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Asked: 2026-05-12T18:01:20+00:00

(This is all in ortho mode, origin is in the top left corner, x

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(This is all in ortho mode, origin is in the top left corner, x is positive to the right, y is positive down the y axis)

I have a rectangle in world space, which can have a rotation m_rotation (in degrees).

I can work with the rectangle fine, it rotates, scales, everything you could want it to do.

The part that I am getting really confused on is calculating the rectangles world coordinates from its local coordinates.

I’ve been trying to use the formula: 

x' = x*cos(t) - y*sin(t) 
y' = x*sin(t) + y*cos(t)

where (x, y) are the original points,
(x', y') are the rotated coordinates,
and t is the angle measured in radians

from the x-axis. The rotation is
counter-clockwise as written. 
-credits duffymo

I tried implementing the formula like this:

//GLfloat Ax = getLocalVertices()[BOTTOM_LEFT].x * cosf(DEG_TO_RAD( m_orientation )) - getLocalVertices()[BOTTOM_LEFT].y * sinf(DEG_TO_RAD( m_orientation ));
//GLfloat Ay = getLocalVertices()[BOTTOM_LEFT].x * sinf(DEG_TO_RAD( m_orientation )) + getLocalVertices()[BOTTOM_LEFT].y * cosf(DEG_TO_RAD( m_orientation ));

//Vector3D BL = Vector3D(Ax,Ay,0);

I create a vector to the translated point, store it in the rectangles world_vertice member variable. That’s fine. However, in my main draw loop, I draw a line from (0,0,0) to the vector BL, and it seems as if the line is going in a circle from the point on the rectangle (the rectangles bottom left corner) around the origin of the world coordinates.

Basically, as m_orientation gets bigger it draws a huge circle around the (0,0,0) world coordinate system origin. edit: when m_orientation = 360, it gets set back to 0.

I feel like I am doing this part wrong:

and t is the angle measured in radians
from the x-axis.

Possibly I am not supposed to use m_orientation (the rectangles rotation angle) in this formula?

Thanks!

edit: the reason I am doing this is for collision detection. I need to know where the coordinates of the rectangles (soon to be rigid bodies) lie in the world coordinate place for collision detection.

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1 Answer

  1. Editorial Team

    What you do is rotation [ special linear transformation] of a vector with angle Q on 2d.It keeps vector length and change its direction around the origin.

    alt text

    [linear transformation : additive L(m + n) = L(m) + L(n) where {m, n} € vector , homogeneous L(k.m) = k.L(m) where m € vector and k € scalar ] So:

    You divide your vector into two pieces. Like m[1, 0] + n[0, 1] = your vector.
    Then as you see in the image, rotation is made on these two pieces, after that your vector take
    the form:

    m[cosQ, sinQ] + n[-sinQ, cosQ] = [mcosQ – nsinQ, msinQ + ncosQ]

    you can also look at Wiki Rotation

    If you try to obtain eye coordinates corresponding to your object coordinates, you should multiply your object coordinates by model-view matrix in opengl.

    For M => model view matrix and transpose of [x y z w] is your object coordinates you do:

    M[x y z w]T = Eye Coordinate of [x y z w]T

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