Sphere 3D

This program plots a Lissajous-style parametric curve on the screen using the equations x = 125 + g·sin(a) and y = 87 + g·sin(0.95a)·cos(a), where g is a user-supplied size value and a steps from 0 to 125.7 in increments of 0.03. The resulting shape is a closed or near-closed figure-eight or knot pattern depending on the irrational frequency ratio (0.95). After drawing, all plotted points are stored in the string array b$, with each coordinate packed as a single CHR$ character, allowing the curve to be redrawn from memory without recalculating. The program uses a 4200-element two-character-wide string array to buffer coordinates, exploiting the fact that screen coordinates fit within the 0–255 range of a single byte stored as a character code. Redrawing from the buffer on the second pass demonstrates an efficient coordinate caching technique using CODE to recover the numeric values from stored characters.

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Program Analysis

Program Structure

The program divides into three logical phases:

1. Initialization (line 5): Sets display attributes, clears the screen, and dimensions the coordinate buffer array.
2. Plotting loop (lines 20–50): Prompts for a size parameter, iterates through the parametric angle, computes and plots each point, and stores coordinates in the buffer.
3. Redraw phase (lines 100–110): Waits for a keypress, clears the screen, and replots the entire curve from the buffered data.

Parametric Equations

The curve is defined by:

• x = 125 + g * SIN(a)
• y = 87 + g * SIN(0.95 * a) * COS(a)

The parameter a runs from 0 to 125.7 in steps of 0.03, giving approximately 4190 points. The irrational frequency ratio of 0.95 (= 19/20) means the x and y oscillations have a near but not exactly integer relationship, producing a dense, slowly precessing Lissajous-like figure. The center is offset to approximately the middle of the 256×176 pixel display area.

Coordinate Buffer Technique

The array b$(4200,2) is declared as a two-column string array, where each element holds a single character. The x coordinate is stored as CHR$(x) in column 1, and the y coordinate as CHR$(y) in column 2. During the redraw phase, CODE b$(a,1) and CODE b$(a,2) recover the numeric values. This is an efficient packing scheme that exploits the 0–255 range of a character code matching the screen coordinate space exactly, avoiding any floating-point recalculation on the second pass.

Key BASIC Idioms

Line	Idiom	Purpose
5	DIM b$(4200,2)	Allocates a fixed-size 2-column string array as a coordinate store
40	CHR$(x) / CHR$(y)	Packs integer coordinates into single characters for compact storage
100	FLASH 1 / PAUSE 0	Attracts attention then waits for any keypress before redrawing
110	CODE b$(a,1)	Unpacks stored character back to its numeric coordinate value

Notable Techniques

The use of PRINT #0; on line 100 directs the flashing prompt to the lower status area (stream 0) rather than the main screen, preserving the drawn curve while awaiting user input. The counter variable c tracks how many points were actually plotted, so the redraw loop on line 110 iterates exactly c-1 times rather than assuming all 4200 slots are populated.

Potential Issues

With a step of 0.03 over a range of 125.7, the loop generates approximately 4190 iterations. The buffer is sized at 4200, leaving a small safety margin of about 10 elements. However, if g is large enough to push computed x or y values outside the 0–255 range, CHR$ would produce an error. No bounds checking is performed on the coordinate values before storing them, which could cause an out-of-range error for very large size inputs.