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blender-archive/source/blender/blenlib/intern/easing.c
Joshua Leung 179e7eaf39 Bugfix for Elastic and Back easing types 
** TO BE PORTED BACK TO 2.71 **

As pointed out by Thomas Beck (plasmasolutions), the current behaviour and/or
default values for their parameters didn't quite make sense:

1) Back Easing - The old default value of 0.0 results in some overshoot being applied,
while trying to tweak it up or down resulted in some odd jumps and discontinities.

I've ended up removing some code here which forcibly using a "back" value of 1.7
when users wanted 0.0 instead. There doesn't seem to be any good reason for this.
To ensure that there is still an effect initially, keyframes now get created
with back set to 1.7


2) Elastic Easing - The old default settings of <amplitude = 0, period = 0> resulted
in a curve without any elastic bounce, which wasn't very useful for motion graphics.

Now, default values of amplitude = 0.8 and period = 4.1 get set. These were hand picked
by Thomas to work well when the duration of the motion is 10 frames long (i.e. the
typical length of such effects when doing motion graphics).
2014-06-20 01:34:35 +12:00

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/*
* Copyright © 2001 Robert Penner
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* * 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.
*
* * Neither the name of the author nor the names of contributors may be
* used to endorse or promote products derived from this software without
* specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND 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 <COPYRIGHT HOLDER> 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.
*/
/** \file blender/blenlib/intern/easing.c
* \ingroup bli
*/
#include "BLI_math_base.h"
#include "BLI_easing.h" /* own include */
#include "BLI_strict_flags.h"
/* blend if (amplitude < fabsf(change) */
#define USE_ELASTIC_BLEND
float BLI_easing_back_ease_in(float time, float begin, float change, float duration, float overshoot)
{
time /= duration;
return change * time * time * ((overshoot + 1) * time - overshoot) + begin;
}
float BLI_easing_back_ease_out(float time, float begin, float change, float duration, float overshoot)
{
time = time / duration - 1;
return change * (time * time * ((overshoot + 1) * time + overshoot) + 1) + begin;
}
float BLI_easing_back_ease_in_out(float time, float begin, float change, float duration, float overshoot)
{
overshoot *= 1.525f;
if ((time /= duration / 2) < 1.0f) {
return change / 2 * (time * time * ((overshoot + 1) * time - overshoot)) + begin;
}
time -= 2.0f;
return change / 2 * (time * time * ((overshoot + 1) * time + overshoot) + 2) + begin;
}
float BLI_easing_bounce_ease_out(float time, float begin, float change, float duration)
{
time /= duration;
if (time < (1 / 2.75f)) {
return change * (7.5625f * time * time) + begin;
}
else if (time < (2 / 2.75f)) {
time -= (1.5f / 2.75f);
return change * ((7.5625f * time) * time + 0.75f) + begin;
}
else if (time < (2.5f / 2.75f)) {
time -= (2.25f / 2.75f);
return change * ((7.5625f * time) * time + 0.9375f) + begin;
}
else {
time -= (2.625f / 2.75f);
return change * ((7.5625f * time) * time + 0.984375f) + begin;
}
}
float BLI_easing_bounce_ease_in(float time, float begin, float change, float duration)
{
return change - BLI_easing_bounce_ease_out(duration - time, 0, change, duration) + begin;
}
float BLI_easing_bounce_ease_in_out(float time, float begin, float change, float duration)
{
if (time < duration / 2)
return BLI_easing_bounce_ease_in(time * 2, 0, change, duration) * 0.5f + begin;
else
return BLI_easing_bounce_ease_out(time * 2 - duration, 0, change, duration) * 0.5f + change * 0.5f + begin;
}
float BLI_easing_circ_ease_in(float time, float begin, float change, float duration)
{
time /= duration;
return -change * (sqrtf(1 - time * time) - 1) + begin;
}
float BLI_easing_circ_ease_out(float time, float begin, float change, float duration)
{
time = time / duration - 1;
return change * sqrtf(1 - time * time) + begin;
}
float BLI_easing_circ_ease_in_out(float time, float begin, float change, float duration)
{
if ((time /= duration / 2) < 1.0f)
return -change / 2 * (sqrtf(1 - time * time) - 1) + begin;
time -= 2.0f;
return change / 2 * (sqrtf(1 - time * time) + 1) + begin;
}
float BLI_easing_cubic_ease_in(float time, float begin, float change, float duration)
{
time /= duration;
return change * time * time * time + begin;
}
float BLI_easing_cubic_ease_out(float time, float begin, float change, float duration)
{
time = time / duration - 1;
return change * (time * time * time + 1) + begin;
}
float BLI_easing_cubic_ease_in_out(float time, float begin, float change, float duration)
{
if ((time /= duration / 2) < 1.0f)
return change / 2 * time * time * time + begin;
time -= 2.0f;
return change / 2 * (time * time * time + 2) + begin;
}
#ifdef USE_ELASTIC_BLEND
/**
* When the amplitude is less then the change, we need to blend
* \a f when we're close to the crossing point (int time), else we get an ugly sharp falloff.
*/
static float elastic_blend(float time, float change, float duration, float amplitude, float s, float f)
{
if (change) {
/* Looks like a magic number,
* but this is a part of the sine curve we need to blend from */
const float t = fabsf(s);
if (amplitude) {
f *= amplitude / fabsf(change);
}
