How to calculate a point with an given center, angle and radius?

Question

In this SO question, someone asked for calculating an angle from three points. I need to do the opposite thing.

I want to draw a clock, and I have tiny tick images. An art dude made 60 of them, each with an individual and accurate shadow. So there are 60 distinct images at 10x10 points in size, already correctly rotated in the center of that square.

So every 6 degrees one tick image has to be placed. I would just need to calculate the x/y coordinate based on a center point, an radius and an angle.

So I have:

• an center point
• an radius
• an angle

Is there an easy way to calculate the x/y coordinate with this? Maybe cocoa-touch already has a useful function or method for this?

Answer 1

let a be the angle, (x,y) the center point and r the radius, then your point will be at

(x + r*cos(a), y + r*sin(a))

Answer 2

In mathematics, to calculate the Cartesian coordinates from the polar coordinates:

x = r * cos(A) + x0;
y = r * sin(A) + y0;

where (x0, y0) is the centre of your circle, r is the radius and A is the angle.

But that assumes the mathematics coordinate convention i.e. x increases as you move rightwards, y increases as you move upwards. This is the default for views on Mac OS X Cocoa but I don't know if it is the same on the iPhone.

Also angles start at 3 o clock and go anti-clockwise i.e. 3 o clock is 0 degrees, 12 o clock is 90 degrees, 9 o clock is 180 degrees and 6 o clock is 270 degrees.

Also, the C sine and cosine functions work in radians.