---
title: "Circle Fill"
id: 71181
type: "computer_media"
slug: "circle-fill"
url: "http://localhost/computer_media/circle-fill/"
markdown_url: "http://localhost/computer_media/circle-fill.md"
published_at: "2026-08-31T07:38:11+00:00"
modified_at: "2026-08-31T07:38:11+00:00"
author: "David Anderson"
featured_image:
  url: "http://localhost/wp-content/uploads/2026/08/circle-fill.png"
  alt: "Circle Fill screen"
excerpt: "A clever scan-line algorithm fills a circle using Pythagorean geometry, accepting custom ink color, center coordinates, and radius — all in under ten lines."
category:
  - name: "Archived Media"
    slug: "archived-media"
    taxonomy: "category"
    url: "http://localhost/category/archived-media/"
post_tag:
  - name: "Downloadable"
    slug: "downloadable"
    taxonomy: "post_tag"
    url: "http://localhost/tag/downloadable/"
  - name: "TS 2068"
    slug: "ts2068"
    taxonomy: "post_tag"
    url: "http://localhost/tag/ts2068/"
model:
  - name: "Timex/Sinclair 2068"
    slug: "ts-2068"
    taxonomy: "model"
    url: "http://localhost/model/ts-2068/"
genre:
  - name: "Demo"
    slug: "demo"
    taxonomy: "genre"
    url: "http://localhost/type/demo/"
media_type: "Program"
download_url: "https://archive.org/download/timex-sinclair-software-archive/Circle%20Fill%20%28198x%29%28-%29%28TS2068%29%28US%29%28Program%29.zip"
mediadate: "198x"
images:
  - url: "http://localhost/wp-content/uploads/2026/08/circle-fill.png"
    alt: "Circle Fill screen"
media_type_tags: "Demo"
---

# Circle Fill

Circle Fill draws a filled circle on screen by combining the built-in CIRCLE command with a scan-line fill algorithm. The program accepts user-specified ink color, center coordinates, and radius, then iterates from N=0 to R, computing the horizontal half-chord length at each vertical offset using the Pythagorean relationship XX=SQR(R²−N²). Two vertical DRAW strokes are plotted symmetrically on either side of the center X coordinate to paint the interior column by column. Because it fills using vertical line segments rather than horizontal scan lines, it exploits the PLOT/DRAW command pair efficiently without needing to track left and right pixel boundaries per row.

***

### Program Structure

The program is a short, linear routine with no subroutines or complex branching. It collects five inputs (ink color, X, Y, and radius), draws the circle outline using the built-in `CIRCLE` command at line 35, then fills the interior with a `FOR` loop spanning lines 40–90.

| Lines | Purpose |
| --- | --- |
| 1 | Input ink color `A` |
| 5 | Set INK, PAPER, and BORDER attributes |
| 10–30 | Input center coordinates `X`, `Y`, and radius `R` |
| 35 | Draw circle outline with built-in `CIRCLE` |
| 40–90 | Fill loop: iterate `N` from 0 to `R`, plot vertical chords |

### Fill Algorithm

The fill works by iterating `N` across the horizontal range 0 to `R`. For each column offset `N`, the half-chord height `XX` is computed as `SQR(R²−N²)` — a direct application of the Pythagorean theorem. Two vertical line segments are then drawn: one at `X+N` and one at `X−N`, both starting at `Y+XX` and extending downward by `2*XX`. This symmetrically fills left and right halves of the circle simultaneously, meaning each pass covers two columns at once (except at `N=0`, where both `PLOT`/`DRAW` pairs coincide on the center column).

### Key BASIC Idioms

- `LET Z=R^2` and `LET ZZ=N^2` at line 50 cache the squared values to avoid recomputing them twice within the same iteration — a minor but sensible optimization in interpreted BASIC.
- `DRAW 0,-XY` draws a purely vertical line downward of length `2*XX`, making use of the two-argument form of `DRAW` with zero horizontal displacement.
- The `INK A:PAPER 0:BORDER 0` idiom at line 5 chains attribute-setting commands on a single line, keeping the setup compact.

### Notable Techniques

Using vertical chord segments rather than horizontal scan lines is an unconventional but valid approach. Horizontal scan-line filling is more common because display memory is organized in rows, but vertical chord filling is geometrically equivalent and requires no per-row boundary tracking. The trade-off is that for large radii, very thin columns near the edges (where `N` approaches `R`) will have very short chords, and floating-point rounding in `SQR` could leave occasional unfilled pixels near the circle’s leftmost and rightmost extremes.

### Potential Issues and Anomalies

- Line 1 inputs `A` for ink color but provides no prompt string, which may confuse users unfamiliar with the expected input order.
- No bounds checking is performed: entering coordinates or a radius that would cause pixels to fall outside the screen area will produce an error rather than clipping gracefully.
- At `N=0`, both `PLOT X+0,YY: DRAW 0,-XY` and `PLOT X-0,YY: DRAW 0,-XY` address the same column, resulting in the center vertical chord being drawn twice — a harmless but redundant operation.
- The `CIRCLE` at line 35 draws the outline before the fill loop runs. Depending on floating-point precision in the chord computation, the fill may not perfectly reach the outline in all directions, potentially leaving a thin gap at the perimeter.

## Source Code

```
  1 INPUT A
  5 INK A:PAPER 0:BORDER 0
 10 INPUT "X COORDINATE (0-255) ";X
 20 INPUT "Y COORDINATE (0-175) ";Y
 30 INPUT "RADIUS ";R
 35 CIRCLE X,Y,R
 40 FOR N=0 TO R
 50 LET Z=R^2:LET ZZ=N^2
 55 LET XX= SQR (Z-ZZ)
 60 LET YY=Y+XX:LET XY=2*XX
 70 PLOT X+N,YY:DRAW 0,-XY
 80 PLOT X-N,YY:DRAW 0,-XY
 90 NEXT N
```