else {
f = 0.0f;
}
if (fabsf(time * duration) < t) {
float l = fabsf(time * duration) / t;
f = (f * l) + (1.0f - l);
}
}
return f;
}
#endif
float BLI_easing_elastic_ease_in(float time, float begin, float change, float duration, float amplitude, float period)
{
float s;
float f = 1.0f;
if (time == 0.0f)
return begin;
if ((time /= duration) == 1.0f)
return begin + change;
time -= 1.0f;
if (!period)
period = duration * 0.3f;
if (!amplitude || amplitude < fabsf(change)) {
s = period / 4;
#ifdef USE_ELASTIC_BLEND
f = elastic_blend(time, change, duration, amplitude, s, f);
#endif
amplitude = change;
}
else
s = period / (2 * (float)M_PI) * asinf(change / amplitude);
return (-f * (amplitude * powf(2, 10 * time) * sinf((time * duration - s) * (2 * (float)M_PI) / period))) + begin;
}
float BLI_easing_elastic_ease_out(float time, float begin, float change, float duration, float amplitude, float period)
{
float s;
float f = 1.0f;
if (time == 0.0f)
return begin;
if ((time /= duration) == 1.0f)
return begin + change;
time = -time;
if (!period)
period = duration * 0.3f;
if (!amplitude || amplitude < fabsf(change)) {
s = period / 4;
#ifdef USE_ELASTIC_BLEND
f = elastic_blend(time, change, duration, amplitude, s, f);
#endif
amplitude = change;
}
else
s = period / (2 * (float)M_PI) * asinf(change / amplitude);
return (f * (amplitude * powf(2, 10 * time) * sinf((time * duration - s) * (2 * (float)M_PI) / period))) + change + begin;
}
float BLI_easing_elastic_ease_in_out(float time, float begin, float change, float duration, float amplitude, float period)
{
float s;
float f = 1.0f;
if (time == 0.0f)
return begin;
if ((time /= duration / 2) == 2.0f)
return begin + change;
time -= 1.0f;
if (!period)
period = duration * (0.3f * 1.5f);
if (!amplitude || amplitude < fabsf(change)) {
s = period / 4;
#ifdef USE_ELASTIC_BLEND
f = elastic_blend(time, change, duration, amplitude, s, f);
#endif
amplitude = change;
}
else
s = period / (2 * (float)M_PI) * asinf(change / amplitude);
if (time < 0.0f) {
f *= -0.5f;
return (f * (amplitude * powf(2, 10 * time) * sinf((time * duration - s) * (2 * (float)M_PI) / period))) + begin;
}
else {
time = -time;
f *= 0.5f;
return (f * (amplitude * powf(2, 10 * time) * sinf((time * duration - s) * (2 * (float)M_PI) / period))) + change + begin;
}
}
float BLI_easing_expo_ease_in(float time, float begin, float change, float duration)
{
return (time == 0.0f) ? begin : change * powf(2, 10 * (time / duration - 1)) + begin;
}
float BLI_easing_expo_ease_out(float time, float begin, float change, float duration)
{
return (time == duration) ? begin + change : change * (-powf(2, -10 * time / duration) + 1) + begin;
}
float BLI_easing_expo_ease_in_out(float time, float begin, float change, float duration)
{
if (time == 0.0f)
return begin;
if (time == duration)
return begin + change;
if ((time /= duration / 2) < 1)
return change / 2 * powf(2, 10 * (time - 1)) + begin;
time -= 1.0f;
return change / 2 * (-powf(2, -10 * time) + 2) + begin;
}
float BLI_easing_linear_ease(float time, float begin, float change, float duration)
{
return change * time / duration + begin;
}
float BLI_easing_quad_ease_in(float time, float begin, float change, float duration)
{
time /= duration;
return change * time * time + begin;
}
float BLI_easing_quad_ease_out(float time, float begin, float change, float duration)
{
time /= duration;
return -change * time * (time - 2) + begin;
}
float BLI_easing_quad_ease_in_out(float time, float begin, float change, float duration)
{
if ((time /= duration / 2) < 1.0f)
return change / 2 * time * time + begin;
time -= 1.0f;
return -change / 2 * (time * (time - 2) - 1) + begin;
}
float BLI_easing_quart_ease_in(float time, float begin, float change, float duration)
{
time /= duration;
return change * time * time * time * time + begin;
}
float BLI_easing_quart_ease_out(float time, float begin, float change, float duration)
{
time = time / duration - 1;
return -change * (time * time * time * time - 1) + begin;
}
float BLI_easing_quart_ease_in_out(float time, float begin, float change, float duration)
{
if ((time /= duration / 2) < 1.0f)
return change / 2 * time * time * time * time + begin;
time -= 2.0f;
return -change / 2 * ( time * time * time * time - 2) + begin;
}
float BLI_easing_quint_ease_in(float time, float begin, float change, float duration)
{
time /= duration;
return change * time * time * time * time * time + begin;
}
float BLI_easing_quint_ease_out(float time, float begin, float change, float duration)
{
time = time / duration - 1;
return change * (time * time * time * time * time + 1) + begin;
}
float BLI_easing_quint_ease_in_out(float time, float begin, float change, float duration)
{
if ((time /= duration / 2) < 1.0f)
return change / 2 * time * time * time * time * time + begin;
time -= 2.0f;
return change / 2 * (time * time * time * time * time + 2) + begin;
}
float BLI_easing_sine_ease_in(float time, float begin, float change, float duration)
{
return -change * cosf(time / duration * (float)M_PI_2) + change + begin;
}
float BLI_easing_sine_ease_out(float time, float begin, float change, float duration)
{
return change * sinf(time / duration * (float)M_PI_2) + begin;
}
float BLI_easing_sine_ease_in_out(float time, float begin, float change, float duration)
{
return -change / 2 * (cosf((float)M_PI * time / duration) - 1) + begin;
}
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