DJM: Compact Base Meshes for Displacement Mapping using Triangle Jacobians

2026-06-22

AI Summary

This work addresses the inherent trade-off between base mesh compactness and detail fidelity in high-fidelity geometric reconstruction by proposing a novel base mesh construction method based on the Displacement Jacobian Metric (DJM). The approach introduces triangle-wise Jacobian constraints during mesh simplification to explicitly preserve correspondence between the input and the base mesh, and employs inverse barycentric coordinates to solve for the displacement field. This formulation simultaneously ensures bijective mapping, low parametrization distortion, and high reconstruction accuracy. Experimental results demonstrate that the method significantly reduces the number of base mesh faces while outperforming state-of-the-art techniques, exhibiting superior robustness and practicality in applications such as micro-mesh rendering and neural geometric encoding.

Abstract

Representing complex geometry as a displacement function defined over a coarse base mesh enables compact storage and accelerated rendering. The core challenge in converting detailed triangle meshes into this representation is computing base meshes that have as few triangles as possible, while also supporting displacement functions that accurately approximate the input. Accurate approximation requires the supported displacement functions to bijectively map the input surface onto the base with low parametric distortion. We observe that this distortion can be measured by evaluating the pointwise Jacobian of the displacement functions. Our new DJM (Displacement Jacobian Metric)-based base-mesh construction method uses the Jacobian of the displacement functions to guide base mesh computation, enabling us to outperform prior approaches in terms of accuracy to size trade-off. We achieve this goal by proposing a variant of the QEM-based simplification scheme that constrains the displacement mapping between the input and the base to be bijective and low distortion (defined as satisfying a lower bound on the mapping Jacobian). When evaluating and encoding the displacement maps, we avoid unreliable ray-mesh intersections by explicitly storing the mapping between the input mesh and the base throughout the construction process, and use this mapping within a robust inverse barycentric displacement solver to obtain dense base-to-mesh correspondences to assist all computations. We demonstrate DJM to outperform alternative schemes in terms of reconstruction accuracy to size trade-off, and demonstrate its robustness and usability for micromesh-based rendering and neural encoding.

Problem

• displacement mapping
• base mesh
• parametric distortion
• bijective mapping
• mesh simplification

Innovation

• Displacement Mapping
• Jacobian Metric
• Base Mesh Simplification
• Bijective Parameterization
• Micromesh Rendering