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#ifndef POLYONOMIAL_CURVE_H
#define POLYONOMIAL_CURVE_H
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);
#endif // POLYONOMIAL_CURVE_H
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