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Diffstat (limited to 'src/3rdparty/2geom/tests/bezier-utils-test.cpp')
| -rw-r--r-- | src/3rdparty/2geom/tests/bezier-utils-test.cpp | 333 |
1 files changed, 333 insertions, 0 deletions
diff --git a/src/3rdparty/2geom/tests/bezier-utils-test.cpp b/src/3rdparty/2geom/tests/bezier-utils-test.cpp new file mode 100644 index 0000000..6f95ccd --- /dev/null +++ b/src/3rdparty/2geom/tests/bezier-utils-test.cpp @@ -0,0 +1,333 @@ +#include "utest.h" +#include <glib.h> + +/* MenTaLguY disclaims all responsibility for this evil idea for testing + static functions. The main disadvantages are that we retain the + #define's and `using' directives of the included file. */ +#include "../bezier-utils.cpp" + +using Geom::Point; + +static bool range_approx_equal(double const a[], double const b[], unsigned len); + +/* (Returns false if NaN encountered.) */ +template<class T> +static bool range_equal(T const a[], T const b[], unsigned len) { + for (unsigned i = 0; i < len; ++i) { + if ( a[i] != b[i] ) { + return false; + } + } + return true; +} + +inline bool point_approx_equal(Geom::Point const &a, Geom::Point const &b, double const eps) +{ + using Geom::X; using Geom::Y; + return ( Geom_DF_TEST_CLOSE(a[X], b[X], eps) && + Geom_DF_TEST_CLOSE(a[Y], b[Y], eps) ); +} + +static inline double square(double const x) { + return x * x; +} + +/** Determine whether the found control points are the same as previously found on some developer's + machine. Doesn't call utest__fail, just writes a message to stdout for diagnostic purposes: + the most important test is that the root-mean-square of errors in the estimation are low rather + than that the control points found are the same. +**/ +static void compare_ctlpts(Point const est_b[], Point const exp_est_b[]) +{ + unsigned diff_mask = 0; + for (unsigned i = 0; i < 4; ++i) { + for (unsigned d = 0; d < 2; ++d) { + if ( fabs( est_b[i][d] - exp_est_b[i][d] ) > 1.1e-5 ) { + diff_mask |= 1 << ( i * 2 + d ); + } + } + } + if ( diff_mask != 0 ) { + printf("Warning: got different control points from previously-coded (diffs=0x%x).\n", + diff_mask); + printf(" Previous:"); + for (unsigned i = 0; i < 4; ++i) { + printf(" (%g, %g)", exp_est_b[i][0], exp_est_b[i][1]); // localizing ok + } + putchar('\n'); + printf(" Found: "); + for (unsigned i = 0; i < 4; ++i) { + printf(" (%g, %g)", est_b[i][0], est_b[i][1]); // localizing ok + } + putchar('\n'); + } +} + +static void compare_rms(Point const est_b[], double const t[], Point const d[], unsigned const n, + double const exp_rms_error) +{ + double sum_errsq = 0.0; + for (unsigned i = 0; i < n; ++i) { + Point const fit_pt = bezier_pt(3, est_b, t[i]); + Point const diff = fit_pt - d[i]; + sum_errsq += dot(diff, diff); + } + double const rms_error = sqrt( sum_errsq / n ); + UTEST_ASSERT( rms_error <= exp_rms_error + 1.1e-6 ); + if ( rms_error < exp_rms_error - 1.1e-6 ) { + /* The fitter code appears to have improved [or the floating point calculations differ + on this machine from the machine where exp_rms_error was calculated]. */ + printf("N.B. rms_error regression requirement can be decreased: have rms_error=%g.