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.
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)