3D Shape

This program draws a 3D wireframe cube using a full 4×4 homogeneous transformation matrix pipeline. It defines the cube’s eight vertices and twelve edges via READ/DATA statements, computes the centroid of the shape, builds a combined rotation/scaling/translation matrix, transforms each vertex, and then plots each edge pixel-by-pixel using a manual line-drawing loop with direction cosines rather than the built-in DRAW command. The rotation angles are set in degrees and converted to radians (40°, 20°, 50° for X, Y, Z axes respectively), with scaling factors of 0.3 on all axes. A notable anomaly exists at line 900: the subroutine body (lines 910–960) draws a border rectangle, but the REM line 900 is missing from the listing, and line 70 calls GO SUB 900 before variable initialisation. Originally printed in Nick Hampshire’s Color Graphics.

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Program Structure

The program is divided into clearly labelled subroutines, each beginning at a round-numbered line and ending with RETURN. Execution flows as follows:

1. Lines 1–4: Introduction text, wait for keypress, clear screen.
2. Line 70: GO SUB 900 — draw a border rectangle.
3. Lines 100–200: Declare arrays and set transformation parameters.
4. Lines 410–450: Call four subroutines in sequence (shape init, centroid, matrix build, transform, draw), then STOP.
5. Lines 900–960: Border-drawing subroutine using PLOT/DRAW.
6. Lines 1000–1900: Shape initialisation — reads vertex coordinates and edge connectivity from DATA.
7. Lines 2000–2900: Draw subroutine — plots each edge pixel by pixel.
8. Lines 3000–3900: Builds the 4×4 rotation matrix a() and the combined scaling/translation matrix b().
9. Lines 4000–4900: Applies the transformation matrix to each vertex, storing results in m().
10. Lines 5000–5900: Computes the centroid (xc, yc, zc) of the shape.

Shape Definition

The cube is defined by np=8 vertices and ne=12 edges stored in arrays s(3,np) and e(ne,2). Vertices are unit-cube coordinates scaled to 200 units, read from DATA at lines 1210–1220. Edge connectivity pairs are read at lines 1310–1330 and describe the 12 edges of the cube.

Array	Dimensions	Contents
s(3,np)	3×8	Original vertex coordinates (x,y,z)
e(ne,2)	12×2	Edge endpoint index pairs
m(3,np)	3×8	Transformed vertex coordinates
a(4,4)	4×4	Rotation matrix
b(4,4)	4×4	Combined scale + translation matrix

Transformation Pipeline

The program implements a classical homogeneous coordinate transformation pipeline. The rotation matrix a() is constructed at lines 3010–3160 from Euler angles rx, ry, rz (40°, 20°, 50° converted to radians). It is a combined Rx·Ry·Rz rotation. The b() matrix (lines 3210–3350) folds in per-axis scaling (sx, sy, sz = 0.3) by multiplying rows 1–3 of a(), and sets the translation row (b(4,1..3)) to tx,ty,tz = 1,1,1.

The actual transform at lines 4020–4070 centres each point around the centroid before applying b(), then re-adds the centroid offset — a correct centre-of-shape rotation technique.

Edge Drawing Technique

Rather than using the built-in DRAW command, the draw subroutine (lines 2000–2900) manually interpolates along each edge. For each edge it computes the Euclidean length r and direction cosines lx = p/r, ly = q/r, then steps from 0 to r in increments of ds=1, plotting each pixel. Bounds checking at lines 2180–2210 clips points outside the 0–255 (x) and 0–175 (y) screen range.

Notable Techniques and Idioms

• Degrees-to-radians conversion is done inline: 40*PI/180 etc. (lines 180–200).
• The centroid subroutine (5000) reuses variable names p, q, r which are also used in the draw subroutine — this is safe only because the centroid is computed before drawing, but it is a potential confusion point.
• The loop variable e at line 1150 shadows the array name e(); BASIC allows this because the array is distinguished by its parentheses, but it is unusual style.
• Line 2045 checks IF v1=0 THEN GO TO 2240, skipping to the outer NEXT e — this acts as a guard for uninitialised or null edge entries, though all 12 edges are populated by the data.