Area and center of a contact patch

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Area and center of a contact patch

Postby kallaspriit » Mon Jul 26, 2010 12:50 pm

In the ray/convex-cast car I'm making, currently I'm applying force to all the contacts that are found, but this is not very optimal.

I'm thinking that contacts found using convex-cast can make up an approximation of the size of the contact patch of the tire.

Image

Contact patch area with load gives good idea about how much force the tire can generate. As I know the penetration (load) of each contact-point, this gives additional information.

Four contacts by convex cast of a cylinder on a plane.
5.jpg
Contact patch points
5.jpg (231.87 KiB) Viewed 1441 times


So my math related question is how to calculate the area of a convex hull, that is made up of these points in 3D space. I'm not so great in this sort of math, I guess it's a matter of triangulating the points into a convex hull and then adding up the areas of the triangles (that is half the magnitude of the cross product of the vectors creating the triangle).

6.jpg
Contact patch with 3 vertices on a tilted tire.
6.jpg (241.02 KiB) Viewed 1441 times


Does anyone know a simple algorithm, that, given n points (basically n vector3's) in 3D space, calculates the area of the convex hull made of these points and how to find the center and normal (not sure you can talk about a normal with more that 3 vertices, average normal or something?) of this convex hull? :P
kallaspriit
 
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