All the cool animation curves from `CAMediaTimingFunction` but not limited to use with CoreAnimation. See what you can do with cubic Bezier curves here: http://netcetera.org/camtf-playground.html To get started just "Download Gist", throw the .h and .m fi

All the cool animation curves from `CAMediaTimingFunction` but not limited to use with CoreAnimation. See what you can do with cubic Bezier curves here: http://netcetera.org/camtf-playground.html To get started just "Download Gist", throw the .h and .m files into your Xcode project and you're good to go!

	//
	// RSTimingFunction.m
	//
	// Created by Raphael Schaad https://github.com/raphaelschaad on 2013-09-28.
	// This is free and unencumbered software released into the public domain.
	// The cubic Bezier math code is licensed under its original copyright notice included below.
	// You can use this code (e.g. in your iOS project) without worries as long as you don't remove that notice.
	//


	#import "RSTimingFunction.h"
	#include <tgmath.h> // type generic math, yo: http://en.wikipedia.org/wiki/Tgmath.h#tgmath.h


	// Same values as `CAMediaTimingFunction` defines, so they can be used interchangeably.
	NSString * const kRSTimingFunctionLinear = @"linear";
	NSString * const kRSTimingFunctionEaseIn = @"easeIn";
	NSString * const kRSTimingFunctionEaseOut = @"easeOut";
	NSString * const kRSTimingFunctionEaseInEaseOut = @"easeInEaseOut";
	NSString * const kRSTimingFunctionDefault = @"default";


	// Replicate exact same curves as `CAMediaTimingFunction` defines.
	static const CGPoint kLinearP1 = {0.0, 0.0};
	static const CGPoint kLinearP2 = {1.0, 1.0};
	static const CGPoint kEaseInP1 = {0.42, 0.0};
	static const CGPoint kEaseInP2 = {1.0, 1.0};
	static const CGPoint kEaseOutP1 = {0.0, 0.0};
	static const CGPoint kEaseOutP2 = {0.58, 1.0};
	static const CGPoint kEaseInEaseOutP1 = {0.42, 0.0};
	static const CGPoint kEaseInEaseOutP2 = {0.58, 1.0};
	static const CGPoint kDefaultP1 = {0.25, 0.1};
	static const CGPoint kDefaultP2 = {0.25, 1.0};


	// NSCoding
	static NSString * const kControlPoint1Key = @"controlPoint1";
	static NSString * const kControlPoint2Key = @"controlPoint2";
	static NSString * const kDurationKey = @"duration";


	// Internal constants
	static const NSTimeInterval kDurationDefault = 1.0;


	// For once use private ivars instead of properties for code readability (also omit leading underscore) and to avoid performance hits.
	@interface RSTimingFunction ()
	{
	// Polynomial coefficients
	CGFloat ax;
	CGFloat bx;
	CGFloat cx;

	CGFloat ay;
	CGFloat by;
	CGFloat cy;
	}
	@end


	@implementation RSTimingFunction

	#pragma mark - Accessors

	@synthesize controlPoint1 = p1;

	- (void)setControlPoint1:(CGPoint)controlPoint1
	{
	if (!CGPointEqualToPoint(p1, [[self class] normalizedPoint:controlPoint1])) {
	p1 = controlPoint1;

	[self calculatePolynomialCoefficients];
	}
	}


	@synthesize controlPoint2 = p2;

	- (void)setControlPoint2:(CGPoint)controlPoint2
	{
	if (!CGPointEqualToPoint(p2, [[self class] normalizedPoint:controlPoint2])) {
	p2 = controlPoint2;

	[self calculatePolynomialCoefficients];
	}
	}


	@synthesize duration = dur;

	- (void)setDuration:(NSTimeInterval)duration
	{
	// Only allow non-negative durations.
	duration = MAX(0.0, duration);
	if (dur != duration) {
	dur = duration;
	}
	}


	#pragma mark - Life Cycle

	// Privat designated initializer
	- (instancetype)initWithControlPoint1:(CGPoint)controlPoint1 controlPoint2:(CGPoint)controlPoint2 duration:(NSTimeInterval)duration
	{
	self = [super init];
	if (self) {
	// Don't initialize control points through setter to avoid triggering `-calculatePolynomicalCoefficients` unnecessarily twice.
	p1 = [[self class] normalizedPoint:controlPoint1];
	p2 = [[self class] normalizedPoint:controlPoint2];

	// Manually initialize polynomial coefficients with newly set control points.
	[self calculatePolynomialCoefficients];

	// Use setter to leverage its value sanitanization.
	self.duration = duration;
	}
	return self;
	}


