Image rotation & tracking locations

I am rotating an image around it center point but need to track a location on the image as it rotates.

Given:

1. Origin at 0,0
2. Image width and height of 100, 100
3. Rotation point at C(5开发者_运维技巧0,50)
4. Angle of "a" (say 90 degrees in this example)
5. Point P starts at (25,25) and after the rotation it is at Pnew(75,25)

I haven't touched trig in 20 years but guessing the formula is simple...

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I haven't touched trig in 20 years but guessing the formula is simple...

Yep, fairly. To map the point (x1,y1) via rotation around the origin:

x2 = cos(a) * x1 + sin(a) * y1;
y2 = cos(a) * y1 - sin(a) * x1;

... so you just first need to translate to the origin i.e. (-50,-50) in your example and translate back after rotation.

x2 = cos(a) * (x1 - 50) + sin(a) * (y1 - 50) + 50;
y2 = cos(a) * (y1 - 50) - sin(a) * (x1 - 50) + 50;

... Or something like that. (You can generate a matrix which will do all three transformations, I'll leave that for another answer or as an exercise...)