt2);
CHECK_INVARIANT(ptEq(npt1, opt1), "");
CHECK_INVARIANT(ptEq(npt2, opt2), "");
}
