Torus Sketch is a simple, descriptively-named interactive program for drawing on a square torus. “Simple” means freehand drawing with no editing capability, and no hidden-line removal. The image below is a screenshot. Please visit the link for the live software.
Instructions: The 10×10 square grid on the left is the drawing canvas. Each 5×5 sub-grid makes a unit square, which “wraps once” around the torus at right. Place your mouse cursor over the square grid on the left. Click and hold while moving the mouse to draw. The “corresponding” path is also drawn in the torus canvas.
Preferences: Click on the palette to select the pen color, or on the color swatch labeled “Pen” to open a color-picker. “Snap to grid” subdivides each square into a (virtual, undrawn) 4×4 grid and restricts the pen location to points of that grid, a bit like a coarse Etch-A-Sketch with chess-king steps. “Size” controls the canvas size in pixels.
Viewpoint: The torus can be rotated in space using the arrow keys. Up and Down pitch the torus, while Left and Right yaw the torus. The canvas can be translated, which amounts to “internal” rotations of the torus. The z-x keys translate the domain horizontally. The c-v keys translate the domain vertically.