**Computational Geometry**

- Testing whether a tree may be represented as Euclidean minimum spanning tree
- Unit disk graph recognition (Unit disk graphs are intersection graphs of circles of unit radius in the plane)
- Many motion planning among polygonal obstacles in the plane are NP-hard.
- Planar partitioning into connected subassemblies: Given a set A of non-overlapping (but possibly touching) polygons in the plane, decide if there is a proper subset S of A that can be separated from AS by a collision-free rigid motion of S, and such that both S and AS are connected.

- Art gallery problem and its variations.

Read more about this topic: List Of NP-complete Problems

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... Core problems are curve and surface modelling and representation ... The most important instruments here are parametric curves and parametric surfaces, such as Bezier curves, spline curves and surfaces ...

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**computational geometry**... two major, largely nonoverlapping categories Combinatorial**computational geometry**, which deals with collections of discrete objects or defined in discrete terms points, lines, polygons, polytopes, etc ... of discrete/combinatorial character are used Numerical**computational geometry**, also known as geometric modeling and computer-aided geometric design (CAGD), which deals with modelling of shapes ...### Famous quotes containing the word geometry:

“... *geometry* became a symbol for human relations, except that it was better, because in *geometry* things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.”

—Louise Bourgeois (b. 1911)

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