PieChart

This program draws a pie chart by plotting dots in polar coordinates, reading wedge definitions from DATA statements at lines 500–540. Each DATA record supplies a dot-density value, a start angle, and an end angle (all in degrees), which are converted to radians internally. The dot density parameter controls both the radial step and the angular step, with the angular increment scaled by 40/r to keep dot spacing roughly uniform across radii. A subroutine at line 400 draws a rectangular border using PLOT/DRAW before the chart is rendered. The program halts when it reads a density value of 0, acting as a sentinel terminator for the DATA list.

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Program Structure

The program is divided into four logical sections:

1. Introduction (lines 1–4): Displays a description and waits for a keypress via the INKEY$="" polling loop at line 3.
2. Main loop (lines 60–330): Sets colours, calls the border subroutine, reads one wedge record, and plots it; then loops back via GO TO 100 (note: line 100 does not exist — see Bugs section).
3. Border subroutine (lines 410–460): Draws a full-screen rectangle using PLOT/DRAW.
4. Data (lines 500–540): Four wedge records plus a sentinel 0,0,0.

Rendering Algorithm

Each wedge is filled by iterating over two nested loops: an outer loop over radius r (from ds to ra in steps of ds) and an inner loop over angle p (from as to ae). The angular step at line 250 is d*(40/r), where d is the density converted to radians. Dividing by r compensates for the increasing arc length at larger radii, keeping dot spacing approximately uniform across the filled area. Each dot is plotted by converting polar (r, p) to Cartesian and offsetting by the centre (xc, yc).

Data Format

Line	ds (density)	Start angle °	End angle °
500	4	1	70
510	3	71	200
520	2	201	300
530	1	301	360
540	0	0	0

A density of 4 produces the sparsest fill (fewest dots) because both the radial step and the angular step are largest. A density of 1 produces the densest fill. The sentinel record (ds=0) triggers STOP at line 150.

Key BASIC Idioms

• IF INKEY$="" THEN GO TO 3 — busy-wait keypress loop; no PAUSE 0 needed here, though it is less efficient.
• READ ds then READ as,ae — reads from the same sequential DATA pointer across two statements, which is valid but slightly unusual; a single READ ds,as,ae would be equivalent.
• All angles are stored in degrees in the DATA but immediately converted to radians using *PI/180, keeping the data human-readable.

Notable Techniques

The angular step formula d*(40/r) at line 250 is an elegant way to achieve roughly constant dot spacing without trigonometric overhead. Since arc length ≈ r·θ, dividing the angular step by r (scaled by a constant 40, matching ra) maintains near-uniform density. The centre coordinates xc=100, yc=100 and radius ra=40 are hardcoded at lines 110–120, placing the chart well within the visible screen area.