\n", rms_error); // localizing ok + } +} + +int main(int argc, char *argv[]) { + utest_start("bezier-utils.cpp"); + + UTEST_TEST("copy_without_nans_or_adjacent_duplicates") { + Geom::Point const src[] = { + Point(2., 3.), + Point(2., 3.), + Point(0., 0.), + Point(2., 3.), + Point(2., 3.), + Point(1., 9.), + Point(1., 9.) + }; + Point const exp_dest[] = { + Point(2., 3.), + Point(0., 0.), + Point(2., 3.), + Point(1., 9.) + }; + g_assert( G_N_ELEMENTS(src) == 7 ); + Point dest[7]; + struct tst { + unsigned src_ix0; + unsigned src_len; + unsigned exp_dest_ix0; + unsigned exp_dest_len; + } const test_data[] = { + /* src start ix, src len, exp_dest start ix, exp dest len */ + {0, 0, 0, 0}, + {2, 1, 1, 1}, + {0, 1, 0, 1}, + {0, 2, 0, 1}, + {0, 3, 0, 2}, + {1, 3, 0, 3}, + {0, 5, 0, 3}, + {0, 6, 0, 4}, + {0, 7, 0, 4} + }; + for (unsigned i = 0 ; i < G_N_ELEMENTS(test_data) ; ++i) { + tst const &t = test_data[i]; + UTEST_ASSERT( t.exp_dest_len + == copy_without_nans_or_adjacent_duplicates(src + t.src_ix0, + t.src_len, + dest) ); + UTEST_ASSERT(range_equal(dest, + exp_dest + t.exp_dest_ix0, + t.exp_dest_len)); + } + } + + UTEST_TEST("bezier_pt(1)") { + Point const a[] = {Point(2.0, 4.0), + Point(1.0, 8.0)}; + UTEST_ASSERT( bezier_pt(1, a, 0.0) == a[0] ); + UTEST_ASSERT( bezier_pt(1, a, 1.0) == a[1] ); + UTEST_ASSERT( bezier_pt(1, a, 0.5) == Point(1.5, 6.0) ); + double const t[] = {0.5, 0.25, 0.3, 0.6}; + for (unsigned i = 0; i < G_N_ELEMENTS(t); ++i) { + double const ti = t[i], si = 1.0 - ti; + UTEST_ASSERT( bezier_pt(1, a, ti) == si * a[0] + ti * a[1] ); + } + } + + UTEST_TEST("bezier_pt(2)") { + Point const b[] = {Point(1.0, 2.0), + Point(8.0, 4.0), + Point(3.0, 1.0)}; + UTEST_ASSERT( bezier_pt(2, b, 0.0) == b[0] ); + UTEST_ASSERT( bezier_pt(2, b, 1.0) == b[2] ); + UTEST_ASSERT( bezier_pt(2, b, 0.5) == Point(5.0, 2.75) ); + double const t[] = {0.5, 0.25, 0.3, 0.6}; + for (unsigned i = 0; i < G_N_ELEMENTS(t); ++i) { + double const ti = t[i], si = 1.0 - ti; + Point const exp_pt( si*si * b[0] + 2*si*ti * b[1] + ti*ti * b[2] ); + Point const pt(bezier_pt(2, b, ti)); + UTEST_ASSERT(point_approx_equal(pt, exp_pt, 1e-11)); + } + } + + Point const c[] = {Point(1.0, 2.0), + Point(8.0, 4.0), + Point(3.0, 1.0), + Point(-2.0, -4.0)}; + UTEST_TEST("bezier_pt(3)") { + UTEST_ASSERT( bezier_pt(3, c, 0.0) == c[0] ); + UTEST_ASSERT( bezier_pt(3, c, 1.0) == c[3] ); + UTEST_ASSERT( bezier_pt(3, c, 0.5) == Point(4.0, 13.0/8.0) ); + double const t[] = {0.5, 0.25, 0.3, 0.6}; + for (unsigned i = 0; i < G_N_ELEMENTS(t); ++i) { + double const ti = t[i], si = 1.0 - ti; + UTEST_ASSERT( LInfty( bezier_pt(3, c, ti) + - ( si*si*si * c[0] + + 3*si*si*ti * c[1] + + 3*si*ti*ti * c[2] + + ti*ti*ti * c[3] ) ) + < 1e-4 ); + } + } + + struct Err_tst { + Point pt; + double u; + double err; + } const err_tst[] = { + {c[0], 0.0, 0.0}, + {Point(4.0, 13.0/8.0), 0.5, 0.0}, + {Point(4.0, 2.0), 0.5, 9.0/64.0}, + {Point(3.0, 2.0), 0.5, 1.0 + 9.0/64.0}, + {Point(6.0, 2.0), 0.5, 4.0 + 9.0/64.0}, + {c[3], 1.0, 0.0}, + }; + + UTEST_TEST("compute_max_error_ratio") { + Point d[G_N_ELEMENTS(err_tst)]; + double u[G_N_ELEMENTS(err_tst)]; + for (unsigned i = 0; i < G_N_ELEMENTS(err_tst); ++i) { + Err_tst const &t = err_tst[i]; + d[i] = t.pt; + u[i] = t.u; + } + g_assert( G_N_ELEMENTS(u) == G_N_ELEMENTS(d) ); + unsigned max_ix = ~0u; + double const err_ratio = compute_max_error_ratio(d, u, G_N_ELEMENTS(d), c, 1.0, &max_ix); + UTEST_ASSERT( fabs( sqrt(err_tst[4].err) - err_ratio ) < 1e-12 ); + UTEST_ASSERT( max_ix == 4 ); + } + + UTEST_TEST("chord_length_parameterize") { + /* n == 2 */ + { + Point const d[] = {Point(2.9415, -5.8149), + Point(23.021, 4.9814)}; + double u[G_N_ELEMENTS(d)]; + double const exp_u[] = {0.0, 