Blended Chart Surfaces: A Seamless Explicit Representation for Smooth Surface Fitting

2026-06-16 · Source: Computer Vision and Pattern Recognition · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems, Computational Geometry & Graphics · Depth: Expert, quick

Summary

Blended Chart Surfaces (BCS) introduces a novel, network-free, and explicit surface representation designed to overcome limitations of existing neural implicit and explicit map methods, which often struggle with smoothness, compactness, or parametrization. BCS is smooth by construction and anchored to user-provided topology, utilizing a coarse proxy mesh for approximate geometry. It jointly optimizes polynomial maps at each proxy vertex to fit an implicit target shape, eliminating the need for input parametrization. A smooth "one-ring coordinate" blending scheme fuses neighboring maps, decoupling topology from geometric details. This construction ensures global smoothness, full differentiability, stable derivative evaluation, and direct access to differential quantities. BCS is also equivariant to rigid motions and scaling. Evaluations show BCS achieves a favorable trade-off in compactness, simplicity, differential quantity access, and expressivity compared to alternatives like mesh-displacement MLPs, maintaining smoothness across patch boundaries.

Key takeaway

For Computer Vision Engineers or Graphics Scientists developing smooth surface representations, Blended Chart Surfaces offer a compelling alternative to neural implicit fields or explicit neural maps. You should consider this network-free, explicit method for applications requiring global smoothness, stable differential quantity access, and user-defined topology. Its ability to decouple coarse geometry from fine details and avoid input parametrization simplifies complex surface fitting tasks, potentially streamlining your geometry processing workflows.

Key insights

Blended Chart Surfaces offer a network-free, explicit, and globally smooth surface representation using polynomial maps and a blending scheme.

Principles

• Decouple topology/coarse geometry from fine details.
• Achieve global smoothness via local polynomial blending.
• Ensure differentiability for direct quantity access.

Method

Optimize polynomial maps at proxy vertices to fit an implicit target, then blend neighboring maps using a "one-ring coordinate" scheme for global smoothness.

In practice

• Use a coarse proxy mesh to define surface topology.
• Employ off-the-shelf optimizers for polynomial map fitting.
• Leverage direct access to surface energies for optimization.

Topics

• Blended Chart Surfaces
• Surface Representation
• Geometry Processing
• Polynomial Maps
• Differentiable Surfaces
• Computational Geometry

Best for: Research Scientist, AI Scientist, Computer Vision Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Computer Vision and Pattern Recognition.