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A Graphic Vision of APL

by Graeme Robertson

Vector 1:1, page 36

graphics APL in perspective

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 36

Many graphics packages written in APL have appeared on the I.P. Sharp Associates system over the last seven years. Their capabilities are indicated in some forty slides prepared on a flatbed plotter using software packages SUPERPLOT, SAGA, DRAWMAPS, ROUTEMAPS, STARMAP, DRAWNET, PLOT3DH, PRISMPLOT, PICTURES and GRAPHICS.

A close analogy exists between the vector algebraic approach of APL notation and that of GRAPHICS, the inspiration behind these other packages.

GRAPHICS is used to represent APL arrays of different ranks. Lines are generated which represent real and complex numeric vectors. Surfaces are generated which represent real numeric matrices. Solid wireframe lattices are used in the representation of three and four dimensional arrays. Finally, all these attempts are abandoned in favour of a recursive definition which can in principle yield a visual representation of a real or complex numeric APL array of any rank whatever.

These results were exhibited in the seminar using twenty colourful slides. Arrays which are generated as the results of APL functions give very pleasing images which, it was argued, can be used to help students to understand the nature of complicated mathematical functions.

Structure of the Seminar

  1. An Overview of Computer Graphics
    • 1.1 A definition of Graphics
    • 1.2 A cursory history of computer graphics
    • 1.3 Application areas
  2. From Business Graphics to Art
    • 2.1 Towards Graphical Representations
    • 2.2 Business Graphics
    • 2.3 Into 3-D
    • 2.4 Art
  3. APL and Graphics
    • 3.1 Graphic Variables
    • 3.2 Graphic Primitive Functions
    • 3.3 A Graphic Operator
    • 3.4 Graphic APL-like Utility Functions
  4. Representations of Numeric Data and Functions
    • 4.1 Result Rank 1
    • 4.2 Result Rank 2
    • 4.3 Result Rank 3
    • 4.4 Result Rank 4
    • 4.5 Arbitrary Rank

Fig.1 — Greek Domestic Light Transport Flights for May 1983

Map of Greece with flight routes radiating from Athens, concentric distance rings, and a legend for Shorts 330, Britten Norman Islander and Shorts Skyvan. Courtesy of I.P. Sharp Associates; OAG data copyright 1984 by Official Airline Guides Inc., Oak Brook, Illinois

Fig.2 — Total Reserves minus Gold (Billions of U.S. Dollars)

A 3-D grid of stacked columns by year (1975–1979) and quarter (first to fourth), each column divided into United States, Canada and Australia. Produced using PLOT3DH, I.P. Sharp Associates

Fig.3 — I.P. Sharp Associates London Office Location

Street map around Victoria Station, London, marking I.P. Sharp at 132 Buckingham Palace Road, (01) 730 4567, Victoria Coach Station and British Airways. Produced with I.P. Sharp SAGA graphics utility

Fig.4 — Computer Aided Instructions Using Graphics

A teaching screen on relativity: a lattice of clocks; a dialogue between a master (S) and a pupil (K) about two reference frames A and B moving at velocity ABX1V; a right-angled triangle of clocks with sides ABX1V×AT, C×BT and C×AT; and the relation between the clocks given by Pythagoras

Fig.5 — Set of Typefaces

Plotter typefaces: Light Block (Roman Simplex), Heavy Block (Roman Duplex), Light Serif (Roman Complex), Heavy Serif (Roman Triplex), Light Italic (Italic Complex), Heavy Italic (Italic Triplex), Light Script (Script Simplex), Heavy Script (Script Complex), English Gothic, German Gothic, Italian Gothic

Fig.6 — Rank Five Complex Array

A rank-five complex array drawn as nested 3×3 grids of short strokes, their angle turning from vertical to oblique across the grids