Riley: A computational framework for higher-order finite element image synthesis applied to digital image correlation uncertainty quantification

Abstract

Image-based measurements such as digital image correlation (DIC) have the potential to reduce the cost and risk associated with validation experiments for high-value components in fusion engineering. To use DIC effectively in this setting, we need to design experiments computationally before physically realising them, including the effects of camera placement, image formation, finite-element deformation, and measurement uncertainty.

We present Riley, a dependency-free software rasteriser written in Zig for creation of synthetic DIC images directly from deformed finite-element surface meshes. Riley supports rendering linear triangular tri3, quadratic triangular tri6, linear quadrilateral quad4, and quadratic quadrilateral quad8/quad9 elements. Riley also supports mixed-mesh scenes, multiple cameras, analytic and nodal shaders, and higher-order texture sampling. Our method uses inverse-mapped rasterisation, projected-residual Newton solves for higher-order elements, adaptive hulls for raster-space rejection and tile assignment, compile-time kernel specialisation, and explicit single instruction multiple data (SIMD) execution.

We verify our renderer using targeted tests of inverse-mapping reprojection error, silhouette coverage, pixel sub-sampling convergence, and depth-buffer visibility. The Newton pathway gives reprojection errors below 10^-12 px for regular and affine-shear cases and below approximately 10^-10 px for challenging bulge cases. Rendered single-element silhouettes match independently generated reference masks exactly, with area errors no more than 3 x 10^-3%. Performance benchmarks show single-threaded raster throughput of 242 MPx/s for the direct tri3 nodal pathway, and adaptive hulls combined with SIMD provide up to 12.99x raster-loop speedup. Thread-scaling analysis yields fitted parallel fractions of 99.0% for in-memory and 98.8% for disk-output workflows. These results show that Riley provides a verified and performant foundation for large-scale DIC uncertainty quantification and simulation-driven experimental design.