How to draw a Perspective-Correct Grid in 2D
I have an application that defines a real world rectangle on top of an image/photograph, of course in 2D it may not be a rectangle because you are looking at it from an angle.
The problem is, say that the rectangle needs to have grid lines drawn on it, for example if it is 3x5 so I need to draw 2 lines from side 1 to side 3, and 4 lines from side 2 to side 4.
As of right now I am breaking up each line into equidistant parts, to get the start and end point of all the grid lines. However the more of an angle the rectangle is on, the more "incorrect" these lines become, as horizontal lines further from you should be closer together.
Does anyone know the name of the algorithm that I should be searching for?
Yes I know you can do this in 3D, however I am limited to 2D for this particular application.
Answer
Here's the solution.
The basic idea is you can find the perspective correct "center" of your rectangle by connecting the corners diagonally. The intersection of the two resulting lines is your perspective correct center. From there you subdivide your rectangle into four smaller rectangles, and you repeat the process. The number of times depends on how accurate you want it. You can subdivide to just below the size of a pixel for effectively perfect perspective.
Then in your subrectangles you just apply your standard uncorrected "textured" triangles, or rectangles or whatever.
You can perform this algorithm without going to the complex trouble of building a 'real' 3d world. it's also good for if you do have a real 3d world modeled, but your textriangles are not perspective corrected in hardware, or you need a performant way to get perspective correct planes without per pixel rendering trickery.