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I am reading a paper on collision detection in cloth simulation, please help me understanding following lines written in the paper :

To check if a point x4 is closer than some thickness h to a triangle x1 x2 x3 with normal n we first check if the point is close to the plane containing the triangle: |x43 · n| < h. If so, we project the point onto the plane and compute the barycentric coordinates w1, w2, w3 with respect to the triangle x1 x2 x3.

If the barycentric coordinates are all within the interval [−δ , 1 + δ ] where δ is h divided by a characteristic length of the triangle, the point is close.

Please help me understanding 2nd paragraph, what does characteristic length of the triangle mean?

Qmechanic
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user2481909
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  • Which paper? Characteristic length of a triangle could be many things. E.g. the square root of the triangle's area. – Qmechanic Aug 27 '13 at 16:39
  • I am reading "Robust Treatment of Collisions, Contact and Friction for Cloth Animation" by robert bridson – user2481909 Aug 27 '13 at 17:41
  • This question appears to be off-topic because it is about pure mathematics without a physical context. – David Z May 13 '14 at 01:48

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I found from google books, Numerical Flow Simulation II: CNRS-DFG Collaborative Research Programme Results 1998-2000 page 22.

http://books.google.ca/books?id=PBfwmEQHrQUC&pg=PA22&lpg=PA22&dq=characteristic+length+of+triangle&source=bl&ots=01kjH_CSlK&sig=nzN6ZCBh7YD0foMjs5f40gtTalQ&hl=en&sa=X&ei=tqlEU9TWBujLsASf_YCgDg&ved=0CEgQ6AEwBQ#v=onepage&q=characteristic%20length%20of%20triangle&f=false

"the characteristic length of a triangle is the square root of the area"

codethink
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