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Waveform graphics

Waveform graphics is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Waveform graphics rather than just read about it. In short: Waveform graphics is a simple vector graphics system introduced by Digital Equipment Corporation (DEC) on the VT55 and VT105 terminals in the mid-1970s. It was used to produce graphics output from mainframes and minicomputers.

Waveform graphics — main illustration
Waveform graphics — illustration

Key takeaways

  • Waveform graphics belongs to computer science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Waveform graphics to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Waveform graphics from memory before moving on to harder problems.

Reference excerpt

Waveform graphics is a simple vector graphics system introduced by Digital Equipment Corporation (DEC) on the VT55 and VT105 terminals in the mid-1970s. It was used to produce graphics output from mainframes and minicomputers. DEC used the term "waveform graphics" to refer specifically to the hardware, but it was used more generally to describe the whole system. The system was designed to use as little computer memory as possible. At any given X location it could draw two dots at given Y locations, making it suitable for producing two superimposed waveforms, line charts or histograms. Text and graphics could be mixed, and there were additional tools for drawing axes and markers. The waveform graphics system was used only for a short period of time before it was replaced by the more sophisticated ReGIS system, first introduced on the VT125 in 1981. ReGIS allowed the construction of arbitrary vectors and other shapes. Whereas DEC normally provided a backward compatible solution in newer terminal models, they did not choose to do this when ReGIS was introduced, and waveform graphics disappeared from later terminals.

Description Waveform graphics was introduced on the VT55 terminal in October 1975, an era when memory was extremely expensive. Although it was technically possible to produce a bitmap display using a framebuffer using technology of the era, the memory needed to do so at a reasonable resolution was typically beyond the price point that made it practical. All sorts of systems were used to replace computer memory with other concepts, like the storage tubes used in the Tektronix 4010 terminals, or the zero memory racing-the-beam system used in the Atari 2600. DEC chose to attack this problem through a clever use of a small buffer representing only the vertical positions on the screen. Such a system could not draw arbitrary shapes, but would allow the display of graph data. The system was based on a 512 by 236 pixel display, producing 512 vertical columns along the X-axis, and 236 horizontal rows on the Y-axis. Y locations were counted up from the bottom, so the coordinate 0,0 was in the lower left, and 511, 235 in the upper right. Had this been implemented using a framebuffer with each location represented by a single bit, 512 × 236 × 1 = 120,832 bits, or 15,104 bytes, would have been required. At the time, memory cost about $50 per kilobyte, so the buffer alone would cost over $700 (equivalent to $4,570 in 2025). Instead, the waveform graphic system used one byte of memory for each X axis location, with the byte's value representing the Y location. This required only 512 bytes for each graph, a total of 1024 bytes for the two graphs. Drawing a line required the programmer to construct a series of Y locations and send them as individual points, the terminal could not connect the dots itself. To make this easier, the terminal automatically incremented the X location every time an Y coordinate was received, so a graph line could be sent as a long string of numbers for subsequent Y locations instead of having to repeatedly send the X location every time. Drawing normally started by sending a single instruction to set the initial X location, often 0 on the left, and then sending in data for the entire curve. The system also included storage for up to 512 markers on both lines. These were always drawn centered on the Y value of the line they were associated with, meaning that a simple on/off indication for X locations was all that was needed, requiring only 1024 bits, or 128 bytes, in total. The markers extended 16 pixels vertically, and could only be aligned on 16-pixel boundaries, so they were not necessarily centered across the underlying graph. Markers were used to indicate important points on the graph, where a symbol of some sort would normally be used. The system also allowed a vertical line to be drawn for every horizontal location and a horizontal one at every vertical location. These were also stored as simple on/off bits, requiring another 128 bytes of memory. These lines were used to draw axes and scale lines, or could be used for a screen-spanning crosshair cursor. A separate set of two 7-bit registers held additional information about the drawing style and other settings. Although complex from the user's perspective, this system was easy to implement in hardware. A cathode ray tube produces a display by scanning the screen in a series of horizontal motions, moving down one vertical line after each horizontal scan. At any given instant during this process, the display hardware examines a few memory locations to see if anything needs to be displayed. For instance, it can determine whether to draw a marker on graph 0 by examining register 1 to see if markers are turned on, looking in the marker buffer to see if there is a 1 at the current X location, and then examining the Y location of graph 0 to see if it is within 16 pixels of the current scan line. If all of these are true, a spot is drawn to present that portion of the marker. As this will be true for 16 vertical locations during the scanning process, a 16-pixel high marker will be drawn. Sold alone, the VT55 was priced at $2,496 (equivalent to $16,295 in 2025),. Like other models of the VT50 series, the terminal could be equipped with an optional wet-paper printer in a panel on the right of the screen. This added $800 (equivalent to $5,223 in 2025) to the price. DEC also offered VT55 in a package with a small model of the PDP-11 to create one model of the DEClab 11/03 system. The DEClab normally sold for $14,000 (equivalent to $91,397 in 2025) with a DECwriter II (LA36) hard-copy terminal for $15,000 (equivalent to $97,925 in 2025), with the VT55. The system had I/O channels for up to 15 lab devices, and included libraries for FORTRAN and BASIC for reading the data and creating graphs. The fairly extensive VT55 Programmers Manual covered the latter in depth.

Commands and data

… excerpt ends here. Continue reading the full article.

Illustrations

Waveform graphics: Waveform graphics were limited, but could still produce useful output when used in conjunction with programs like gnuplot.
Waveform graphics were limited, but could still produce useful output when used in conjunction with programs like gnuplot.
Waveform graphics: Histogram mode fills in the area under the curve. This example illustrates why the system was called waveform graphics.
Histogram mode fills in the area under the curve. This example illustrates why the system was called waveform graphics.

Worked examples

Example 1 — a first encounter with Waveform graphics

Start with the simplest possible case. Write down what Waveform graphics claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Waveform graphics before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Waveform graphics ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Waveform graphics

In research
Waveform graphics appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Waveform graphics in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Waveform graphics is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer graphics, Graphical terminals, Vector graphics, so understanding it makes those chapters shorter.
In everyday life
Look for Waveform graphics outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Waveform graphics in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Waveform graphics means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Waveform graphics out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Waveform graphics in simple terms?

Waveform graphics is a simple vector graphics system introduced by Digital Equipment Corporation (DEC) on the VT55 and VT105 terminals in the mid-1970s. It was used to produce graphics output from mainframes and minicomputers.

Why does Waveform graphics matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Waveform graphics?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Waveform graphics.

Tags

  • Computer graphics
  • Graphical terminals
  • Vector graphics

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