DJM: Compact Base Meshes for Displacement Mapping using Triangle Jacobians
2026-06-22 • Graphics
Graphics
AI summaryⓘ
The authors developed a new method to simplify complex 3D shapes into smaller base meshes that can still accurately represent the original shape using displacement functions. They measure how well the base mesh matches the shape by looking at something called the Jacobian, which shows how much the shape is distorted when mapped. Their approach ensures the mapping is smooth and doesn't overlap, which leads to better accuracy with fewer triangles. This method improves on older ones by keeping track of correspondences between the detailed shape and the base mesh throughout the process, making it more reliable and useful for rendering and encoding.
displacement functionbase meshJacobianparametric distortionQEM simplificationbijective mappinginverse barycentric solvermesh simplificationmicromesh renderingneural encoding
Authors
Congyi Zhang, Nicholas Vining, Yanhong Lin, Alireza Khatami, Ziyu Sun, Xiaohu Guo, Wenping Wang, Alla Sheffer
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.