	- (instancetype)initWithName:(NSString *)name
	{
	CGPoint controlPoint1 = [[self class] controlPoint1ForTimingFunctionWithName:name];
	CGPoint controlPoint2 = [[self class] controlPoint2ForTimingFunctionWithName:name];
	return [self initWithControlPoint1:controlPoint1 controlPoint2:controlPoint2];
	}


	+ (instancetype)timingFunctionWithName:(NSString *)name
	{
	return [[self alloc] initWithName:name];
	}


	- (instancetype)initWithControlPoint1:(CGPoint)controlPoint1 controlPoint2:(CGPoint)controlPoint2
	{
	return [self initWithControlPoint1:controlPoint1 controlPoint2:controlPoint2 duration:kDurationDefault];
	}


	+ (instancetype)timingFunctionWithControlPoint1:(CGPoint)controlPoint1 controlPoint2:(CGPoint)controlPoint2
	{
	return [[self alloc] initWithControlPoint1:controlPoint1 controlPoint2:controlPoint2];
	}


	#pragma mark - NSObject Method Overrides
	#pragma mark Describing Objects

	- (NSString *)description
	{
	NSString *description = [super description];

	description = [description stringByAppendingFormat:@" controlPoint1 = %@;", NSStringFromCGPoint(self.controlPoint1)];
	description = [description stringByAppendingFormat:@" controlPoint2 = %@;", NSStringFromCGPoint(self.controlPoint2)];
	description = [description stringByAppendingFormat:@" duration = %f;", self.duration];

	return description;
	}


	- (NSString *)debugDescription
	{
	NSString *debugDescription = [self description];

	debugDescription = [debugDescription stringByAppendingFormat:@" ax = %f;", ax];
	debugDescription = [debugDescription stringByAppendingFormat:@" bx = %f;", bx];
	debugDescription = [debugDescription stringByAppendingFormat:@" cx = %f;", cx];

	debugDescription = [debugDescription stringByAppendingFormat:@" ay = %f;", ay];
	debugDescription = [debugDescription stringByAppendingFormat:@" by = %f;", by];
	debugDescription = [debugDescription stringByAppendingFormat:@" cy = %f;", cy];

	return debugDescription;
	}


	#pragma mark - NSCoding Protocol

	- (id)initWithCoder:(NSCoder *)decoder
	{
	CGPoint controlPoint1 = [decoder decodeCGPointForKey:kControlPoint1Key];
	CGPoint controlPoint2 = [decoder decodeCGPointForKey:kControlPoint2Key];
	NSTimeInterval duration = [decoder decodeDoubleForKey:kDurationKey];

	return [self initWithControlPoint1:controlPoint1 controlPoint2:controlPoint2 duration:duration];
	}


	- (void)encodeWithCoder:(NSCoder *)encoder
	{
	[encoder encodeCGPoint:self.controlPoint1 forKey:kControlPoint1Key];
	[encoder encodeCGPoint:self.controlPoint2 forKey:kControlPoint2Key];
	[encoder encodeDouble:self.duration forKey:kDurationKey];
	}


	#pragma mark - Public Methods

	- (CGFloat)valueForX:(CGFloat)x
	{
	CGFloat epsilon = [self epsilon];
	CGFloat xSolved = [self solveCurveX:x epsilon:epsilon];
	CGFloat y = [self sampleCurveY:xSolved];
	return y;
	}


	#pragma mark - Private Methods
	#pragma mark Cubic Bezier Math

	// Cubic Bezier math code is based on WebCore (WebKit)
	// http://opensource.apple.com/source/WebCore/WebCore-955.66/platform/graphics/UnitBezier.h
	// http://opensource.apple.com/source/WebCore/WebCore-955.66/page/animation/AnimationBase.cpp

	/*
	* Copyright (C) 2007, 2008, 2009 Apple Inc. All rights reserved.
	*
	* Redistribution and use in source and binary forms, with or without
	* modification, are permitted provided that the following conditions
	* are met:
	*
	* 1. Redistributions of source code must retain the above copyright
	* notice, this list of conditions and the following disclaimer.
	* 2. Redistributions in binary form must reproduce the above copyright
	* notice, this list of conditions and the following disclaimer in the
	* documentation and/or other materials provided with the distribution.
	* 3. Neither the name of Apple Computer, Inc. ("Apple") nor the names of
	* its contributors may be used to endorse or promote products derived
	* from this software without specific prior written permission.
	*
	* THIS SOFTWARE IS PROVIDED BY APPLE AND ITS CONTRIBUTORS "AS IS" AND ANY
	* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
	* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
	* DISCLAIMED. IN NO EVENT SHALL APPLE OR ITS CONTRIBUTORS BE LIABLE FOR ANY
	* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
	* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
	* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
	* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
	* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
	* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	*/


