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Computationally efficient tire models are needed to meet the timing and accuracy demands of the iterative vehicle design process. Axisymmetric, circumferentially isotropic, planar, discretized models defined by their quasi-static constraint modes have been proposed that are parameterized by a single stiffness parameter and two shape parameters. These models predict the deformed shape independently from the overall tire stiffness and the forces acting on the tire, but the parameterization of these models is not well defined. This work develops an admissible domain of the shape parameters based on the deformation limitations of a physical tire, such that the tire stiffness properties cannot be negative, the deformed shape of the tire under quasi-static loading cannot be dominated by a single harmonic, and the low spatial frequency components must contribute more than higher frequency components to the overall tire shape.

Standard visual database modeling practices in driving simulation reduce geometric complexity of terrain surfaces by using texture maps to simulate high frequency detail. Typically the vehicle dynamics model queries a correlated database that contains the polygons from the high level of detail of the visual database. However the vehicle dynamics database does not contain any of the high frequency information included in the texture maps. To overcome this issue and enhance both the visual and vehicle dynamics databases, a mathematical model of the high frequency content of the ground surface is developed using a set of Non-Uniform Rational B-Splines (NURBS) patches. The patches are combined in the terrain query by superimposing them over the low-frequency polygonal terrain, reintroducing the missing content. The patches are also used to generate Bump Map textures for the image generator so that the visual representation matches the terrain query.