1.0}; + g_assert( G_N_ELEMENTS(u) == G_N_ELEMENTS(exp_u) ); + chord_length_parameterize(d, u, G_N_ELEMENTS(d)); + UTEST_ASSERT(range_equal(u, exp_u, G_N_ELEMENTS(exp_u))); + } + + /* Straight line. */ + { + double const exp_u[] = {0.0, 0.1829, 0.2105, 0.2105, 0.619, 0.815, 0.999, 1.0}; + unsigned const n = G_N_ELEMENTS(exp_u); + Point d[n]; + double u[n]; + Point const a(-23.985, 4.915), b(4.9127, 5.203); + for (unsigned i = 0; i < n; ++i) { + double bi = exp_u[i], ai = 1.0 - bi; + d[i] = ai * a + bi * b; + } + chord_length_parameterize(d, u, n); + UTEST_ASSERT(range_approx_equal(u, exp_u, n)); + } + } + + /* Feed it some points that can be fit exactly with a single bezier segment, and see how + well it manages. */ + Point const src_b[4] = {Point(5., -3.), + Point(8., 0.), + Point(4., 2.), + Point(3., 3.)}; + double const t[] = {0.0, .001, .03, .05, .09, .13, .18, .25, .29, .33, .39, .44, + .51, .57, .62, .69, .75, .81, .91, .93, .97, .98, .999, 1.0}; + unsigned const n = G_N_ELEMENTS(t); + Point d[n]; + for (unsigned i = 0; i < n; ++i) { + d[i] = bezier_pt(3, src_b, t[i]); + } + Point const tHat1(unit_vector( src_b[1] - src_b[0] )); + Point const tHat2(unit_vector( src_b[2] - src_b[3] )); + + UTEST_TEST("generate_bezier") { + Point est_b[4]; + generate_bezier(est_b, d, t, n, tHat1, tHat2, 1.0); + + compare_ctlpts(est_b, src_b); + + /* We're being unfair here in using our t[] rather than best t[] for est_b: we + may over-estimate RMS of errors. */ + compare_rms(est_b, t, d, n, 1e-8); + } + + UTEST_TEST("sp_bezier_fit_cubic_full") { + Point est_b[4]; + int splitpoints[2]; + gint const succ = sp_bezier_fit_cubic_full(est_b, splitpoints, d, n, tHat1, tHat2, square(1.2), 1); + UTEST_ASSERT( succ == 1 ); + + Point const exp_est_b[4] = { + Point(5.000000, -3.000000), + Point(7.5753, -0.4247), + Point(4.77533, 1.22467), + Point(3, 3) + }; + compare_ctlpts(est_b, exp_est_b); + + /* We're being unfair here in using our t[] rather than best t[] for est_b: we + may over-estimate RMS of errors. */ + compare_rms(est_b, t, d, n, .307911); + } + + UTEST_TEST("sp_bezier_fit_cubic") { + Point est_b[4]; + gint const succ = sp_bezier_fit_cubic(est_b, d, n, square(1.2)); + UTEST_ASSERT( succ == 1 ); + + Point const exp_est_b[4] = { + Point(5.000000, -3.000000), + Point(7.57134, -0.423509), + Point(4.77929, 1.22426), + Point(3, 3) + }; + compare_ctlpts(est_b, exp_est_b); + +#if 1 /* A change has been made to right_tangent. I believe that usually this change + will result in better fitting, but it won't do as well for this example where + we happen to be feeding a t=0.999 point to the fitter. */ + printf("TODO: Update this test case for revised right_tangent implementation.\n"); + /* In particular, have a test case to show whether the new implementation + really is likely to be better on average. */ +#else + /* We're being unfair here in using our t[] rather than best t[] for est_b: we + may over-estimate RMS of errors. */ + compare_rms(est_b, t, d, n, .307983); +#endif + } + + return !utest_end(); +} + +/* (Returns false if NaN encountered.) */ +static bool range_approx_equal(double const a[], double const b[], unsigned const len) { + for (unsigned i = 0; i < len; ++i) { + if (!( fabs( a[i] - b[i] ) < 1e-4 )) { + return false; + } + } + return true; +} + +/* + Local Variables: + mode:c++ + c-file-style:"stroustrup" + c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) + indent-tabs-mode:nil + fill-column:99 + End: +*/ +// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : |