Determining the following point on the arc is as simple as knowing the radius, the initial point on the arc, and the angle of change between the two points

Is there a way to determine the next point on an arc given the radius coordinate, initial point on the arc, and angle of change between the initial and next points?

For example, let's say our initial point is at (1117, 453), the radius coordinates are (720, 853), and there is a 3.6 degree change in angle between the next point and the initial point.

What would be the coordinates of the next point on the arc?

I have calculated the radius using the formula provided formula for finding the distance between two points. The radius I obtained is approximately 563.

I am looking for a formula to determine the next point on the arc with a 3.6 degree change in the clockwise direction.

javascriptmathcanvasgeometry

Answer №1

In order to perform a rotation of point (x0, y0) around the center (cx, cy) by an angle fi, you can calculate the new coordinates as follows:

x = cx + (x0 - cx) * cos(fi) - (y0 - cy) * sin(fi)
y = cy + (x0 - cx) * sin(fi) + (y0 - cy) * cos(fi)

Remember to consider whether the angle is given in degrees or radians.

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