4.30: Different Coordinate Systems

def leftTopCoordsOfBox(boxx, boxy):
# Convert board coordinates to pixel coordinates
left = boxx * (BOXSIZE + GAPSIZE) + XMARGIN
top = boxy * (BOXSIZE + GAPSIZE) + YMARGIN
return (left, top)


You should be familiar with Cartesian Coordinate systems. (If you’d like a refresher on this topic, read http://invpy.com/coordinates.) In most of our games we will be using multiple Cartesian Coordinate systems. One system of coordinates that is used in the Memory Puzzle game is for the pixel or screen coordinates. But we will also be using another coordinate system for the boxes. This is because it will be easier to use (3, 2) to refer to the 4th box from the left and 3rd from the top (remember that the numbers start with 0, not 1) instead of using the pixel coordinate of the box’s top left corner, (220, 165). However, we need a way to translate between these two coordinate systems.

Here’s a picture of the game and the two different coordinate systems. Remember that the window is 640 pixels wide and 480 pixels tall, so (639, 479) is the bottom right corner (because the top left corner’s pixel is (0, 0), and not (1, 1)).

The leftTopCoordsOfBox() function will take box coordinates and return pixel coordinates. Because a box takes up multiple pixels on the screen, we will always return the single pixel at the top left corner of the box. This value will be returned as a two-integer tuple. The leftTopCoordsOfBox() function will often be used when we need pixel coordinates for drawing these boxes.