svan
svan

Reputation: 3

How to find the coordinates of a point lying on a circle, knowing the coordinates of another point and the angle between them

I want to find the blue point
I know the red point b
and the angle between 2 radii

image

Upvotes: 0

Views: 40

Answers (1)

LydiasPost
LydiasPost

Reputation: 70

We know that the red point has coordinates (B.x, B.y). We know the origin point (A.x, A.y). We know the angle between the points theta. We want to find (C.x, C.y). I will be assuming 2d geometry, as this is what your reference shows.

Using a rotation matrix, we can subtract B by A to place A at the origin, then applying the matrix with the angle given.

Thus, given

B_new = (B.x - A.x, B.y - A.y),

C = (B_new.x * cos(theta) - B_new.y * sin(theta), B_new.x * sin(theta) + B_new.y * cos(theta)) + (A.x, A.y)

Upvotes: 1

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