{"id":670,"date":"2025-09-26T17:39:10","date_gmt":"2025-09-26T17:39:10","guid":{"rendered":"https:\/\/summergeometry.org\/sgi2025\/?p=670"},"modified":"2025-10-07T19:57:45","modified_gmt":"2025-10-07T19:57:45","slug":"dmesh","status":"publish","type":"post","link":"https:\/\/summergeometry.org\/sgi2025\/dmesh\/","title":{"rendered":"From Triangles to Gradients: Exploring DMesh++"},"content":{"rendered":"\n
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Our work was carried out under the mentorship of Yi Zhuo<\/a> from Adobe Research, whose guidance was instrumental and very much appreciated. We also thank Sanghyun Son<\/a> , the first author of the original DMesh<\/a> and DMesh++<\/a> , for generously sharing his insights and providing invaluable input.<\/p>\n<\/blockquote>\n\n\n\n

Article Composed By<\/strong> : <\/strong>
Gabriel Isaac Alonso Serrato
in collaboration with<\/em>
Amruth Srivathsan

Click Below to Try :<\/p>\n\n\n\n

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Minimum Ball Playground <\/a><\/div>\n<\/div>\n\n\n\n

INTRODUCTION<\/h2>\n\n\n\n

This article introduces Differentiable Mesh++ (DMesh++), exploring what a mesh is, why discrete mesh connectivity blocks gradient flow, how probabilistic faces restore differentiability, and how a local, GPU-friendly tessellation rule replaces a global weighted Delaunay step. We close with a practical optimization workflow and representative applications.<\/p>\n\n\n\n

WHAT IS A MESH?<\/h2>\n\n\n\n

A triangle mesh combines geometry and topology. Geometry is given by vertex coordinates (named points in space such as A, B, C, and D) while topology specifies which vertices are connected by edges and which triplets form triangular faces (e.g., ABC, ACD). Together, these define shape and structure in a compact representation suitable for rendering and computation on complex surfaces.<\/p>\n\n\n\n

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Why Traditional Meshes Fight Gradients?<\/h2>\n\n\n\n

Classical connectivity is discrete: a triangle either exists or it does not. Gradient-based learning, however, requires smooth changes. When connectivity flips on or off, derivatives vanish or become undefined through those choices, preventing gradients from flowing across topology changes and limiting end-to-end optimization<\/p>\n\n\n\n

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Differentiable Meshes<\/h2>\n\n\n\n

Gradients are essential for learning-based pipelines, where losses may be defined in image space, perceptual space, or 3D metric space.<\/p>\n\n\n\n

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Differentiable formulations make it possible to propagate error signals from rendered observations or physical constraints back to vertex positions, enabling tasks such as inverse rendering, shape optimization, and end-to-end 3D reconstruction. This bridges the conceptual gap between discrete geometry and continuous optimization, allowing mesh-based representations to function as both modeling primitives and trainable structures. <\/p>\n\n\n\n

How DMesh++ Works<\/h2>\n\n\n\n

DMesh++ makes meshing a differentiable, GPU-native step. Each point carries learnable features (position, a \u201crealness\u201d score \u03c8, and optional channels).<\/p>\n\n\n\n

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A soft tessellation function<\/strong> turns any triplet into a triangle weight<\/strong> rather than a hard on\/off face.<\/p>\n\n\n\n

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During training, losses back-propagate to both positions and features, so connectivity can evolve smoothly. <\/p>\n\n\n\n

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