Search Me Knot, Render Me Knot: Embedding Search and Differentiable Rendering of Knots in 3D

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dc.contributor.authorGangopadhyay, Aaloken_US
dc.contributor.authorGupta, Parasen_US
dc.contributor.authorSharma, Tarunen_US
dc.contributor.authorSingh, Prajwalen_US
dc.contributor.authorRaman, Shanmuganathanen_US
dc.contributor.editorHu, Ruizhenen_US
dc.contributor.editorLefebvre, Sylvainen_US
dc.date.accessioned2024-06-20T07:55:10Z
dc.date.available2024-06-20T07:55:10Z
dc.date.issued2024
dc.description.abstractWe introduce the problem of knot-based inverse perceptual art. Given multiple target images and their corresponding viewing configurations, the objective is to find a 3D knot-based tubular structure whose appearance resembles the target images when viewed from the specified viewing configurations. To solve this problem, we first design a differentiable rendering algorithm for rendering tubular knots embedded in 3D for arbitrary perspective camera configurations. Utilizing this differentiable rendering algorithm, we search over the space of knot configurations to find the ideal knot embedding. We represent the knot embeddings via homeomorphisms of the desired template knot, where the weights of an invertible neural network parametrize the homeomorphisms. Our approach is fully differentiable, making it possible to find the ideal 3D tubular structure for the desired perceptual art using gradient-based optimization. We propose several loss functions that impose additional physical constraints, enforcing that the tube is free of self-intersection, lies within a predefined region in space, satisfies the physical bending limits of the tube material, and the material cost is within a specified budget. We demonstrate through results that our knot representation is highly expressive and gives impressive results even for challenging target images in both single-view and multiple-view constraints. Through extensive ablation study, we show that each proposed loss function effectively ensures physical realizability. We construct a real-world 3D-printed object to demonstrate the practical utility of our approach.en_US
dc.description.number5
dc.description.sectionheadersModeling for Fabrication
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15138
dc.identifier.issn1467-8659
dc.identifier.pages10 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15138
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15138
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Computing methodologies → Computer graphics; Rendering
dc.subjectComputing methodologies → Computer graphics
dc.subjectRendering
dc.titleSearch Me Knot, Render Me Knot: Embedding Search and Differentiable Rendering of Knots in 3Den_US
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