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Triangle fan

Triangle fan 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 Triangle fan rather than just read about it. In short: A triangle fan is a primitive in 3D computer graphics that saves on storage and processing time. It describes a set of connected triangles that share one central vertex (unlike the triangle strip that connects the next vertex point to the last two used vertices to form a triangle), possibly within a triangle mesh.

Triangle fan — main illustration
Triangle fan — illustration

Key takeaways

  • Triangle fan 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 Triangle fan to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Triangle fan from memory before moving on to harder problems.

Reference excerpt

A triangle fan is a primitive in 3D computer graphics that saves on storage and processing time. It describes a set of connected triangles that share one central vertex (unlike the triangle strip that connects the next vertex point to the last two used vertices to form a triangle), possibly within a triangle mesh. If N is the number of triangles in the fan, the number of vertices describing it is N + 2. This is a considerable improvement over the 3N vertices that are necessary to describe the triangles separately. The graphics pipeline can take advantage by only performing the viewing transformations and lighting calculations once per vertex. While triangle fans were useful in the past with flat shading or Gouraud shading objects without textures and limited RAM, today they cost performance with fragment shaders and multisampling rasterization. For this reason, Triangle fans are deprecated in Direct3D10 and later. Any convex polygon may be triangulated as a single fan, by arbitrarily selecting any point inside it as the center.

See also Triangle strip Fan triangulation

References

Illustrations

Triangle fan: Set of connected triangles described by vertices A through F.
Set of connected triangles described by vertices A through F.

Worked examples

Example 1 — a first encounter with Triangle fan

Start with the simplest possible case. Write down what Triangle fan 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 Triangle fan 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 Triangle fan 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 Triangle fan

In research
Triangle fan 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 Triangle fan 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
Triangle fan is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer graphics, Computer graphics stubs, so understanding it makes those chapters shorter.
In everyday life
Look for Triangle fan 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 Triangle fan in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Triangle fan 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 Triangle fan out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Triangle fan in simple terms?

A triangle fan is a primitive in 3D computer graphics that saves on storage and processing time. It describes a set of connected triangles that share one central vertex (unlike the triangle strip that connects the next vertex point to the last two used vertices to form a triangle), possibly within…

Why does Triangle fan 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 Triangle fan?

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 Triangle fan.

Tags

  • Computer graphics
  • Computer graphics stubs

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