87 lines
2.3 KiB
C
87 lines
2.3 KiB
C
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// Created by Иван Ильин on 26.01.2021.
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//
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#ifndef ENGINE_INTERPOLATION_H
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#define ENGINE_INTERPOLATION_H
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#include "../utils/Point4D.h"
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#include <cmath>
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namespace Interpolation {
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static double Linear(double t);
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static double Cos(double t);
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static double Bezier(const Point4D& p1, const Point4D& p2, double t);
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static double Bouncing(double t);
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static double dLinear(double t, double dt);
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static double dCos(double t, double dt);
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static double dBezier(const Point4D& p1, const Point4D& p2, double t, double dt);
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static double dBouncing(double t, double dt);
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};
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double Interpolation::Linear(double t) {
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if(t < 0)
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t = -t;
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return ((int)trunc(t) % 2) ? 1.0 - (t-trunc(t)) : (t-trunc(t));
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}
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double Interpolation::Cos(double t) {
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return 0.5*(1 - cos(M_PI*Interpolation::Linear(t)));
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}
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double Interpolation::Bezier(const Point4D &p1, const Point4D &p2, double t) {
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t = Interpolation::Linear(t);
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double h = 0.000001;
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double eps = 0.000001;
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// We are trying to find 's' when px = t
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auto f = [=](double s){
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return 3.0*(1.0-s)*(1.0-s)*s*p1.x() + 3.0*(1.0-s)*s*s*p2.x() + s*s*s - t;
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};
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// Using found 's' we will calculate resulting py
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auto py = [=](double s){
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return 3.0*(1.0-s)*(1.0-s)*s*p1.y() + 3.0*(1.0-s)*s*s*p2.y() + s*s*s;
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};
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auto df = [=](double s){
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return (f(s+h) - f(s-h))/(2.0*h);
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};
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// Newton method
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double s1 = 0.0, s2 = 0.5;
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int i = 0;
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while(std::abs(s1 - s2) > eps) {
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s1 = s2;
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s2 = s1 - f(s1) / df(s1);
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i++;
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}
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return py(s1);
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}
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double Interpolation::Bouncing(double t) {
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t = Interpolation::Linear(t);
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return 0.5*(1.0/(1.0 + exp(10.0*(-4.0*t+0.8))) + (1.0 + 2.5*sin(50.0*(t - 1.0/3.0))*exp(-7.0*t))/(1.0+exp(10.0*(-15.0*t + 3.1))));
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}
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double Interpolation::dLinear(double t, double dt) {
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return ((int)trunc(t) % 2) ? -dt : dt;
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}
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double Interpolation::dCos(double t, double dt) {
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return 0.5*M_PI*sin(M_PI*t)*dt;
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}
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double Interpolation::dBezier(const Point4D &p1, const Point4D &p2, double t, double dt) {
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return Interpolation::Bezier(p1, p2, t + dt) - Interpolation::Bezier(p1, p2, t);
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}
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double Interpolation::dBouncing(double t, double dt) {
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return Bouncing(t + dt) - Bouncing(t);
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}
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#endif //INC_3DZAVR_INTERPOLATION_H
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