Interpolation.hpp

#pragma once
#ifndef __H__OCULAR_ENGINE_MATH_INTERPOLATION__H__
#define __H__OCULAR_ENGINE_MATH_INTERPOLATION__H__

#include "Definitions.hpp"
#include <cmath>

//------------------------------------------------------------------------------------------

namespace Ocular
{
    namespace Math
    {
        static float InterpolateLinear(float const from, float const to, float const frac)
        {
            float boundFrac = (frac < 0.0f) ? 0.0f : (frac > 1.0f) ? 1.0f : frac;

            return (from * (1.0f - boundFrac)) + (to * boundFrac);
        }

        static float InterpolateCosine(float const from, float const to, float const frac)
        {
            float boundFrac = (frac < 0.0f) ? 0.0f : (frac > 1.0f) ? 1.0f : frac;
            float x = (1.0f - cosf(boundFrac * static_cast<float>(PI))) * 0.5f;

            return (from * (1.0f - x)) + (to * x);
        }

        static float InterpolateCubic(float const before, float const from, float const to, float const after, float const frac)
        {
            float boundFrac = (frac < 0.0f) ? 0.0f : (frac > 1.0f) ? 1.0f : frac;
            float frac2 = boundFrac * boundFrac;
            float a0 = after - to - before + from;
            float a1 = before - from - a0;
            float a2 = to - before;
            float a3 = from;

            return (a0 * boundFrac * frac2) + (a2 * frac2) + (a2 * boundFrac) + a3;
        }

        static float InterpolateCatmullRom(float const before, float const from, float const to, float const after, float const frac)
        {
            float boundFrac = (frac < 0.0f) ? 0.0f : (frac > 1.0f) ? 1.0f : frac;
            float frac2 = boundFrac * boundFrac;
            float a0 = (-0.5f * before) + (1.5f * from) - (1.5f * to) + (0.5f * after);
            float a1 = before - (2.5f * from) + (2.0f * to) - (0.5f * after);
            float a2 = (-0.5f * before) + (0.5f * to);
            float a3 = from;

            return (a0 * boundFrac * frac2) + (a2 * frac2) + (a2 * boundFrac) + a3;
        }

        static float InterpolateHermite(float const before, float const from, float const to, float const after,
                                        float const frac, float const tension = 0.0f, float const bias = 0.0f)
        {
            float boundFrac = (frac < 0.0f) ? 0.0f : (frac > 1.0) ? 1.0f : frac;
            float frac2 = boundFrac * boundFrac;
            float frac3 = boundFrac * frac2;
            float m0 = ((from - before) * (1.0f + bias) * (1.0f - tension) * 0.5f)
                     + ((to - from)     * (1.0f - bias) * (1.0f - tension) * 0.5f);
            float m1 = ((to - from)     * (1.0f + bias) * (1.0f - tension) * 0.5f)
                     + ((after - to)    * (1.0f - bias) * (1.0f - tension) * 0.5f);
            float a0 = (2.0f * frac3) - (3.0f * frac2) + 1.0f;
            float a1 = frac3 - (2.0f * frac2) + boundFrac;
            float a2 = frac3 - frac2;
            float a3 = (-2.0f * frac3) + (3.0f * frac2);

            return (a0 * from) + (a1 * m0) + (a2 * m1) + (a3 * to);
        }
    }
}
//------------------------------------------------------------------------------------------

#endif