ProjectionMappingApplesoftBasic

This program is a basic 3D Cube Simulation written in Applesoft Basic. You can try it yourself on "https://www.calormen.com/jsbasic/", or on any other emulator by uploading the "CubeSim.txt".

1. Variable Initialization

In Applesoft Basic, only the first two letters of a variable are significant. To avoid confusion, short variable names are used:

• hgr: Initializes high-resolution graphics mode.
• cx, cy, sd: Cube position coordinates and side depth.
• xv, yv, zv: Cube movement velocities.
• dim c3(7,2): Defines a 3D array c3 to hold the 3D coordinates of the cube’s vertices.
• dim c2(7,1): Defines a 2D array c2 to hold the projected 2D coordinates of the cube’s vertices.
• cs: Cube size.
• f: Frame buffer toggle.
• rs: Rotation speed.
• buffer: Boundary buffer size to detect collisions.
• gosub 1000: Calls subroutine 1000 to initialize the cube’s vertices.

2. Main Loop

The main loop calls various subroutines to handle different aspects of the simulation:

Subroutines Called:

• Movement (gosub 4000): Updates the cube's position and applies rotation.
• Projection (gosub 2000): Converts 3D coordinates to 2D.
• Collision Detection (gosub 5000): Checks if the cube hits the screen borders and bounces it back if necessary.
• Drawing (gosub 3000): Renders the cube on the screen.
• Delay (gosub 7000): Adds a delay to control the simulation speed.
• Key Listener (gosub 8000): Handles keyboard input to control the cube.

3. Cube Initialization

Defines the 3D coordinates of the cube’s vertices based on its size and initial position:

Loop: Iterates over the 8 vertices of the cube and sets their coordinates.

4. Coordinate Projection

Converts 3D coordinates to 2D for display:

Projection Logic: Adjusts coordinates by reducing the Z-axis effect to project a 3D point onto a 2D plane.

5. Drawing the Cube

Draws the cube using the 2D projected coordinates:

Frame Buffer: Toggles between frame buffers to avoid flickering. Line Drawing: Connects the vertices to form the cube's edges using hplot.

6. Cube Movement

Updates the cube's position based on velocity and applies rotation if enabled:

Position Update: Moves the cube by adding velocity to its current position. Rotation Application: Calls the rotation subroutine to update the coordinates.

7. Collision Detection

Checks if the cube has hit the screen borders and reverses its direction if it has:

Boundary Check: Reverses velocity when a boundary is hit to make the cube bounce back.

8. Key Listener and Event Manager

Handles keyboard input for controlling the cube:

Key Press Detection:

• 'up' and 'down' Adjust movement speed
• 'r' toggles rotation
• 'f' and 's' modify rotation speed.

9. Rotation Matrices

Applies rotation to the cube around the X, Y, and Z axes:

Rotation Logic: Uses trigonometric functions to rotate the cube's vertices around the axes.

10. Delay Function

Creates a delay to control the simulation speed:

Loop Delay: Iterates over a loop to create a pause, simulating a delay.