Rotate a point by another point in 2D

Question

I want to know how to work out the new co-ordinates for a point when rotated by an angle relative to another point.

I have a block arrow and want to rotate it by an angle theta relative to a point in the middle of the base of the arrow.

This is required to allow me to draw a polygon between 2 onscreen controls. I can't use and rotate an image.

From what I have considered so far what complicates the matter further is that the origin of a screen is in the top left hand corner.

score 135 · Accepted Answer · answered Apr 24 '09 at 16:03

135

If you rotate point (px, py) around point (ox, oy) by angle theta you'll get:

p'x = cos(theta) * (px-ox) - sin(theta) * (py-oy) + ox
p'y = sin(theta) * (px-ox) + cos(theta) * (py-oy) + oy

answered Apr 24 '09 at 16:03

Sophie Alpert

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Do you have the 3D version in memory too? :) – mmx Apr 24 '09 at 16:08
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It depends on which library you're using for the trig functions. In C, you need to pass in radians. – Sophie Alpert Sep 01 '09 at 23:38
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to convert in radians : value * Math.PI / 180; – Goot Feb 19 '13 at 10:35
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The answer to the general 3D problem is [here](http://stackoverflow.com/questions/5188876/rotation-matrix-given-angle-and-point-in-x-y-z/). – Glenn Mar 05 '13 at 18:08
This is great code ... but it is not actually in C#! – A X Jul 12 '19 at 21:05

score 8 · Answer 2 · answered Apr 24 '09 at 15:58

8

If you are using GDI+ to do that, you can use Transform methods of the Graphics object:

graphics.TranslateTransform(point of origin);
graphics.RotateTransform(rotation angle);

Then draw the actual stuff.

answered Apr 24 '09 at 15:58

mmx

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score 2 · Answer 3 · answered Aug 02 '14 at 14:49

If you have the System.Windows.Media namespace available, then you can use the built in transformations:

    using System.Windows.Media;

    var transform = new RotateTransform() {Angle = angleInDegrees, CenterX = center.X, CenterY = center.Y};
    var transformedPoint = transform.Transform(point);

Rotate a point by another point in 2D

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