Catmull-Rom

Math and Physics Programming

Started by MARS_999 December 22, 2010 11:01 AM

3 comments, last by MARS_999 13 years, 3 months ago

MARS_999

1,627

Author

December 22, 2010 11:01 AM

I have this code so far for a Catmull-Rom calculation would these be close?

template<typename T, unsigned int size> cml::vector<T, cml::fixed<size>>& CatmullRom(const cml::vector<T, cml::fixed<size>>& vP0, 											 const cml::vector<T, cml::fixed<size>>& vP1, 											 const cml::vector<T, cml::fixed<size>>& vP2, 											 const cml::vector<T, cml::fixed<size>>& vP3, 											 cml::vector<T, cml::fixed<size>>& result, 											 T t){    T t2 = t  * t;    T t3 = t2 * t;     result = 0.5 * ((2 * vP1) + (-vP0 + vP2) * t +                     (2 * vP0 - 5 *vP1 + 4 * vP2 - vP3) * t2 +                     (-vP0 + 3 * vP1 - 3 * vP2 + vP3) * t3);	return result;}

NX::MATH::CatmullRom<float, 3>(cml::vector3f(1,0,1),
cml::vector3f(2,0,2),
cml::vector3f(3,0,3),
cml::vector3f(4,0,4),
temp,
0);

I get 2,0,2 for a result, if that is correct... But this seems more like a linear interpolation, but I am unsure...

Thanks!

Noggs

141

December 22, 2010 11:52 AM

I've not checked the code but passing in 0 for 't' will give you P1 back - as it has done. Catmull-Rom interpolates between P1 and P2 where (t>=0 && t<=1) using P0 and P3 as control points. If you pass in 0.5 you will get the value halfway between P1 and P2.

In this case that will still be linearly interpolated because your points are all in a straight line!

Try something like (0,0,0), (10,0,0), (10,0,10), (0,0,10) 0.5

Sketching the points out and drawing a smooth line through then will help you visualise what should happen.

MARS_999

1,627

Author

December 22, 2010 12:49 PM

Try something like (0,0,0), (10,0,0), (10,0,10), (0,0,10) 0.5

11.25, 0, 5 is the result

So how can 11.25 be a answer when 10 is the max range?

Thanks

Sneftel

1,788

December 22, 2010 12:57 PM

10 is not the max range. A Catmull-Rom spline passes through all of the control points, and as a result usually is not fully within the convex hull of the control points. Consider -- how would it pass through p2 smoothly on its way from p1, and continue smoothly towards p3, without either an instant turn or approaching and leaving from outside the hull?

MARS_999

1,627

Author

December 22, 2010 01:05 PM

ah I see now, so the curve will probably have only one path for any given set of points...

Thanks

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