Transforming 2D point to 2D object-space

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