cs.GR

Stipple patterns, point sets whose local density tracks a target image, are traditionally produced by per-density iterative optimizers, which are slow, non-differentiable, and must be re-run from scratch for each new target. Learned alternatives have so far addressed only unconditional point generation; capacity-constrained, image-conditioned stippling has remained out of reach. We present the first diffusion-based sampler that simultaneously satisfies a learned local point-distribution prior and a continuous, image-defined capacity constraint at inference. The method is a ControlNet branch built on top of an optimal-transport-grid point-set diffusion baseline, conditioned on the target density map and a high-resolution image. Two design choices make the combination tractable: training and inference are restricted to the late-stage denoising regime, initialized from a density-weighted rejection sample, and the standard zero-convolution injection is replaced with a sigmoid-gated 1x1 projection that preserves the base model's blue-noise structure under hard density signals. A single trained checkpoint accepts arbitrary target densities at inference, generalizes to point budgets that were not seen during training, and produces stipples in time nearly independent of the output point count. On the Icons-50 benchmark, our learned sampler reaches parity with per-density-optimized baselines on every reported metric while remaining differentiable end-to-end.

Accurate real-time simulation of lens optics remains challenging due to the computational expense of full ray tracing and the limitations of existing approximations. The commonly used pinhole model and thin-lens model ignore many optical effects seen in real-world lens systems such as distortion and chromatic aberration. Prior polynomial models approximate a mapping between incident rays and exitant rays through a lens system per wavelength. Prior neural models improve the accuracy of this mapping and also capture wavelength-dependent variations (e.g., chromatic aberration) by integrating wavelength as an input to a unified neural network. Common to those prior models is that they omit Fresnel intensity throughput, precluding accurate simulation of internal reflections and lens flares. We introduce a precomputed lens model that combines wavelength-aware inputs with Fresnel intensity outputs. By classifying rays as valid or occluded via a binary mask in a factorized representation, our method focuses regression on unblocked rays, improving accuracy near discontinuities. Our model avoids per-wavelength approximations in polynomial models and explicitly predicts Fresnel coefficients to enable accurate lens simulation. Designed for static, rotationally symmetric systems under geometric optics, our model captures various lens effects such as chromatic aberration, coma, and lens flares. Our method achieves improved accuracy over polynomial baselines and is an order of magnitude faster than brute force ray tracing. Our method serves as a practical and scalable approach for simulating complex lens systems in applications requiring both accuracy and computational efficiency.