Surface Offsetting: A Survey From Geometric Construction to Neural Implicit Representations.

Area of Science:

• Computer-Aided Design (CAD)
• Geometric Modeling
• Computational Geometry

Background:

• Surface offsetting is crucial for CAD, manufacturing, robotics, and physics simulations.
• Existing methods struggle with complex geometries, leading to self-intersections and topological errors.
• Prior reviews focused on parametric methods, leaving a gap in surveying newer techniques.

Purpose of the Study:

• To provide a structured overview of recent advances in surface offsetting techniques.
• To introduce a new taxonomy for classifying surface offsetting algorithms.
• To identify challenges and future research directions in the field.

Main Methods:

• Literature review of surface offsetting algorithms.
• Development of a taxonomy categorizing algorithms into five classes: Constructive, Spatial Discretization, Optimization-based, Field-based, and Learning-based.
• Analysis of 46 representative algorithms to identify trade-offs.

Main Results:

• Identified inherent trade-offs between geometric accuracy and topological correctness in offsetting algorithms.
• Representation choices significantly impact algorithm complexity and constraints.
• Learning-based and neural implicit representations represent a significant recent advancement.

Conclusions:

• Robust and efficient surface offsetting for complex geometries remains a challenge.
• Open problems include handling open boundaries, preserving thin features, and resolving self-intersections.
• Future research should focus on non-manifold domains, scalable predicates, and hybrid neural representations.