We present a new approach, called controlled linear perturbation (CLP), to the robustness problem in computational geometry and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Large errors can occur when predicates are assigned inconsistent truth values because the computation assigns incorrect signs to the associated polynomials. CLP enforces consistency by performing a small input perturbation, which it computes using differential calculus. CLP enables us to compute Minkowski sums via convex convolution, whereas prior work uses convex decomposition, which has far greater complexity. Our program is fast and accurate even on inputs with many degeneracies.

Abstract We propose a novel rendering method which supports interactive BRDF editing as well as relighting on a 3D scene. For interactive BRDF editing, we linearize an analytic BRDF model with basis BRDFs obtained from a principal component analysis. For each basis BRDF, the radiance transfer is precomputed and stored in vector form. In rendering time, illumination of a point is computed by multiplying the radiance transfer vectors of the basis BRDFs by the incoming radiance from gather samples and then linearly combining the results weighted by user‐controlled parameters. To improve the level of accuracy, a set of sub‐area samples associated with a gather sample refines the glossy reflection of the geometric details without increasing the precomputation time. We demonstrate this program with a number of examples to verify the real‐time performance of relighting and BRDF editing on 3D scenes with complex lighting and geometry.

We describe a parametric synthesis algorithm for planar mechanical systems comprised of higher kinematic pairs in which each part translates along a fixed axis or rotates around a fixed point. Kinematic function is computed from the CAD models of the parts and is represented graphically as configuration spaces. The designer uses the mouse to request changes in the configuration spaces. The program computes parameter values that achieve the changes. The computation is iterative: the program repeatedly linearizes the mapping from design parameters to kinematics around the current values, pseudo-inverts the linear mapping, and performs a small parameter modification that moves the system toward the desired kinematics. At each iteration, the program matches the current kinematics against the initial kinematics. If it detects an unintended change, it backs up, adds kinematic constraints that prevent the change, and resumes iteration.