computer science

Newell's algorithm

Newell's algorithm 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 Newell's algorithm rather than just read about it. In short: Newell's Algorithm is a 3D computer graphics procedure for elimination of polygon cycles in the depth sorting required in hidden surface removal. It was proposed in 1972 by brothers Martin Newell and Dick Newell, and Tom Sancha, while all three were working at CADCentre.

Key takeaways

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

Reference excerpt

Newell's Algorithm is a 3D computer graphics procedure for elimination of polygon cycles in the depth sorting required in hidden surface removal. It was proposed in 1972 by brothers Martin Newell and Dick Newell, and Tom Sancha, while all three were working at CADCentre. In the depth sorting phase of hidden surface removal, if two polygons have no overlapping extents or extreme minimum and maximum values in the x, y, and z directions, then they can be easily sorted. If two polygons, Q and P, do have overlapping extents in the Z direction, then it is possible that cutting is necessary.

In that case, Newell's algorithm tests the following:

Test for Z overlap; implied in the selection of the face Q from the sort list The extreme coordinate values in X of the two faces do not overlap (minimax test in X) The extreme coordinate values in Y of the two faces do not overlap (minimax test in Y) All vertices of P lie deeper than the plane of Q All vertices of Q lie closer to the viewpoint than the plane of P The rasterisation of P and Q do not overlap The tests are given in order of increasing computational difficulty. The polygons must be planar. If the tests are all false, then switch the order of P and Q in the sort, record having done so, and try again. If there is an attempt to switch the order of a polygon a second time, there is a visibility cycle, and the polygons must be split. Splitting is accomplished by selecting one polygon and cutting it along the line of intersection with the other polygon. The above tests are again performed, and the algorithm continues until all polygons pass the above tests.

References Sutherland, Ivan E.; Sproull, Robert F.; Schumacker, Robert A. (1974), "A characterization of ten hidden-surface algorithms", Computing Surveys, 6 (1): 1–55, CiteSeerX 10.1.1.132.8222, doi:10.1145/356625.356626, S2CID 14222390 {{citation}}: Cite uses deprecated parameter |citeseerx= (help). Newell, M. E.; Newell, R. G.; Sancha, T. L. (1972), "A new approach to the shaded picture problem", Proc. ACM National Conference, pp. 443–450.

See also Painter's algorithm Boolean operations on polygons

Worked examples

Example 1 — a first encounter with Newell's algorithm

Start with the simplest possible case. Write down what Newell's algorithm 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 Newell's algorithm 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 Newell's algorithm 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 Newell's algorithm

In research: Newell's algorithm 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 Newell's algorithm 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: Newell's algorithm is common in secondary-school and first-year university syllabi. It links to neighbouring topics 3D computer graphics, Computer graphics algorithms, Computer graphics stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Newell's algorithm 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 Newell's algorithm in 20 minutes

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

Frequently asked questions

What is Newell's algorithm in simple terms?

Why does Newell's algorithm 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 Newell's algorithm?

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 Newell's algorithm.