Rigid Physically based Superquadrics
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Publisher Summary Superquadric ellipsoids and toroids are recent geometric shapes, which are useful for computer graphics modeling. This chapter illustrates equations that calculate the motion of those shapes in rigid physically based modelling and presents closed-form algebraic expressions for the volume, center of mass, and rotational inertia tensor for superquadric shapes. The chapter reviews superquadrics, the equations of rigid body motion of Newtonian physics, and ancillary mathematical definitions and derivations. Superquadrics are three-dimensional extensions of Piet Hein's two-dimensional superellipses. They allow us to easily represent rounded, square, cylindrical, pinched, and toroidal shapes with relatively simple equations. The superquadric parametric surface function is a profile surface based on trigonometric functions raised to exponents. The chapter presents the volume and nonzero components of the inertia tensors for particular superquadric ellipsoids.