Variational geometry processing by Wang, Yu

“…In this thesis, two basic topics in geometry processing—curve/surface smoothing and reconstruction are discussed. …”
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Sum-of-squares geometry processing by Marschner, Zoë, Zhang, Paul, Palmer, David, Solomon, Justin

“…<jats:p> Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. …”
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Variational methods for geometry processing by Wu, Xiaoqun

“…Three types of geometry processing problems are studied under the similar variational framework. …”
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Surpassing Local Optimality in Geometry Processing by Zhang, Paul

“…Geometry processing is a diverse field studying questions such as how to represent a shape, how to modify a shape, and how shapes respond to perturbation. …”
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Relaxing Topological Barriers in Geometry Processing by Palmer, David R.

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Volumetric Mapping for Medical Imaging and Geometry Processing by Abulnaga, Sayed Mazdak

“…This application presents a challenging problem setting relevant for mapping tasks in computer graphics and geometry processing as a whole. We propose an automatic segmentation method to extract placental shapes from MRI. …”
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Steklov geometry processing : an extrinsic approach to spectral shape analysis by Yu, Wang, S.M. Massachusetts Institute of Technology

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Robust discrete geodesic and its applications in digital geometry processing by Dao Thi Phuong Quynh

“…First, we present three applications in common geometry processing including texture mapping, DIG-based D2 shape signature and DIG-based Heat Kernel Signature (HKS). …”
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Generalized edge-weighted centroidal Voronoi tessellations for geometry processing by Wang, Yu, Ju, Lili, Wang, Desheng, Wang, Xiaoqiang

“…In this paper, we propose a generalized edge-weighted centroidal Voronoi tessellation (GEWCVT) model and corresponding solution algorithms, then apply them for geometry processing such as curve/surface smoothing and reconstruction. …”
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Steklov Spectral Geometry for Extrinsic Shape Analysis by Wang, Yu, Ben-Chen, Mirela, Polterovich, Iosif, Solomon, Justin

“…We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.…”
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SimJEB: Simulated Jet Engine Bracket Dataset by Whalen, E., Beyene, A., Mueller, C.

“…The result is a collection of 381 diverse, high-quality and application-focused designs for advancing geometric deep learning, engineering surrogate modeling, automated cleaning and related geometry processing tasks.…”
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Deep Learning on Geometry Representations by Smirnov, Dmitriy

“…On the other hand, decades of computer graphics and geometry processing research have resulted in specialized algorithms and tools that use representations without such regular structure. …”
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Planar surface parameterization and texture mapping by Sun, Qingshuan.

“…Surface parameterization has been a well researched topic in computer graphics, due to its importance in computer geometry processing, computer vision and visualization. …”
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Optimal transport-based polar interpolation of directional fields by Solomon, Justin, Vaxman, Amir

“…We propose an algorithm that interpolates between vector and frame fields on triangulated surfaces, designed to complement field design methods in geometry processing and simulation. Our algorithm is based on a polar construction, leveraging a conservation law from the Hopf-Poincaré theorem to match singular points using ideas from optimal transport; the remaining detail of the field is interpolated using straightforward machinery. …”
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A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains by Mattos Da Silva, Leticia

“…In addition, we demonstrate the versatility of our method on a number of linear and nonlinear PDE that appear in diffusion tasks in geometry processing.…”
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Vectorization of Line Drawings via Polyvector Fields by Bessmeltsev, Mikhail, Solomon, Justin

“…Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean line drawings, modern algorithms often fail to faithfully vectorize junctions, or points at which curves meet; this produces vector drawings with incorrect connectivity. …”
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Using affinity set on mining the necessity of computed tomography scanning by Chen , Yuh Wen, Larbani, Moussa, Li, Tzung Hung, Chen, Chao-Wen

“…Computed tomography (CT) is a medical imaging method of tomography. Digital geometry processing is used to generate a three-dimensional image of the inside of a patient from a large series of two-dimensional X-ray images taken around a single axis of rotation. …”
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Reversible Harmonic Maps between Discrete Surfaces by Ezuz, Danielle, Solomon, Justin, Ben-Chen, Mirela

“…Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. …”
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A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains by Mattos Da Silva, Leticia, Stein, Oded, Solomon, Justin

“…In addition, we demonstrate the versatility of our method on a number of linear and nonlinear PDE that appear in diffusion and front propagation tasks in geometry processing.…”
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Evolutionary in solid state recycling techniques of aluminium : a review by Mohammad Amri Lajis, Zhong, Zhao Wei, Shamsudin, Shazarel

“…The review relates the extrudates quality of the solid state recycled aluminium to certain aspects noted as chips preparation, reinforced materials addition, die geometry, processing parameters, and performance of miscellaneous solid state recycling techniques. …”
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