3D DRAW

This program renders a wireframe 3D cube on screen using a full 3×3 rotation matrix combined with scaling and translation transforms. The shape is defined by 8 vertices and 12 edges stored in DATA statements, with rotation angles set to 40°, 20°, and 50° around the X, Y, and Z axes respectively. The transformation matrix (subroutine 720) is itself stored as DATA expressions using trigonometric functions, which are read with RESTORE and evaluated at runtime. Rather than using DRAW for edges, the program manually steps along each edge in unit increments using direction cosines, plotting individual points and clipping against screen boundaries. A centroid-finding routine (line 1000) computes the geometric center of the shape to serve as the pivot point for the rotation.

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Program Structure

The program is organized into a main control sequence (lines 10–240) that calls a series of subroutines in order, plus a border-drawing routine at line 250. Execution flows as follows:

1. Display introduction text and wait for a keypress (lines 20–40)
2. Draw a screen border (line 250 subroutine)
3. Initialize the shape data — vertices and edges — from DATA (line 260 subroutine)
4. Find the centroid of the shape (line 1000 subroutine)
5. Build the 4×4 transformation matrix from trig DATA (line 720 subroutine)
6. Apply the combined rotation/scale/translation to each vertex (line 900 subroutine)
7. Draw the transformed edges (line 460 subroutine)
8. STOP

Shape Definition

The cube is stored as two parallel arrays: s(3,np) holds the X, Y, Z coordinates of np=8 vertices, and e(ne,2) holds the vertex-index pairs for ne=12 edges. Coordinate values range from 0 to 200 in each axis, forming a 200-unit cube. The DATA at lines 390–440 encodes these values; lines 420–440 list edge connectivity pairs such as 1,2 (vertex 1 to vertex 2).

Transformation Matrix Construction

The rotation matrix is stored as DATA expressions at lines 730–810, using COS and SIN of the pre-calculated angles rx, ry, rz. These are read into the 4×4 array a(4,4) via RESTORE 720 at line 820. The loop uses SGN PI (which evaluates to 1) as the loop start value — a slightly indirect way to write FOR e=1 TO 4.

The combined scaling and translation matrix b(4,4) is then built at lines 840–890 by reading another DATA block (line 870) that multiplies rows of a by scale factors sx, sy, sz and appends translation values tx, ty, tz. Notably, the DATA at line 870 is embedded inline within the loop rather than placed at a separate location, relying on RESTORE 850 to position the DATA pointer correctly at the start of the subroutine entry.

Translation/Rotation Application

Subroutine 900 applies the combined matrix b to each vertex. Each vertex is first offset relative to the centroid (xc, yc, zc), matrix-multiplied, and then the centroid is added back. This ensures rotation occurs about the shape’s geometric center rather than the origin. Results are stored in m(3,np); only the X (m(1,q)) and Y (m(2,q)) components are used for 2D screen plotting — no explicit perspective divide is performed, making this an orthographic projection.

Edge Drawing Routine

Rather than using the built-in DRAW command, subroutine 460 manually steps along each edge. For each edge, it computes direction cosines lx and ly by dividing the delta components by the Euclidean distance r, then iterates from 0 to r in steps of ds=1, computing and PLOTting each point. Screen boundary clipping is performed inline at lines 640–670, checking that each point lies within 0–255 (X) and 0–175 (Y) before plotting.

A check at line 500 skips any edge whose first vertex index is 0 (IF v1=0 THEN GO TO 700), providing a mechanism to encode “pen up” moves, though no such entries exist in the current DATA.

Notable Techniques and Anomalies

• Storing trigonometric expressions directly as DATA (lines 730–810) is an unusual technique; the BASIC interpreter evaluates these expressions when they are READ at runtime.
• The SGN PI idiom at line 820 evaluates to 1 and is used as the loop lower bound — functionally equivalent to FOR e=1 but more circuitous.
• Variables p, q, and r are reused in subroutine 1000 (centroid calculation) and also in subroutine 460 (edge drawing), which would cause a conflict if both were active simultaneously — but since they are called sequentially, no actual collision occurs at runtime.
• Similarly, the loop variable e is used both as the edge-index loop variable (lines 350, 470) and as a matrix row index (line 820, 850), which works only because BASIC reuses the same variable name in separate loop contexts.
• The scaling matrix construction at line 870 repeats each scale factor three times (e.g., sx*a(i,1), sx*a(i,1), sx*a(i,1)) — this applies the same scale to all three columns of each row, effectively making sx=sy=sz regardless of their individual values set at lines 90–110.
• No perspective projection is applied; the result is a parallel (orthographic) projection onto the XY plane.

Variable Summary

Variable	Purpose
sx, sy, sz	Scale factors (all set to 0.3)
tx, ty, tz	Translation offsets (all set to 1)
rx, ry, rz	Rotation angles in radians (40°, 20°, 50°)
np, ne	Number of points (8) and edges (12)
s(3,np)	Original vertex coordinates
e(ne,2)	Edge vertex-index pairs
m(3,np)	Transformed vertex coordinates
a(4,4)	Rotation matrix
b(4,4)	Combined scale/translate/rotation matrix
xc, yc, zc	Centroid coordinates