hermet pushed a commit to branch master. http://git.enlightenment.org/core/efl.git/commit/?id=633202a0f93661d35a340dae692208dfcc792a41
commit 633202a0f93661d35a340dae692208dfcc792a41 Author: Wonki Kim <[email protected]> Date: Tue May 19 13:05:11 2020 +0900 ecore_anim: rework bezier curve function Summary: current cubic bezier function isn't accurate at sometime. to make it more accurate, this patch rework bezier curve by using a cardano's algorithm. (refer to https://pomax.github.io/bezierinfo/) Reviewers: Hermet, bu5hm4n Reviewed By: Hermet Subscribers: cedric, #reviewers, #committers Tags: #efl Differential Revision: https://phab.enlightenment.org/D11819 --- src/lib/ecore/ecore_anim.c | 137 ++++++++++++++++++++++++++++----------------- 1 file changed, 86 insertions(+), 51 deletions(-) diff --git a/src/lib/ecore/ecore_anim.c b/src/lib/ecore/ecore_anim.c index f2ec2d61c8..a5bde81ff6 100644 --- a/src/lib/ecore/ecore_anim.c +++ b/src/lib/ecore/ecore_anim.c @@ -626,68 +626,103 @@ _pos_map_spring(double pos, return _pos_map_sin((M_PI / 2.0) + (p2 * len)) * decay; } -static double -_cubic_bezier_a (double a1, double a2) +static inline double +cuberoot(double v) { - return 1.0 - 3.0 * a2 + 3.0 * a1; + if (v < 0.0) + return -pow(-v, 1. / 3.); + else + return pow(v, 1. / 3.); } static double -_cubic_bezier_b (double a1, double a2) +_bezier_t_get(double _x, double _x1, double _x2) { - return 3.0 * a2 - 6.0 * a1; -} + if (_x < 0.0 || _x > 1.0) return _x; + + // Cardano's algorithm + double\ + pa = _x - 0.0, + pb = _x - _x1, + pc = _x - _x2, + pd = _x - 1.0; + + double\ + a = 3*pa-6*pb+3*pc, + b = -3*pa+3*pb, + c = pa, + d = -pa+3*pb-3*pc+pd; + + a /= d; + b /= d; + c /= d; + + double\ + p = (3*b-a*a)/3.0, + p3 = p/3.0, + q = (2*a*a*a-9*a*b+27*c)/27.0, + q2 = q/2.0, + discriminant = q2*q2 + p3*p3*p3; + + double u1, v1, root1, root2, root3; + + if (discriminant < 0) + { + double\ + mp3 = -p/3.0, + mp33 = mp3*mp3*mp3, + r = sqrt(mp33), + t = -q / (2*r), + cosphi = t<-1.0 ? -1.0 : t>1.0 ? 1.0 : t, + phi = acos(cosphi), + crtr = cuberoot(r), + t1 = 2*crtr; + root1 = t1 * cos(phi/3.0) - a/3.0; + root2 = t1 * cos((phi+2*M_PI)/3.0) - a/3.0; + root3 = t1 * cos((phi+4*M_PI)/3.0) - a/3.0; + + if (root1 >= 0.0 && root1 <= 1.0) return root1; + if (root2 >= 0.0 && root2 <= 1.0) return root2; + if (root3 >= 0.0 && root3 <= 1.0) return root3; + } + else if (discriminant == 0) + { + u1 = q2 < 0 ? cuberoot(-q2) : -cuberoot(q2); + root1 = 2*u1 - a/3.0; + root2 = -u1 - a/3.0; -static double -_cubic_bezier_c(double a1) -{ - return 3.0 * a1; -} + if (root1 >= 0.0 && root1 <= 1.0) return root1; + if (root2 >= 0.0 && root2 <= 1.0) return root2; + } + else + { + double sd = sqrt(discriminant); + u1 = cuberoot(sd - q2); + v1 = cuberoot(sd + q2); + root1 = u1 - v1 - a/3.0; -static double -_cubic_bezier_calc(double t, - double a1, - double a2) -{ - return ((_cubic_bezier_a(a1, a2) * t + - _cubic_bezier_b(a1, a2)) * t + - _cubic_bezier_c(a1)) * t; -} + if (root1 >= 0.0 && root1 <= 1.0) return root1; + } -static double -_cubic_bezier_slope_get(double t, - double a1, - double a2) -{ - return 3.0 * _cubic_bezier_a(a1, a2) * t * t + - 2.0 * _cubic_bezier_b(a1, a2) * t + - _cubic_bezier_c(a1); + return _x; } static double -_cubic_bezier_t_get(double a, - double x1, - double x2) +_bezier_calc(double t, double y1, double y2) { -#define APPROXIMATE_RANGE(val) \ - ((((val) < 0.01) && ((val) > -0.01)) ? EINA_TRUE : EINA_FALSE) - - const int LIMIT = 100; - double current_slope; - double change; - double current_x; - double guess_t = a; - - for (int i = 0; i < LIMIT; i++) - { - current_slope = _cubic_bezier_slope_get(guess_t, x1, x2); - if (EINA_DBL_EQ(current_slope, 0.0)) return guess_t; - current_x = _cubic_bezier_calc(guess_t, x1, x2) - a; - change = current_x / current_slope; - guess_t -= change; - if (APPROXIMATE_RANGE(change)) break; - } - return guess_t; + double y0 = 0.0; + double y3 = 1.0; + + double u = 1.0 - t; + double t2 = t*t; + double t3 = t*t*t; + double u2 = u*u; + double u3 = u*u*u; + + return u3 * y0 + + 3.0 * u2 * t * y1 + + 3.0 * u * t2 * y2 + + t3 * y3; } static double @@ -700,7 +735,7 @@ _pos_map_cubic_bezier(double pos, if (EINA_DBL_EQ(x1, y1) && EINA_DBL_EQ(x2, y2)) return pos; - return _cubic_bezier_calc(_cubic_bezier_t_get(pos, x1, x2), y1, y2); + return _bezier_calc(_bezier_t_get(pos, x1, x2), y1, y2); } #define DBL_TO(Fp) eina_f32p32_double_to(Fp) --
