PhD Dissertation Proposal: Vikas Thamizharasan, Generative Models for Parametric Curves and Surfaces
Content
Speaker:
Abstract:
This thesis investigates generative models for parametric curves and surfaces. These representations are resolution-independent, compact, and editable, making them fundamental to applications in vector graphics, CAD modeling, animation, simulation, and manufacturing. Common examples include Bézier curves, B-splines, and NURBS, which represent freeform and analytic shapes in both 2D and 3D using control points, weights, and knot vectors. Parametric curves and surfaces can be layered (along with appearance properties) to form vector images such as SVGs, or combined with topological structure to form boundary representations (B-Reps).
Despite their broad use, authoring high-quality parametric shapes remains challenging and labor-intensive, even for experts. This motivates learning generative priors over such representations, enabling the synthesis of high-quality shapes with desired geometric properties and supporting downstream tasks such as reconstruction and design assistance. We study two complementary paradigms.
The first develops feed-forward deep generative models for vector graphics and B-Reps. In VecFusion [1], we present a neural architecture for generating vector fonts with varying topological structures and precise control point placement. The method uses a cascaded diffusion framework, with a raster diffusion model followed by a vector diffusion model. To synthesize long and complex curves, the vector stage employs a transformer-based architecture together with a novel representation, enabling supervision on variable-length vector curves. In BRepFacetGen [4], we introduce a generative framework that formulates CAD structure inference as a latent variable problem conditioned on continuous surface geometry. Our representation couples a pretrained geometry latent set with a geometry-conditioned label latent space that models multiple plausible dense surface segmentations, naturally handling permutation ambiguity and structural non-uniqueness. Joint decoding yields a faceted mesh whose segments correspond to B-Rep faces that can be recovered through surface fitting and topology reconstruction.
The second explores training-free optimization methods that distills prior from pre-trained models, typically in the image domain, to parametric shape representations, where rich learned priors are lacking. These methods cast conditional-sampling of pre-trained diffusion models as a gradient-based optimization problem through score-distillation sampling (SDS), using tractable proxies for the density gradient to optimize randomly initialized shape parameters. In NIVeL [2], we introduce a neural vector graphic representation based on a decomposable set of implicit fields, which captures arbitrary topology and is easier to optimize with SDS than traditional vector representations. In MSD [3], we analyze the bias and high variance of SDS gradients and propose a diffusion distillation technique that yields a provably good proxy for the gradient of the diffusion output distribution. Derived from mean-shift mode seeking on the distribution, our method aligns its extrema with distributional modes and admits an efficient product-distribution sampling procedure for gradient evaluation. We show that it improves mode alignment and convergence in both synthetic and practical setups, producing higher-fidelity results.
Finally, we are investigating a new formulation for B-Rep generation. Although the performance of current 3D generative models has improved dramatically, models that produce B-Reps remain limited to simple shapes, resulting in a significant gap in capability. This discrepancy stems from both limited data availability and the challenge of designing representations suitable for learning-based pipelines. To address this, we reformulate B-Rep generation as a boundary-generation problem, treating boundaries themselves as shapes. We hypothesize that, because the boundaries of NURBS patches reflect the complexity of the underlying geometry, priors from pretrained 3D generative models that can capture complex high-fidelity shapes may also capture complementary surface signals such as patch boundaries.
Advisor:
Evangelos Kalogerakis