Browsing by Author "Alexa, Marc"

Now showing items 1-9 of 9

    • ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells 

      Finnendahl, Ugo; Schwartz, Matthias; Alexa, Marc (© 2023 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2023)
      As‐rigid‐as‐possible (ARAP) surface modelling is widely used for interactive deformation of triangle meshes. We show that ARAP can be interpreted as minimizing a discretization of an elastic energy based on non‐conforming ...

    • Constrained Modelling of 3‐Valent Meshes Using a Hyperbolic Deformation Metric 

      Richter, Ronald; Kyprianidis, Jan Eric; Springborn, Boris; Alexa, Marc (© 2017 The Eurographics Association and John Wiley & Sons Ltd., 2017)
      Polygon meshes with 3‐valent vertices often occur as the frame of free‐form surfaces in architecture, in which rigid beams are connected in rigid joints. For modelling such meshes, it is desirable to measure the deformation ...

    • The Diamond Laplace for Polygonal and Polyhedral Meshes 

      Bunge, Astrid; Botsch, Mario; Alexa, Marc (The Eurographics Association and John Wiley & Sons Ltd., 2021)
      We introduce a construction for discrete gradient operators that can be directly applied to arbitrary polygonal surface as well as polyhedral volume meshes. The main idea is to associate the gradient of functions defined ...

    • Efficient Computation of Smoothed Exponential Maps 

      Herholz, Philipp; Alexa, Marc (© 2019 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2019)
      Many applications in geometry processing require the computation of local parameterizations on a surface mesh at interactive rates. A popular approach is to compute local exponential maps, i.e. parameterizations that ...

    • Fast Updates for Least-Squares Rotational Alignment 

      Zhang, Jiayi Eris; Jacobson, Alec; Alexa, Marc (The Eurographics Association and John Wiley & Sons Ltd., 2021)
      Across computer graphics, vision, robotics and simulation, many applications rely on determining the 3D rotation that aligns two objects or sets of points. The standard solution is to use singular value decomposition (SVD), ...

    • Gauss Stylization: Interactive Artistic Mesh Modeling based on Preferred Surface Normals 

      Kohlbrenner, Maximilian; Finnendahl, Ugo; Djuren, Tobias; Alexa, Marc (The Eurographics Association and John Wiley & Sons Ltd., 2021)
      Extending the ARAP energy with a term that depends on the face normal, energy minimization becomes an effective stylization tool for shapes represented as meshes. Our approach generalizes the possibilities of Cubic ...

    • Poisson Manifold Reconstruction - Beyond Co-dimension One 

      Kohlbrenner, Maximilian; Lee, Singchun; Alexa, Marc; Kazhdan, Misha (The Eurographics Association and John Wiley & Sons Ltd., 2023)
      Screened Poisson Surface Reconstruction creates 2D surfaces from sets of oriented points in 3D (and can be extended to codimension one surfaces in arbitrary dimensions). In this work we generalize the technique to manifolds ...

    • Polygon Laplacian Made Robust 

      Bunge, Astrid; Bukenberger, Dennis R.; Wagner, Sven Dominik; Alexa, Marc; Botsch, Mario (The Eurographics Association and John Wiley & Sons Ltd., 2024)
      Discrete Laplacians are the basis for various tasks in geometry processing. While the most desirable properties of the discretization invariably lead to the so-called cotangent Laplacian for triangle meshes, applying the ...

    • Properties of Laplace Operators for Tetrahedral Meshes 

      Alexa, Marc; Herholz, Philipp; Kohlbrenner, Max; Sorkine-Hornung, Olga (The Eurographics Association and John Wiley & Sons Ltd., 2020)
      Discrete Laplacians for triangle meshes are a fundamental tool in geometry processing. The so-called cotan Laplacian is widely used since it preserves several important properties of its smooth counterpart. It can be derived ...