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I'm working on a program where I can set objects along arbitrary parametric paths.

Moving left is easy:

X = x - dT(V)

Y = y

Moving in a circle is easy:

X = x+ Cos(dt*Pi)

Y = y+ Sin(dt*Pi)

So I tried to combine them to move left while also moving in a circle, likeso:

X = x- dT(V) + Cos(dt*Pi)

Y = y + Sin(dt*Pi)

However, this didn't give me the circular movement towards the left that I expected. My goal is a parametric equation where the object will move along the circumference of the circle with a constant speed.

How can I adjust the parametric equation to achieve both constant speed along the x axis and along the radius of the circle? The rotational speed and the leftwards speed need not be the same, just constant relative to each other.

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Take a look at the cycloid. It might give you some ideas. – Matthew Conroy Apr 16 '12 at 4:52
up vote 0 down vote accepted

It turns out that I'm asking for the impossible.

Constant rotational speed along a circle is... a circle.

The equation above will provide the expected path. (Though it might help proving it if you have more than a single point involved in visualizing it)

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