AI summaryⓘ
The authors developed a method to create special kinds of triangle meshes on closed surfaces where edges follow the shortest paths on the surface, and faces are built from the original shape's geometry. They start from an existing mesh and improve it step-by-step using operations like swapping or splitting edges, without changing the original shape. Their technique carefully controls triangle size and quality using exact calculations of distances, speeding this up with an efficient search method. This approach works both for making the mesh finer or coarser and helps generate higher-quality meshes more directly than older methods. They tested their method on a large dataset with thousands of complex shapes to show its effectiveness.
intrinsic triangulationgeodesic pathsedge swapsedge splitsmesh refinementcontinuous DijkstraA* searchtriangle qualityhigh-order mesh generationThingi10K dataset
Authors
Tim Gabriel, Jean-François Remacle, Christophe Geuzaine
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.