This paper presents a nonlinear kinematic tolerance analysis algorithm for planar mechanical systems comprised of higher kinematic pairs. The pan profiles consist of line and circle segments. Each part translates along a planar axis or rotates around an orthogonal axis. The part shapes and motion axes are parameterized by a vector of tolerance parameters with range limits. A system is analyzed in two steps. The first step conslIUcts generalized configuration spaces, called conlact zones, that bound the worst-case kinematic variation of the pairs over the tolerance parameter range. The zones specify the variation of the pairs at every contact configuration and reveal failure modes, such as jamming. due to qua!iffitive changes in kinematic function. The second step bounds the worsE-case system variation at selected configurations by composing the zones. Case studies show that the algorithm is accurate, fast, and far superior to a prior algorithm that constructs and composes linear approximations of con[act zones.

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We present a Minkowski sum algorithm for polyhedra based on convolution. We develop robust CPU and GPU implementations, using our ACP robustness technique to enforce a user-specified backward error bound. We test the programs on 45 inputs with an error bound of 10 −8 . The CPU program outperforms prior work, including non-robust programs. The GPU program exhibits a median speedup factor of 36, which increases to 68 on the 6 hardest tests. For example, it computes a Minkowski sum with a million features in 20 seconds.Figure 1: Star and cube snapshots (a) and Minkowski sum (b).

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.