Abstract

Implicit representations have become a dominant paradigm in computational settings ranging from learning-based geometry generation to advanced manufacturing. While treating geometry as the level set of a black-box function provides significant modeling flexibility, converting these representations into explicit surface meshes remains a major challenge. Standard volumetric extraction methods are fundamentally designed for smooth manifolds and therefore struggle to capture sharp geometric features such as creases, corners, and non-manifold junctions that are critical for high-fidelity industrial design and engineering tasks. Many of these intricate features arise from modeling multiple implicit functions. Examples include Constructive Solid Geometry (CSG), material interfaces, and more general implicit arrangements. This thesis presents a computational framework for robustly discretizing such multi-function representations. Building on classical volumetric grid generation, we introduce an adaptive grid subdivision strategy that directs refinement toward regions where multiple level sets intersect. This enables the accurate extraction of lower-dimensional intersection curves and points that define sharp geometric detail, ensuring that the resulting meshes faithfully reflect the intended design. We further show that this multi-function framework naturally extends to another geometric representation, sweep volumes. We find that many intricate features from sweep volumes can be avoided when we lift them into a higher dimension, and these sharp features can be defined precisely by the self-intersection after the projection. By deriving a new characterization of generalized sweep volumes, we identify the sweep boundary as an intersection of two implicit surfaces in the higher-dimensional space-time domain. Applying our adaptive discretization framework to this setting resolves long-standing difficulties in computing watertight sweep boundaries that retain internal cavities and sharp creases created by self-collisions of shapes during motion. Taken together, this thesis presents a unified pipeline for modeling high-fidelity geometries represented by multiple implicit functions. By integrating adaptive grid generation with intersection-aware iso-surfacing, the thesis demonstrates how sharp geometric features can be robustly reconstructed from implicit definitions in both static and dynamic scenarios.

Committee Chair

Tao Ju

Committee Members

Nathan Jacobs; Netanel Raviv; Ning Zhang; Qingnan Zhou; Tao Ju

Degree

Doctor of Philosophy (PhD)

Author's Department

Computer Science & Engineering

Author's School

McKelvey School of Engineering

Document Type

Dissertation

Date of Award

1-29-2026

Language

English (en)

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