IAPDemo/Libraries/cocos2d/cocos/rparticle/PolynomialCurve.h

//
//  PolynomialCurve.h
//  cocos2d_libs
//
//  Created by 徐俊杰 on 2020/4/24.
//

#ifndef PolynomialCurve_h
#define PolynomialCurve_h

#include "rparticle/Macros/RParticleMacros.h"

NS_RRP_BEGIN

template<class T>
class AnimationCurveTpl;
typedef AnimationCurveTpl<float> AnimationCurve;
//class Vector2f;

struct Polynomial
{
    static float EvalSegment (float t, const float* coeff)
    {
        return (t * (t * (t * coeff[0] + coeff[1]) + coeff[2])) + coeff[3];
    }
    
    float coeff[4];
};

// Smaller, optimized version
struct OptimizedPolynomialCurve
{
    enum { kMaxPolynomialKeyframeCount = 3, kSegmentCount = kMaxPolynomialKeyframeCount-1, };
    
    Polynomial segments[kSegmentCount];
    
    float timeValue;
    float velocityValue;
    
    // Evaluate double integrated Polynomial curve.
    // Example: position = EvaluateDoubleIntegrated (normalizedTime) * startEnergy^2
    // Use DoubleIntegrate function to for example turn a force curve into a position curve.
    // Expects that t is in the 0...1 range.
    float EvaluateDoubleIntegrated (float t) const
    {
        DebugAssert(t >= -0.01F && t <= 1.01F);
        float res0, res1;
        
        // All segments are added together. At t = 0, the integrated curve is always zero.
        
        // 0 segment is sampled up to the 1 keyframe
        // First key is always assumed to be at 0 time
        float t1 = std::min(t, timeValue);
        
        // 1 segment is sampled from 1 key to 2 key
        // Last key is always assumed to be at 1 time
        float t2 = std::max(0.0F, t - timeValue);
        
        res0 = Polynomial::EvalSegment(t1, segments[0].coeff) * t1 * t1;
        res1 = Polynomial::EvalSegment(t2, segments[1].coeff) * t2 * t2;
        
        float finalResult = res0 + res1;
        
        // Add velocity of previous segments
        finalResult += velocityValue * std::max(t - timeValue, 0.0F);
        
        return finalResult;
    }
    
    // Evaluate integrated Polynomial curve.
    // Example: position = EvaluateIntegrated (normalizedTime) * startEnergy
    // Use Integrate function to for example turn a velocity curve into a position curve.
    // Expects that t is in the 0...1 range.
    float EvaluateIntegrated (float t) const
    {
        DebugAssert(t >= -0.01F && t <= 1.01F);
        float res0, res1;
        
        // All segments are added together. At t = 0, the integrated curve is always zero.
        
        // 0 segment is sampled up to the 1 keyframe
        // First key is always assumed to be at 0 time
        float t1 = std::min(t, timeValue);
        
        // 1 segment is sampled from 1 key to 2 key
        // Last key is always assumed to be at 1 time
        float t2 = std::max(0.0F, t - timeValue);
        
        res0 = Polynomial::EvalSegment(t1, segments[0].coeff) * t1;
        res1 = Polynomial::EvalSegment(t2, segments[1].coeff) * t2;
        
        return (res0 + res1);
    }
    
    // Evaluate the curve
    // extects that t is in the 0...1 range
    float Evaluate (float t) const
    {
        DebugAssert(t >= -0.01F && t <= 1.01F);
        
        float res0 = Polynomial::EvalSegment(t,                segments[0].coeff);
        float res1 = Polynomial::EvalSegment(t - timeValue, segments[1].coeff);
        
        float result;
        if (t > timeValue)
            result = res1;
        else
            result = res0;
        
        return result;
    }
    
    // Find the maximum of a double integrated curve (x: min, y: max)
    Vector2f FindMinMaxDoubleIntegrated() const;
    
    // Find the maximum of the integrated curve (x: min, y: max)
    Vector2f FindMinMaxIntegrated() const;
    
    // Precalculates polynomials from the animation curve and a scale factor
    bool BuildOptimizedCurve (const AnimationCurve& editorCurve, float scale);
    
    // Integrates a velocity curve to be a position curve.
    // You have to call EvaluateIntegrated to evaluate the curve
    void Integrate ();
    
    // Integrates a velocity curve to be a position curve.
    // You have to call EvaluateDoubleIntegrated to evaluate the curve
    void DoubleIntegrate ();
    
