Finding the coordinates on the edge of a circle

Question

Using C#:

How do I get the (x, y) coordinates on the edge of a circle for any given degree, if I have the center coordinates and the radius?

There is probably SIN, TAN, COSIN and other grade ten math involved... :)

That's the kind of question to ask on http://mathoverflow.net/ — Lucero, Jan 19 '10 at 12:42
@Lucero: No, I doubt this one would count as a "research level math question" — Niki, Jan 19 '10 at 12:44
@nikie, true, but on the other hand it's even less a programming question. It's simple geometry. — Lucero, Jan 19 '10 at 14:34
Either way, he would be absolutely flamed to death on Math Overflow if he posted that. They're much more strict about keeping it "by mathematicians, for mathematicians" than we are over here. — Adrian Petrescu, Jan 19 '10 at 18:49
Possible duplicate of [Calculating point on a circle's circumference from angle in C#?](http://stackoverflow.com/questions/674225/calculating-point-on-a-circles-circumference-from-angle-in-c) — Peter O., Nov 21 '16 at 07:12
I'm voting to close this question as off-topic because it is a geometry question, not a programming question. — tripleee, Aug 17 '18 at 09:56
http://en.wikipedia.org/wiki/Trigonometry is your friend, the calculations are quite simple. Check the Math Namespace for Sin() & Cos() — , Jan 19 '10 at 12:30
All of these comments are why the StackOverflow websites have a reputation as being unfriendly and hostile to newcomers. Not every programming beginner is good at maths (or even educated in maths!) — Lou, Jun 17 '23 at 18:25

score 87 · Accepted Answer · edited May 20 '21 at 17:06

87

Here's the mathematical solution which can be applied in any language:

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

x0 and y0 are the coordinates of the centre, r is the radius, and theta is in radians. The angle is measured anticlockwise from the x-axis.

This is the code for C# specifically if your angle is in degrees:

double x = x0 + r * Math.Cos(theta * Math.PI / 180);
double y = y0 + r * Math.Sin(theta * Math.PI / 180);

edited May 20 '21 at 17:06

Alan W. Smith

answered Jan 19 '10 at 12:30

David M

2

It funny on these types of questions how almost identical the answers are. Even down to the structure of the answer :P – Alastair Pitts Jan 19 '10 at 12:36

score 9 · Answer 2 · answered Jan 19 '10 at 12:35

using Pythagoras Theorem (where x1,y1 is the edge point):

x1 = x + rcos(theta)
y1 = y + rsin(theta)

in C#, this would look like:

x1 = x + radius * Math.Cos(angle * (Math.PI / 180));
y1 = y + radius * Math.Sin(angle * (Math.PI / 180));

where all variables are doubles and angle is in degrees

score 4 · Answer 3 · answered Jan 19 '10 at 12:30

4

For a circle with origin (j, k), radius r, and angle t in radians:

   x(t) = r * cos(t) + j       
   y(t) = r * sin(t) + k

answered Jan 19 '10 at 12:30

Daniel Vassallo

3 Answers3