Fourier collision detection

Abstract

We investigate a new approach to narrowphase collision detection for rigid objects based on a Fourier series expansion. This new collision test scales with respect to accuracy (in the Hausdorff sense), which we show rigorously in the case of translational motions. Because our new form of the collision test is also a smooth inequality, it can be used as a holonomic unilateral constraint in many applications, such as path planning, rigid body dynamics, nesting or tool placement, replacing the need for more ad-hoc normal/contact-based constraint solvers. Moreover, we also show how this constraint can be directly differentiated via Fourier multipliers with only a constant factor overhead, which leads to a simple method for constructing a Jacobian for both normal forces and rotational torques.