We introduce a framework allowing domain experts to manipulate computational terms in the interest of deriving better, more efficient implementations.It employs deductive reasoning to generate provably correct efficient implementations from a very high-level specification of an algorithm, and inductive constraint-based synthesis to improve automation. Semantic information is encoded into program terms through the use of refinement types.

A parallel simplification method based on vertex clustering for out-of-core meshes is presented in this paper. To reduce file I/O, only one linear scan is performed in this method to partition the original model into equal batches. Then vertex normal vectors and coefficients of each triangle plane are calculated with some inter-task communications. The portion assigned to each processor is simplified by an improved vertex clustering method. Finally, all reduced data are sent back to the master node and assembled into the simplified mesh. The partition stitching is fulfilled simply by using a global vertex index. A lot of experiments have demonstrated that the proposed method can handle extremely large data set and speed up the execution time obviously as well as produce approximations with high quality.

A general parallel framework is presented in this paper for simplification of very large mesh models. This framework is implemented on a dedicated cluster. To guarantee not to thrash the virtual memory system, load balancing is performed in this framework by providing an intelligent partitioning of the inputting model using a parallel global sorting. This partitioning ensures a near optimal utilization of the computational resources, and then ensures high quality output, low runtime and high parallel efficiency. To test the usability of this framework, we have implemented a parallel version of an improved vertex clustering simplification. A serial of experimental results have demonstrated that using this framework the parallel simplification is memory efficient and can handle extremely large data set as well as speed up the execution obviously.