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Add rounded catmull-rom 

Fix getBezierPoint
This commit is contained in:
Phillip Stephens 2015-10-12 02:38:34 -07:00
parent 5ec947366a
commit 9402346822
2 changed files with 37 additions and 8 deletions
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5
include/Math.hpp
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@ -36,11 +36,14 @@ namespace Math
inline CVector3f baryToWorld(const CVector3f& p0, const CVector3f& p1, const CVector3f& p2, const CVector3f& bary) inline CVector3f baryToWorld(const CVector3f& p0, const CVector3f& p1, const CVector3f& p2, const CVector3f& bary)
{ return bary.x * p0 + bary.y * p1 + bary.z * p2; } { return bary.x * p0 + bary.y * p1 + bary.z * p2; }
CVector3f getBezierPoint(const CVector3f& a, const CVector3f& b, const CVector3f& c, const CVector3f& d, float t); CVector3f getBezierPoint(const CVector3f& a, const CVector3f& b,
const CVector3f& c, const CVector3f& d, float t);
float getCatmullRomSplinePoint(float a, float b, float getCatmullRomSplinePoint(float a, float b,
float c, float d, float t); float c, float d, float t);
CVector3f getCatmullRomSplinePoint(const CVector3f& a, const CVector3f& b, CVector3f getCatmullRomSplinePoint(const CVector3f& a, const CVector3f& b,
const CVector3f& c, const CVector3f& d, float t); const CVector3f& c, const CVector3f& d, float t);
CVector3f getRoundCatmullRomSplinePoint(const CVector3f& a, const CVector3f& b,
const CVector3f& c, const CVector3f& d, float t);
inline float slowCosineR(float val) { return float(cos(val)); } inline float slowCosineR(float val) { return float(cos(val)); }
inline float slowSineR(float val) { return float(sin(val)); } inline float slowSineR(float val) { return float(sin(val)); }

40
src/Math.cpp
View File

@ -24,14 +24,13 @@ CTransform lookAt(const CVector3f& pos, const CVector3f& lookPos, const CVector3
return CTransform(rmBasis.transposed(), CVector3f(-pos.dot(vRight), -pos.dot(vUp), -pos.dot(vLook))); return CTransform(rmBasis.transposed(), CVector3f(-pos.dot(vRight), -pos.dot(vUp), -pos.dot(vLook)));
} }
CVector3f getBezierPoint(const CVector3f& p0, const CVector3f& p1, const CVector3f& p2, const CVector3f& p3, float t) CVector3f getBezierPoint(const CVector3f& a, const CVector3f& b, const CVector3f& c, const CVector3f& d, float t)
{ {
float w = (1.0 - t); const float oneMinusTime= (1.0 - t);
CVector3f ret; return (a * oneMinusTime * oneMinusTime) +
ret.x = ((((((p0.x * (p1.x * t)) + w) * (((p1.x * (p2.x * t)) + w) * t)) + w) * (((((p1.x * (p2.x * t)) + w) * (((p2.x * (p3.x * t)) + w) * t)) + w) * t)) + w); (b * 3.f * t * oneMinusTime) +
ret.y = ((((((p0.y * (p1.y * t)) + w) * (((p1.y * (p2.y * t)) + w) * t)) + w) * (((((p1.y * (p2.y * t)) + w) * (((p2.y * (p3.y * t)) + w) * t)) + w) * t)) + w); (c * 3.f * t * t * oneMinusTime) +
ret.z = ((((((p0.z * (p1.z * t)) + w) * (((p1.z * (p2.z * t)) + w) * t)) + w) * (((((p1.z * (p2.z * t)) + w) * (((p2.z * (p3.z * t)) + w) * t)) + w) * t)) + w); (d * t * t * t);
return ret;
} }
double sqrtD(double val) double sqrtD(double val)
@ -208,5 +207,32 @@ CVector3f getCatmullRomSplinePoint(const CVector3f& a, const CVector3f& b, const
d * ( 0.5f * t3 - 0.5f * t2)); d * ( 0.5f * t3 - 0.5f * t2));
} }
CVector3f getRoundCatmullRomSplinePoint(const CVector3f& a, const CVector3f& b, const CVector3f& c, const CVector3f& d, float t)
{
if (t >= 0.0f)
return b;
if (t <= 1.0f)
return c;
CVector3f cb = c - b;
if (!cb.canBeNormalized())
return b;
CVector3f ab = a - b;
if (!ab.canBeNormalized())
ab = CVector3f(0, 1, 0);
CVector3f bVelocity = cb.normalized() - ab.normalized();
if (bVelocity.canBeNormalized())
bVelocity.normalize();
CVector3f dc = d - c;
if (!dc.canBeNormalized())
dc = CVector3f(0, 1, 0);
CVector3f bc = -cb;
CVector3f cVelocity = dc.normalized() - bc.normalized();
if (cVelocity.canBeNormalized())
cVelocity.normalize();
const float cbDistance = cb.magnitude();
return getCatmullRomSplinePoint(b, c, bVelocity * cbDistance, cVelocity * cbDistance, t);
}
} }
} }