The numerical simulation of three dimensional environments is of central importance for many industrial applications. The realistic simulation of lighting thereby poses a particular challenge, for which existing technologies are often unable to meet specified error tolerances while staying computationally efficient.

Hölder adaptive image synthesis provides a deterministic, adaptive ray tracing technique that is able to meet desired error tolerances in a computed image with minimal computational costs. With this, the computational effort scales with the desired accuracy while the veracity of the obtained solution, up to the specified tolerance, can be guaranteed. Alternatively, the technique is also able to provide the optimal visual fidelity for a given computational budget. These properties are enabled by the use of reproducing kernel theory, which leads to a number of ray tracing samples provably close to the theoretical minimum while defining optimal yet numerically practical reconstruction kernels. Sampling and reconstruction can be tiled across the image plane, enabling a parallel implementation on CPU and GPU. The present invention hence provides a technique that enables a more efficient rendering of three dimensional environments while being able to meet required error tolerances in a computed image.