We present a new system for robustly performing Boolean operations on linear, 3D polyhedra. Our system is exact, meaning that all internal numeric predicates are exactly decided in the sense of exact geometric computation. Our BSP-tree based system is 16-28× faster at performing iterative computations than CGAL's Nef Polyhedra based system, the current best practice in robust Boolean operations, while being only twice as slow as the non-robust modeler Maya. Meanwhile, we achieve a much smaller substrate of geometric subroutines than previous work, comprised of only 4 predicates, a convex polygon constructor, and a convex polygon splitting routine. The use of a BSP-tree based Boolean algorithm atop this substrate allows us to explicitly handle all geometric degeneracies without treating a large number of cases.

We propose a novel representation of motion data and control that enables characters with both highly agile responses to user input and natural handling of arbitrary external disturbances. The representation organizes motion data as samples in a high dimensional generalization of a vector field we call a 'motion field'. Our runtime motion synthesis mechanism freely 'flows' in the motion field and is capable of creating novel and natural motions that are highlyresponsive to the real time user input, and generally not explicitly specified in the data.

Designing efficient, application-specialized hardware accelerators requires assessing trade-offs between a hardware module's performance and resource requirements. To facilitate hardware design space exploration, we describe Aetherling, a system for automatically compiling data-parallel programs into statically scheduled, streaming hardware circuits. Aetherling contributes a space-and time-aware intermediate language featuring data-parallel operators that represent parallel or sequential hardware modules, and sequence data types that encode a module's throughput by specifying when sequence elements are produced or consumed. As a result, well-typed operator composition in the space-time language corresponds to connecting hardware modules via statically scheduled, streaming interfaces.We provide rules for transforming programs written in a standard data-parallel language (that carries no information about hardware implementation) into equivalent spacetime language programs. We then provide a scheduling algorithm that searches over the space of transformations to quickly generate area-efficient hardware designs that achieve a programmer-specified throughput. Using benchmarks from the image processing domain, we demonstrate that Aetherling enables rapid exploration of hardware designs with different throughput and area characteristics, and yields results that require 1.8-7.9× fewer FPGA slices than those of prior hardware generation systems.

We propose a novel representation of motion data and control that enables characters with both highly agile responses to user input and natural handling of arbitrary external disturbances. The representation organizes motion data as samples in a high dimensional generalization of a vector field we call a 'motion field'. Our runtime motion synthesis mechanism freely 'flows' in the motion field and is capable of creating novel and natural motions that are highlyresponsive to the real time user input, and generally not explicitly specified in the data.

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