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arXiv · 2607.04989

Intrinsic Meshing of Closed Surfaces Using Geodesic Distances

Tim Gabriel·Jean-François Remacle·Christophe Geuzaine
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Abstract

We present a method for constructing intrinsic triangulations of closed discrete surfaces, in which edges correspond to shortest geodesic paths and faces decompose into geometric primitives inherited from the underlying mesh. Starting from a watertight input triangulation, the method progressively builds an intrinsic mesh through local optimization operations -- edge swaps, edge splits, edge collapses, and triangle splits -- performed directly on the surface without modifying the original geometry. Element size is controlled via a characteristic length field, and quality is enforced through angle-based criteria derived from intrinsic distances. Geodesic distances are computed exactly using a continuous Dijkstra approach, accelerated by an A* search strategy that reduces computation to roughly $3\%$ of the cost of standard propagation. The framework supports both refinement and coarsening, overcoming a key limitation of prior intrinsic methods based on developable triangles. As a by-product, the intrinsic triangulation provides a natural foundation for direct high-order mesh generation, bypassing the classical pipeline of first constructing a linear mesh and subsequently curving it. The method is validated on the Thingi10K dataset across nearly 5,000 geometrically complex models.

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Tim Gabriel, Jean-François Remacle, Christophe Geuzaine. 2026-07-06. Intrinsic Meshing of Closed Surfaces Using Geodesic Distances. https://arxiv.org/abs/2607.04989

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