Non-singular developable triangular Bézier patches

We show a characterisation of developable surfaces in the form of B´ezier triangular patches. • Constructions used for rectangular patches are not useful, since they produce degenerate triangular patches. • Explicit constructions of non-degenerate developable triangular patches are provided. • Interpolation of a developable triangle between a curve c(u), the last ruling and initial velocity of the other bounding curve d(u)

IFC-based calculation of the Flemish Energy Performance Standard

This paper illustrates our findings concerning space based design methodologies and interoperability issues for today's Building Information Modeling (BIM) environments. A method is elaborated which enables building designers to perform an automated energy use analysis, based oil an Industry Foundation Classes (IFC) model derived from a commercial BIM environment, in this case Autodesk Revit 9.1. A prototype application was built, which evaluates the building model as well as vendor-neutral exchange mechanisms, in accordance with the Flemish Energy Performance Regulation (EPR) standard. Several issues regarding the need for space-based building models are identified and algorithms are developed to overcome possible shortcomings

Random sampling of plane partitions

This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are slightly superlinear: the complexity is $O(n (\ln n)^3)$ in approximate-size sampling and $O(n^{4/3})$ in exact-size sampling (under a real-arithmetic computation model). To our knowledge, these are the first polynomial-time samplers for plane partitions according to the size (there exist polynomial-time samplers of another type, which draw plane partitions that fit inside a fixed bounding box). The same principles yield efficient samplers for $(a\times b)$-boxed plane partitions (plane partitions with two dimensions bounded), and for skew plane partitions. The random samplers allow us to perform simulations and observe limit shapes and frozen boundaries, which have been analysed recently by Cerf and Kenyon for plane partitions, and by Okounkov and Reshetikhin for skew plane partitions.Comment: 23 page

Towards Practical Oblivious RAM

We take an important step forward in making Oblivious RAM (O-RAM) practical. We propose an O-RAM construction achieving an amortized overhead of 20X-35X (for an O-RAM roughly 1 terabyte in size), about 63 times faster than the best existing scheme. On the theoretic front, we propose a fundamentally novel technique for constructing Oblivious RAMs: specifically, we partition a bigger O-RAM into smaller O-RAMs, and employ a background eviction technique to obliviously evict blocks from the client-side cache into a randomly assigned server-side partition. This novel technique is the key to achieving the gains in practical performance