I need to calculate the grid coordinates for a point on an arc using the distance traveled along it.
I'm given the endpoints, radius, center, clockwise direction, and distance.
How can I calculate the coordinates for the new point marked by the distance traveled?
If I had the angle of the arc point relative the the positive x axis, I could simple use the Radius, Cos(angle), and Sin(angle) to figure out the coordinate. But in this case it isn't given. I think I need to figure out x-axis angle for each endpoint by subtracting the center from each endpoint and then dividing by the radius. This then could be used with inverse tangent to find the angle for each endpoint. But how do I find the coordinates for the point traveling along the arc?
Use the fact that $\text{arc length} = \text{angle in radians} \cdot \text{radius of circle}$. See this page for a picture. This essentially boils down to the formula for the circumference of a circle and calculating the fraction of a circle that an arc makes up.
With this formula, you can convert from distance traveled to angle, and as you noted you can convert from angle to coordinates.