| 摘要 |
A method and system providing formulae that express integrals of quadratic homogeneous polynomials on polygons and polyhedra, such as entries of the moment of inertia tensor, in terms of vertex coordinates. The formulae for a triangle provide the mass properties without integration, and can be combined (using a signed sum) to determine the mass properties for any polygon. Likewise, the concept extends to a polyhedron, which may be built from a plurality of signed pyramids. An algorithm combines the formulae to determine the mass properties of a polyhedron. The formulae and algorithm may be used in a graphics processing environment.
|