	- (CGFloat)epsilon
	{
	// Higher precision in the timing function for longer duration to avoid ugly discontinuities
	return 1.0 / (200.0 * dur);
	}


	- (void)calculatePolynomialCoefficients
	{
	// Implicit first and last control points are (0,0) and (1,1).
	cx = 3.0 * p1.x;
	bx = 3.0 * (p2.x - p1.x) - cx;
	ax = 1.0 - cx - bx;

	cy = 3.0 * p1.y;
	by = 3.0 * (p2.y - p1.y) - cy;
	ay = 1.0 - cy - by;
	}


	- (CGFloat)sampleCurveX:(CGFloat)t
	{
	// 'ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
	return ((ax * t + bx) * t + cx) * t;
	}


	- (CGFloat)sampleCurveY:(CGFloat)t
	{
	return ((ay * t + by) * t + cy) * t;
	}


	- (CGFloat)sampleCurveDerivativeX:(CGFloat)t
	{
	return (3.0 * ax * t + 2.0 * bx) * t + cx;
	}


	// Given an x value, find a parametric value it came from.
	- (CGFloat)solveCurveX:(CGFloat)x epsilon:(CGFloat)epsilon
	{
	CGFloat t0;
	CGFloat t1;
	CGFloat t2;
	CGFloat x2;
	CGFloat d2;
	NSUInteger i;

	// First try a few iterations of Newton's method -- normally very fast.
	for (t2 = x, i = 0; i < 8; i++) {
	x2 = [self sampleCurveX:t2] - x;
	if (fabs(x2) < epsilon) {
	return t2;
	}
	d2 = [self sampleCurveDerivativeX:t2];
	if (fabs(d2) < 1e-6) {
	break;
	}
	t2 = t2 - x2 / d2;
	}

	// Fall back to the bisection method for reliability.
	t0 = 0.0;
	t1 = 1.0;
	t2 = x;

	if (t2 < t0) {
	return t0;
	}
	if (t2 > t1) {
	return t1;
	}

	while (t0 < t1) {
	x2 = [self sampleCurveX:t2];
	if (fabs(x2 - x) < epsilon) {
	return t2;
	}
	if (x > x2) {
	t0 = t2;
	} else {
	t1 = t2;
	}
	t2 = (t1 - t0) * 0.5 + t0;
	}

	// Failure.
	return t2;
	}


	#pragma mark Helpers

	+ (CGPoint)normalizedPoint:(CGPoint)point
	{
	CGPoint normalizedPoint = CGPointZero;

	// Clamp to interval [0..1]
	normalizedPoint.x = MAX(0.0, MIN(1.0, point.x));
	normalizedPoint.y = MAX(0.0, MIN(1.0, point.y));

	return normalizedPoint;
	}


	+ (CGPoint)controlPoint1ForTimingFunctionWithName:(NSString *)name
	{
	CGPoint controlPoint1 = CGPointZero;

	if ([name isEqual:kRSTimingFunctionLinear]) {
	controlPoint1 = kLinearP1;
	} else if ([name isEqual:kRSTimingFunctionEaseIn]) {
	controlPoint1 = kEaseInP1;
	} else if ([name isEqual:kRSTimingFunctionEaseOut]) {
	controlPoint1 = kEaseOutP1;
	} else if ([name isEqual:kRSTimingFunctionEaseInEaseOut]) {
	controlPoint1 = kEaseInEaseOutP1;
	} else if ([name isEqual:kRSTimingFunctionDefault]) {
	controlPoint1 = kDefaultP1;
	} else {
	// Not a predefined timing function
	}

	return controlPoint1;
	}


	+ (CGPoint)controlPoint2ForTimingFunctionWithName:(NSString *)name
	{
	CGPoint controlPoint2 = CGPointZero;

	if ([name isEqual:kRSTimingFunctionLinear]) {
	controlPoint2 = kLinearP2;
	} else if ([name isEqual:kRSTimingFunctionEaseIn]) {
	controlPoint2 = kEaseInP2;
	} else if ([name isEqual:kRSTimingFunctionEaseOut]) {
	controlPoint2 = kEaseOutP2;
	} else if ([name isEqual:kRSTimingFunctionEaseInEaseOut]) {
	controlPoint2 = kEaseInEaseOutP2;
	} else if ([name isEqual:kRSTimingFunctionDefault]) {
	controlPoint2 = kDefaultP2;
	} else {
	// Not a predefined timing function
	}

	return controlPoint2;
	}


	@end