Transforming 2D point to 2D object-space [closed]

GUI objects in ROBLOX are positioned based on their top-left coordinates when they're not rotated, and they're rotated based on their center coordinates. This can cause some problems when figuring out where things are rendered.

Center Coordinates

Since GUI objects are rotated around their center coordinates, I decided to make a function that told me where the center coordinates are:

local function GetCenterOfGuiObject(guiObject)
    return Vector2.new(
        guiObject.AbsolutePosition.x + guiObject.AbsoluteSize.x/2,
        guiObject.AbsolutePosition.y + guiObject.AbsoluteSize.y/2
    )
end

Center of Edges

Having this function, we can now focus on finding the centers of the edges, which we can then use to determine the placements of the handles. Things to note:

• The rotations go clockwise instead of the natural counterclockwise.
• The y axis is flipped; as you go down, the y-ordinate gets bigger instead of smaller.
• As a GUI object rotates, the center of each edge stays the same distance away from the center of the GUI object; the center of each edge draws a circle around the GUI object as it moves.

Keeping these things in mind, I wrote a simple function to help me determine where the edges of any GUI object would be:

local function GetCenterOfEdge(guiObject, edge)
    local center = GetCenterOfGuiObject(guiObject);
    local size = guiObject.AbsoluteSize;
    local rotation = math.rad(guiObject.Rotation);
    if edge == "Left" then
        size = Vector2.new(size.x, size.x) -- moves like a circle
        rotation = rotation - math.pi;
    elseif edge == "Top" then
        size = Vector2.new(size.y, size.y)
        rotation = rotation - math.pi/2;
    elseif edge == "Right" then
        size = Vector2.new(size.x, size.x)
        rotation = rotation;
    elseif edge == "Bottom" then
        size = Vector2.new(size.y, size.y)
        rotation = rotation + math.pi/2;
    end
    rotation = -rotation; -- clockwise
    return center + (size/2) * Vector2.new(
        math.cos(rotation),
        -math.sin(rotation) -- to fix flipped y-axis
    )
end

Now that we know the centers of any edge, we can easily position the top-left of our handles relative to that. I'm sure you can figure out how to do that, however. :P