Parametric Blending with Geodesic Curves on Triangular Meshes

This paper presents an effective method for generating blending meshes by leveraging geodesic curves on triangular meshes. Depending on whether the input meshes intersect, the blending regions are automatically initialized using either minimum-distance points or intersection curves, while allowing users to intuitively adjust boundary curves directly on the mesh. Each blending region is parameterized via geodesic linear interpolation, and a reparameterization strategy is employed to establish optimal correspondences between boundary curves, ensuring smooth, twist-free connections. The resulting blending mesh is merged with the input meshes through subdivision, trimming, and co-refinement along the boundaries. The proposed method is applicable to both intersecting and non-intersecting meshes and offers flexible control over the shape and curvature of the blending region through various user-defined parameters, such as boundary radius, scaling factor, and blending function parameters. Experimental results demonstrate that the method produces stable and smooth transitions even for complex geometries, highlighting its robustness and practical applicability in diverse domains including digital fabrication, mechanical design, and 3D object modeling.