Calculating vertices of a rotated rectangle

Question

I am trying to calculate the vertices of a rotated rectangle (2D).

It's easy enough if the rectangle has not been rotated, I figured that part out.

If the rectangle has been rotated, I thought of two possible ways to calculate the vertices.

1. Figure out how to transform the vertices from local/object/model space (the ones I figured out below) to world space. I honestly have no clue, and if it is the best way then I feel like I would learn a lot from it if I could figure it out.

2. Use trig to somehow figure out where the endpoints of the rectangle are relative to the position of the rectangle in world space. This has been the way I have been trying to do up until now, I just haven't figured out how.

Here's the function that calculates the vertices thus far, thanks for any help

void Rect::calculateVertices()
{
    if(m_orientation == 0) // if no rotation
    {
        setVertices(
        &Vertex( (m_position.x - (m_width / 2) * m_scaleX), (m_position.y + (m_height / 2) * m_scaleY), m_position.z), 
        &Vertex( (m_position.x + (m_width / 2) * m_scaleX), (m_position.y + (m_height / 2) * m_scaleY), m_position.z),
        &Vertex( (m_position.x + (m_width / 2) * m_scaleX), (m_position.y - (m_height / 2) * m_scaleY), m_position.z),
        &Vertex( (m_position.x - (m_width / 2) * m_scaleX), (m_position.y - (m_height / 2) * m_scaleY), m_position.z) );
    }
    else
    {
        // if the rectangle has been rotated..
    }

    //GLfloat theta = RAD_TO_DEG( atan( ((m_width/2) * m_scaleX) / ((m_height / 2) * m_scaleY) ) );
    //LOG->writeLn(&theta);

}

Answer 1

I would just transform each point, applying the same rotation matrix to each one. If it's a 2D planar rotation, it would look like this:

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.

My recommendation would be to do it out on paper once. Draw a rectangle, calculate the new coordinates, and redraw the rectangle to satisfy yourself that it's correct before you code. Then use this example as a unit test to ensure that you coded it properly.