Closed-Form Swept Volume of Implicit Surfaces
Karim A. Abdel-Malek, James Yang, Denis Blackmore · 2000
Abstract Recent developments in formulations for generating swept volumes have made a significant impact on the efficiency of employing such algorithms and on the extent to which formulations can be used in representing complex shapes. In this paper, we outline a method for employing the representation of implicit surfaces using the Jacobian rank deficiency condition presented earlier for the sweep of parametric surfaces. A numerical and broadly applicable analytic formulation is developed that yields the exact swept volume.