72 lines
1.9 KiB
C++
72 lines
1.9 KiB
C++
//
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// Created by Иван Ильин on 09.11.2021.
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//
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#include <cmath>
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#include "Interpolation.h"
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#include "../Consts.h"
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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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}
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int integer = static_cast<int>(t);
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return (integer % 2) ? 1.0 - (t - integer) : (t - integer);
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}
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double Interpolation::Bezier(const Vec2D &p1, const Vec2D &p2, double t) {
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// TODO: implement bezier curve without finding the root of equation
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t = Interpolation::Linear(t);
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double h = Consts::EPS;
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double eps = Consts::EPS;
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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))) +
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(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 * Consts::PI * sin(Consts::PI * t) * dt;
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}
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double Interpolation::dBezier(const Vec2D &p1, const Vec2D &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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