//// Interpolate.cpp// libraries/shared/src//// Created by David Rowe on 10 Sep 2015.// Copyright 2015 High Fidelity, Inc.//// Distributed under the Apache License, Version 2.0.// See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html//#include "Interpolate.h"#include <assert.h>#include <math.h>#include "NumericalConstants.h"float Interpolate::bezierInterpolate(float y1, float y2, float y3, float u) { // https://en.wikipedia.org/wiki/Bezier_curve assert(0.0f <= u && u <= 1.0f); return (1.0f - u) * (1.0f - u) * y1 + 2.0f * (1.0f - u) * u * y2 + u * u * y3;}float Interpolate::interpolate3Points(float y1, float y2, float y3, float u) { assert(0.0f <= u && u <= 1.0f); if ((u <= 0.5f && y1 == y2) || (u >= 0.5f && y2 == y3)) { // Flat line. return y2; } if ((y2 >= y1 && y2 >= y3) || (y2 <= y1 && y2 <= y3)) { // U or inverted-U shape. // Make the slope at y2 = 0, which means that the control points half way between the value points have the value y2. if (u <= 0.5f) { return bezierInterpolate(y1, y2, y2, 2.0f * u); } else { return bezierInterpolate(y2, y2, y3, 2.0f * u - 1.0f); } } else { // L or inverted and/or mirrored L shape. // Make the slope at y2 be the slope between y1 and y3, up to a maximum of double the minimum of the slopes between y1 // and y2, and y2 and y3. Use this slope to calculate the control points half way between the value points. // Note: The maximum ensures that the control points and therefore the interpolated values stay between y1 and y3. float slope = y3 - y1; float slope12 = y2 - y1; float slope23 = y3 - y2; if (fabsf(slope) > fabsf(2.0f * slope12)) { slope = 2.0f * slope12; } else if (fabsf(slope) > fabsf(2.0f * slope23)) { slope = 2.0f * slope23; } if (u <= 0.5f) { return bezierInterpolate(y1, y2 - slope / 2.0f, y2, 2.0f * u); } else { return bezierInterpolate(y2, y2 + slope / 2.0f, y3, 2.0f * u - 1.0f); } }}float Interpolate::simpleNonLinearBlend(float fraction) { // uses arctan() to map a linear distribution in domain [0,1] to a non-linear blend (slow out, slow in) in range [0,1] const float WIDTH = 20.0f; const float INV_ARCTAN_WIDTH = 0.339875327433f; // 1 / (2 * atan(WIDTH/2)) return 0.5f + atanf(WIDTH * (fraction - 0.5f)) * INV_ARCTAN_WIDTH;}float Interpolate::easeInOutQuad(float lerpValue) { assert(!((lerpValue < 0.0f) || (lerpValue > 1.0f))); if (lerpValue < 0.5f) { return (2.0f * lerpValue * lerpValue); } return (lerpValue*(4.0f - 2.0f * lerpValue) - 1.0f);}
//
// Interpolate.cpp
// libraries/shared/src
//
// Created by David Rowe on 10 Sep 2015.
// Copyright 2015 High Fidelity, Inc.
//
// Distributed under the Apache License, Version 2.0.
// See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html
//
#include "Interpolate.h"
#include <assert.h>
#include <math.h>
#include "NumericalConstants.h"
float Interpolate::bezierInterpolate(float y1, float y2, float y3, float u) {
// https://en.wikipedia.org/wiki/Bezier_curve
assert(0.0f <= u && u <= 1.0f);
return (1.0f - u) * (1.0f - u) * y1 + 2.0f * (1.0f - u) * u * y2 + u * u * y3;
}
float Interpolate::interpolate3Points(float y1, float y2, float y3, float u) {
assert(0.0f <= u && u <= 1.0f);
if ((u <= 0.5f && y1 == y2) || (u >= 0.5f && y2 == y3)) {
// Flat line.
return y2;
}
if ((y2 >= y1 && y2 >= y3) || (y2 <= y1 && y2 <= y3)) {
// U or inverted-U shape.
// Make the slope at y2 = 0, which means that the control points half way between the value points have the value y2.
if (u <= 0.5f) {
return bezierInterpolate(y1, y2, y2, 2.0f * u);
} else {
return bezierInterpolate(y2, y2, y3, 2.0f * u - 1.0f);
}
} else {
// L or inverted and/or mirrored L shape.
// Make the slope at y2 be the slope between y1 and y3, up to a maximum of double the minimum of the slopes between y1
// and y2, and y2 and y3. Use this slope to calculate the control points half way between the value points.
// Note: The maximum ensures that the control points and therefore the interpolated values stay between y1 and y3.
float slope = y3 - y1;
float slope12 = y2 - y1;
float slope23 = y3 - y2;
if (fabsf(slope) > fabsf(2.0f * slope12)) {
slope = 2.0f * slope12;
} else if (fabsf(slope) > fabsf(2.0f * slope23)) {
slope = 2.0f * slope23;
}
if (u <= 0.5f) {
return bezierInterpolate(y1, y2 - slope / 2.0f, y2, 2.0f * u);
} else {
return bezierInterpolate(y2, y2 + slope / 2.0f, y3, 2.0f * u - 1.0f);
}
}
}
float Interpolate::simpleNonLinearBlend(float fraction) {
// uses arctan() to map a linear distribution in domain [0,1] to a non-linear blend (slow out, slow in) in range [0,1]
const float WIDTH = 20.0f;
const float INV_ARCTAN_WIDTH = 0.339875327433f; // 1 / (2 * atan(WIDTH/2))
return 0.5f + atanf(WIDTH * (fraction - 0.5f)) * INV_ARCTAN_WIDTH;
}
float Interpolate::easeInOutQuad(float lerpValue) {
assert(!((lerpValue < 0.0f) || (lerpValue > 1.0f)));
if (lerpValue < 0.5f) {
return (2.0f * lerpValue * lerpValue);
}
return (lerpValue*(4.0f - 2.0f * lerpValue) - 1.0f);
}