We propose SplInter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic–based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants with data invariants. SplInter is property directed, precise, and produces counterexample traces when a property does not hold. Using the novel notion of sp...

Ray tracers are usually regarded as off-line rendering algorithms that are too slow for interactive use. This thesis introduces techniques to accelerate ray tracing and to support interactive editing of ray-traced scenes. These techniques should be useful in many applications, such as architectural walk-throughs, modeling, and games, and will enhance both interactive and batch rendering. This t...

This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions are ra...

Contour trees are extensively used in scalar field analysis. The contour tree is a data structure that tracks the evolution of level set topology in a scalar field. Scalar fields are typically available as samples at vertices of a mesh and are linearly interpolated within each cell of the mesh. A more suitable way of representing scalar fields, especially when a smoother function needs to be mo...

Abstract: Given a smooth, strictly convex planar domain, we investigate point-wise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain. Based on a relation between the discrete Wachspress case and the limit smooth case given by the Wachspress kernel defined by Warren et al., we show that the corresponding sequences ...

(1) inf{‖f ‖p : f ∈ C [0, 1], f(ti) = ei, i = 1, . . . , m}, where ‖ · ‖p is the usual L [0, 1] norm, 1 ≤ p ≤ ∞, and to characterize f for which the above infimum is attained. If m ≤ n, then this problem has a simple solution. There are algebraic polynomials of degree at most n−1 satisfying the interpolation data, and any of these polynomials obviously solve our problem. If m > n then, in gener...

We present a method for interpolation based on DRUP proofs. Interpolants are widely used in model checking, synthesis and other applications. Most interpolation algorithms rely on a resolution proof produced by a SAT-solver for unsatisfaible formulas. The proof is traversed and translated into an interpolant by replacing resolution steps with AND and OR gates. This process is efficient (once th...

We present Counterexample-Guided Accelerated Abstraction Refinement (CEGAAR), a new algorithm for verifying infinite-state transition systems. CEGAAR combines interpolation-based predicate discovery in counterexampleguided predicate abstraction with acceleration technique for computing the transitive closure of loops. CEGAAR applies acceleration to dynamically discovered looping patterns in the...