# what's the difference between concave and convex surfaces

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I've been battling with this for a long time. The descriptions I found in the Opengl redbook and other documents couldn't help me see the difference. If possible please point me to a site that shows this diffence, your explanation will be also valued. Thanx 4 u'r help.

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If you held a sheet of glass in front of you and pushed the middle away from you, that is concave, from your POV. If you pulled the middle that is convex from your POV.

Look here also.

Dave

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Are you wanting to know the difference between the concepts of concave and convex or are you after further information such as why you can only use convex objects in certain applications?

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Further information such as why I can only use convex objects in certain applications.

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For physics systems, convex meshes are prefered for calculation speed.

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Well one distinct difference is that mathematically speaking, convex surfaces are relatively easy to work with as they can be described in terms of a set of intersecting planes such as in halflife's .map format. When defined in terms of planes, physics calculations (player sliding along walls for example) are made somewhat less complex than if they were performed against arbitrarily shaped geometry. Concave surfaces offer no such luxury (that I'm aware of) and are much more difficult to work with in that sense.

Anyhoo, I'm no expert, but I'm sure there are many other differences between the two that perhaps someone with more knowledge could point out.

Cheers,

Steve

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Some more random info for you. One way to define convexity is that a line segment connecting any two points in the object will always be fully contained in the object. Common convex objects include points, linear components, circles and spheres, boxes, triangles, cones, cylinders, capsules, lozenges, ellipsoids, (convex) polygons and (convex) polyhedra. Conversely, most mesh models used in games (such as characters and weapons) are non-convex.

Convex objects have many properties that make them particularly easy to work with. A full discussion would be somewhat lengthy, but suffice to say that most collision detection algorithms in common usage operate on convex objects only. You certainly can do collision detection with non-convex objects, but it introduces a whole new set of problems and often isn't worth the extra trouble.

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