Hardware Adaptive High-Order Interpolation for Real-Time Graphics

Abstract

Interpolation is a core operation that has widespread use in computer graphics. Though higher-order interpolation provides better quality, linear interpolation is often preferred due to its simplicity, performance, and hardware support. We present a unified refactoring of quadratic and cubic interpolations as standard linear interpolation plus linear interpolations of higher-order terms and show how they can be applied to regular grids and (triangular/tetrahedral) simplexes Our formulations can provide significant reduction in computation cost, as compared to typical higher-order interpolations and prior approaches that utilize existing hardware linear interpolation support to achieve higher-order interpolation. In addition, our formulation allows approximating the results by dynamically skipping some higher order terms with low weights for further savings in both computation and storage. Thus, higher-order interpolation can be performed adaptively, as needed. We also describe how relatively minor modifications to existing GPU hardware could provide hardware support for quadratic and cubic interpolations using our approach for both texture filtering operations and barycentric interpolation. We present a variety of examples using triangular, rectangular, tetrahedral, and cuboidal interpolations, showing the effectiveness of our higher-order interpolations in different applications.