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/*
 * Copyright (C) 2023 Parisi Alessandro - [email protected]
 * This file is part of MaterialFX (https://github.com/palexdev/MaterialFX)
 *
 * MaterialFX is free software: you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License
 * as published by the Free Software Foundation; either version 3 of the License,
 * or (at your option) any later version.
 *
 * MaterialFX is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 * See the GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with MaterialFX. If not, see .
 */

package io.github.palexdev.mfxeffects.animations.motion;

import io.github.palexdev.mfxeffects.animations.base.Curve;

/**
 * A cubic polynomial mapping of the unit interval.
 * 
 * Implements third-order Bézier curves.
 * 

 * Video examples of various curves based on this:
 *  - Fast Linear To Slow Ease In
 * 
 - Ease
 * 
 - Ease In
 * 
 - Ease In To Linear
 * 
 - Ease In Sine
 * 
 - Ease In Quad
 * 
 - Ease In Cubic
 * 
 - Ease In Quart
 * 
 - Ease In Quint
 * 
 - Ease In Expo
 * 
 - Ease In Circ
 * 
 - Ease In Back
 * 
 - Ease Out
 * 
 - Linear To Ease Out
 * 
 - Ease Out Sine
 * 
 - Ease Out Quad
 * 
 - Ease Out Cubic
 * 
 - Ease Out Quart
 * 
 - Ease Out Quint
 * 
 - Ease Out Expo
 * 
 - Ease Out Circ
 * 
 - Ease Out Back
 * 
 - Ease In Out
 * 
 - Ease In Out Sine
 * 
 - Ease In Out Quad
 * 
 - Ease In Out Cubic
 * 
 - Ease In Out Quart
 * 
 - Ease In Out Quint
 * 
 - Ease In Out Expo
 * 
 - Ease In Out Circ
 * 
 - Ease In Out Back
 * 
 - Fast Out Slow In
 *  - Slow Middle
 */
public class Cubic extends Curve {
	private final double x1;
	private final double y1;
	private final double x2;
	private final double y2;

	private static final double CUBIC_ERROR_BOUND = 0.001;

	public Cubic(double x1, double y1, double x2, double y2) {
		this.x1 = x1;
		this.y1 = y1;
		this.x2 = x2;
		this.y2 = y2;
	}

	double elevateCubic(double a, double b, double m) {
		return 3 * a * (1 - m) * (1 - m) * m +
				3 * b * (1 - m) * m * m +
				m * m * m;
	}

	@Override
	public double curve(double t) {
		double start = 0.0;
		double end = 1.0;
		while (true) {
			final double midpoint = (start + end) / 2;
			final double estimate = elevateCubic(x1, x2, midpoint);
			if (Math.abs(t - estimate) < CUBIC_ERROR_BOUND) {
				return elevateCubic(y1, y2, midpoint);
			}
			if (estimate < t) {
				start = midpoint;
			} else {
				end = midpoint;
			}
		}
	}
}