    // Add a constant force to a velocity curve
    // Assumes that you have already called Integrate on the velocity curve.
    void AddConstantForceToVelocityCurve (float gravity)
    {
        for (int i=0;i<kSegmentCount;i++)
            segments[i].coeff[1] += 0.5F * gravity;
    }
};

// Bigger, not so optimized version
struct PolynomialCurve
{
    enum{ kMaxNumSegments = 8 };
    
    Polynomial segments[kMaxNumSegments];            // Cached polynomial coefficients
    float integrationCache[kMaxNumSegments];        // Cache of integrated values up until start of segments
    float doubleIntegrationCache[kMaxNumSegments];    // Cache of double integrated values up until start of segments
    float times[kMaxNumSegments];                    // Time value for end of segment
    
    int segmentCount;
    
    // Find the maximum of a double integrated curve (x: min, y: max)
    Vector2f FindMinMaxDoubleIntegrated() const;
    
    // Find the maximum of the integrated curve (x: min, y: max)
    Vector2f FindMinMaxIntegrated() const;
    
    // Precalculates polynomials from the animation curve and a scale factor
    bool BuildCurve(const AnimationCurve& editorCurve, float scale);
    
    // Integrates a velocity curve to be a position curve.
    // You have to call EvaluateIntegrated to evaluate the curve
    void Integrate ();
    
    // Integrates a velocity curve to be a position curve.
    // You have to call EvaluateDoubleIntegrated to evaluate the curve
    void DoubleIntegrate ();
    
    // Evaluates if it is possible to represent animation curve as PolynomialCurve
    static bool IsValidCurve(const AnimationCurve& editorCurve);
    
    // Evaluate double integrated Polynomial curve.
    // Example: position = EvaluateDoubleIntegrated (normalizedTime) * startEnergy^2
    // Use DoubleIntegrate function to for example turn a force curve into a position curve.
    // Expects that t is in the 0...1 range.
    float EvaluateDoubleIntegrated (float t) const
    {
        DebugAssert(t >= -0.01F && t <= 1.01F);
        
        float prevTimeValue = 0.0f;
        for(int i = 0; i < segmentCount; i++)
        {
            if(t <= times[i])
            {
                const float time = t - prevTimeValue;
                return doubleIntegrationCache[i] + integrationCache[i] * time + Polynomial::EvalSegment(time, segments[i].coeff) * time * time;
            }
            prevTimeValue = times[i];
        }
        DebugAssert(!"PolyCurve: Outside segment range!");
        return 1.0f;
    }
    
    // Evaluate integrated Polynomial curve.
    // Example: position = EvaluateIntegrated (normalizedTime) * startEnergy
    // Use Integrate function to for example turn a velocity curve into a position curve.
    // Expects that t is in the 0...1 range.
    float EvaluateIntegrated (float t) const
    {
        DebugAssert(t >= -0.01F && t <= 1.01F);
        
        float prevTimeValue = 0.0f;
        for(int i = 0; i < segmentCount; i++)
        {
            if(t <= times[i])
            {
                const float time = t - prevTimeValue;
                return integrationCache[i] + Polynomial::EvalSegment(time, segments[i].coeff) * time;
            }
            prevTimeValue = times[i];
        }
        DebugAssert(!"PolyCurve: Outside segment range!");
        return 1.0f;
    }
    
    // Evaluate the curve
    // extects that t is in the 0...1 range
    float Evaluate(float t) const
    {
        DebugAssert(t >= -0.01F && t <= 1.01F);
        
        float prevTimeValue = 0.0f;
        for(int i = 0; i < segmentCount; i++)
        {
            if(t <= times[i])
                return Polynomial::EvalSegment(t - prevTimeValue, segments[i].coeff);
            prevTimeValue = times[i];
        }
        DebugAssert(!"PolyCurve: Outside segment range!");
        return 1.0f;
    }
};


void SetPolynomialCurveToValue (AnimationCurve& a, OptimizedPolynomialCurve& c, float value);
void SetPolynomialCurveToLinear (AnimationCurve& a, OptimizedPolynomialCurve& c);
void ConstrainToPolynomialCurve (AnimationCurve& curve);
bool IsValidPolynomialCurve (const AnimationCurve& curve);
void CalculateMinMax(Vector2f& minmax, float value);

NS_RRP_END

#endif /* PolynomialCurve_h */