svg-flatten: Add transform decomposition unit tests

svg-flatten/include/geom2d.hpp

@@ -41,8 +41,8 @@ namespace gerbolyze {
 
     class xform2d {
         public:
-            xform2d(double xx, double yx, double xy, double yy, double x0=0.0, double y0=0.0) :
-                xx(xx), yx(yx), xy(xy), yy(yy), x0(x0), y0(y0) {}
+            xform2d(double xx, double xy, double yx, double yy, double x0=0.0, double y0=0.0) :
+                xx(xx), xy(xy), x0(x0), yx(yx), yy(yy), y0(y0) {}
             
             xform2d() : xform2d(1.0, 0.0, 0.0, 1.0) {}
 
@@ -83,6 +83,20 @@ namespace gerbolyze {
                 return *this;
             }
 
+            xform2d &rotate(double theta) {
+                double s = sin(theta);
+                double c = cos(theta);
+                xform2d xf(c, -s, s, c);
+                transform(xf);
+                return *this;
+            }
+
+            xform2d &skew(double m) {
+                xform2d xf(1, m, 0, 1);
+                transform(xf);
+                return *this;
+            }
+
             xform2d &transform(const xform2d &other) {
                 double n_xx = other.xx * xx + other.yx * xy;
                 double n_yx = other.xx * yx + other.yx * yy;
@@ -112,22 +126,22 @@ namespace gerbolyze {
                 return dist_doc / sqrt(xx*xx + xy*xy);
             }
 
-            void decompose() {
+            std::tuple<double, double, double, double> decompose() {
                 /* FIXME unit tests, especially for degenerate cases! */
                 if (decomposed) {
-                    return;
+                    return {s_x, s_y, m, theta};
                 }
 
                 /* https://math.stackexchange.com/a/3521141 */
                 /* https://stackoverflow.com/a/70381885 */
-                /* xx yx x0
-                 * xy yy y0 */
-                s_x = sqrt(xx*xx + xy*xy);
+                /* xx xy x0
+                 * yx yy y0 */
+                s_x = sqrt(xx*xx + yx*yx);
 
-                if (xx == 0 && xy == 0) {
+                if (xx == 0 && yx == 0) {
                     theta = 0;
                 } else {
-                    theta = atan2(xy, xx);
+                    theta = atan2(yx, xx);
                 }
 
                 double f = (xx*yy - xy*yx);
@@ -135,16 +149,17 @@ namespace gerbolyze {
                 if (f == 0) {
                     m = 0;
                 } else {
-                    m = (xx*yx + yy*xy) / f;
+                    m = (xx*xy + yy*yx) / f;
                 }
 
-                f = xx + m*xy;
-                if (f == 0) {
-                    f = m*xx - xy;
-                    if (f == 0) {
+                f = xx + m*yx;
+                if (fabs(f) < 1e-12) {
+                    f = m*xx - yx;
+                    if (fabs(f) < 1e-12) {
                         s_y = 0;
+                    } else {
+                        s_y = xy*s_x / f;
                     }
-                    s_y = yx*s_x / f;
                 } else {
                     s_y = yy*s_x / f;
                 }
@@ -154,6 +169,7 @@ namespace gerbolyze {
                 f_max = fmax(s_x, b);
 
                 decomposed = true;
+                return {s_x, s_y, m, theta};
             }
 
             bool doc2phys_skew_ok(double dist_doc, double rel_tol, double abs_tol) {
@@ -280,6 +296,7 @@ namespace gerbolyze {
             }
 
             string dbg_str() {
+                decompose();
                 ostringstream os;
                 os << "xform2d< " << setw(5);
                 os << xx << ", " << xy << ", " << x0 << " / ";
@@ -291,9 +308,8 @@ namespace gerbolyze {
             }
 
         private:
-            double xx, yx,
-                   xy, yy,
-                   x0, y0;
+            double xx, xy, x0,
+                   yx, yy, y0;
             double theta, m, s_x, s_y;
             double f_min, f_max;
             bool decomposed = false;

svg-flatten/src/test/nopencv_test.cpp

@@ -7,6 +7,7 @@
 
 #include "util.h"
 #include "nopencv.hpp"
+#include "geom2d.hpp"
 
 #include <subprocess.h>
 #include <minunit.h>
@@ -330,6 +331,31 @@ MU_TEST(chain_approx_test_two_px_inv)         { chain_approx_test("testdata/two-
 MU_TEST(chain_approx_test_contour_tracing_demo_input) { chain_approx_test("testdata/contour_tracing_demo_input.png"); }
 
 
+MU_TEST(test_transform_decomposition) {
+    double scales[] = {0.1, 0.5, 0.9, 0.999999999, 1.0, 1.000000001, 1.1, 1.5, 2.0, 1000};
+    double ms[] = {0, -5.0, -1.0, -0.1, 0.1, 0.5, 1.0, 2.0, 5.0, 6.123, 100.0};
+    for (double &s_x : scales) {
+        for (double &s_y : scales) {
+            for (int i_theta=0; i_theta<25; i_theta++) {
+                double theta = i_theta * std::numbers::pi / 12.0;
+                for (double &m : ms) {
+                    xform2d xf;
+                    //cerr << endl << "testing s_x=" << s_x << ", s_y=" << s_y << ", m=" << m << ", theta=" << theta << endl;
+                    xf.rotate(theta).skew(m).scale(s_x, s_y);
+                    //cerr << "    -> " << xf.dbg_str() << endl;
+                    const auto [dec_s_x, dec_s_y, dec_m, dec_theta] = xf.decompose();
+                    mu_assert(fabs(s_x - dec_s_x) < 1e-9, "s_x incorrect");
+                    mu_assert(fabs(s_y - dec_s_y) < 1e-9, "s_y incorrect");
+                    mu_assert(fabs(m - dec_m) < 1e-9, "m incorrect");
+                    double a = dec_theta - theta + std::numbers::pi;
+                    mu_assert(fabs(a - floor(a/(2*std::numbers::pi)) * 2 * std::numbers::pi - std::numbers::pi) < 1e-12, "theta incorrect");
+                }
+            }
+        }
+    }
+}
+
+
 MU_TEST_SUITE(nopencv_contours_suite) {
     MU_RUN_TEST(test_complex_example_from_paper);
 
@@ -384,6 +410,8 @@ MU_TEST_SUITE(nopencv_contours_suite) {
     MU_RUN_TEST(chain_approx_test_two_px);
     MU_RUN_TEST(chain_approx_test_two_px_inv);
     MU_RUN_TEST(chain_approx_test_contour_tracing_demo_input);
+
+    MU_RUN_TEST(test_transform_decomposition);
 };
 
 int main(int argc, char **argv) {