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to calculate rect moving in curveed path collision detection

i trying to find the best way to use collision detection between rect moving in curved path: here is example of what i have i found few methods and i have hard time to find what is the best way i ...
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accelerated curved bounce

I'm trying to make a simple pong clone and want the ball to curve when the racket was moving on hit. To test out curves I removed all the rackets and just have a ball bouncing around in a rectangle, ...
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(Unity) Is There a Way to Add Multiple Animation Curves Together?

This is a bit of a cross post from answers.unity3d, but I don't know how much exposure my question will get there so I figured I'd try and see if anyone here had a solution for this. You can find it ...
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Constantly interpolated splines

Trying to implement a movement through a curve - I'm trying to find a type of curve/spline that interpolates constantly. What I mean: when I interpolate from t=0 to t=0.1, I want it be the same ...