Maximilian Kohlbrenner


K-Surfaces: Bézier-Splines Interpolating at Gaussian Curvature Extrema (2023) ACM Transactions on Graphics (Proc. of Siggraph Asia)
author = {Djuren, Tobias and Kohlbrenner, Maximilian and Alexa, Marc},
title = {K-Surfaces: B\'{e}zier-Splines Interpolating at Gaussian Curvature Extrema},
year = {2023},
issue_date = {December 2023},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {42},
number = {6},
issn = {0730-0301},
url = {},
doi = {10.1145/3618383},
journal = {ACM Trans. Graph.},
month = {dec},
articleno = {210},
numpages = {13},
keywords = {interactive surface modeling, b\'{e}zier patches, gaussian curvature, b\'{e}zier splines}
Poisson Manifold Reconstruction — Beyond Co-dimension One (2023) Computer Graphics Forum
author = {Kohlbrenner, M. and Lee, S. and Alexa, M. and Kazhdan, M.},
title = {Poisson Manifold Reconstruction — Beyond Co-dimension One},
journal = {Computer Graphics Forum},
volume = {42},
number = {5},
pages = {e14907},
keywords = {CCS Concepts, • Computing methodologies → Shape modeling, • Mathematics of computing → Nonlinear equations, Numerical analysis, curve and surface reconstruction, sub-manifold reconstruction, exterior product, polynomial optimization},
doi = {},
url = {},
eprint = {},
abstract = {Abstract Screened Poisson Surface Reconstruction creates 2D surfaces from sets of oriented points in 3D (and can be extended to co-dimension one surfaces in arbitrary dimensions). In this work we generalize the technique to manifolds of co-dimension larger than one. The reconstruction problem consists of finding a vector-valued function whose zero set approximates the input points. We argue that the right extension of screened Poisson Surface Reconstruction is based on exterior products: the orientation of the point samples is encoded as the exterior product of the local normal frame. The goal is to find a set of scalar functions such that the exterior product of their gradients matches the exterior products prescribed by the input points. We show that this setup reduces to the standard formulation for co-dimension 1, and leads to more challenging multi-quadratic optimization problems in higher co-dimension. We explicitly treat the case of co-dimension 2, i.e., curves in 3D and 2D surfaces in 4D. We show that the resulting bi-quadratic problem can be relaxed to a set of quadratic problems in two variables and that the solution can be made effective and efficient by leveraging a hierarchical approach.},
year = {2023}
Gauss Stylization: Interactive Artistic Mesh Modeling based on Preferred Surface Normals (2021) Computer Graphics Forum
	title = {Gauss Stylization: Interactive Artistic Mesh Modeling based on Preferred Surface Normals},
	author = {Max Kohlbrenner and Ugo Finnendahl and Tobias Djuren and Marc Alexa},
	url = {},
	doi = {},
	year = {2021},
	date = {2021-08-23},
	journal = {Computer Graphics Forum},
	volume = {40},
	number = {5},
	pages = {33-43},
	abstract = {Abstract 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 Stylization: the set of preferred normals can be chosen arbitrarily from the Gauss sphere, including semi-discrete sets to model preference for cylinder- or cone-like shapes. The optimization is designed to retain, similar to ARAP, the constant linear system in the global optimization. This leads to convergence behavior that enables interactive control over the parameters of the optimization. We provide various examples demonstrating the simplicity and versatility of the approach.},
	keywords = {computer graphics, geometric stylization, geometry processing, non-photorealistic rendering, shape modeling},
	pubstate = {published},
	tppubtype = {article}
Properties of Laplace Operators for Tetrahedral Meshes (2020) Computer Graphics Forum
	title = {Properties of Laplace Operators for Tetrahedral Meshes},
	author = {Marc Alexa and Philipp Herholz and Maximilian Kohlbrenner and Olga Sorkine},
	url = {, Project Page},
	doi = {10.1111/cgf.14068},
	year = {2020},
	date = {2020-07-06},
	journal = {Computer Graphics Forum},
	volume = {39},
	number = {5},
	pages = {55-68},
	abstract = {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 from different principles: either considering the piecewise linear nature of the primal elements or associating values to the dual vertices. Both approaches lead to the same operator in the two-dimensional setting. In contrast, for tetrahedral meshes, only the primal construction is reminiscent of the cotan weights, involving dihedral angles. We provide explicit formulas for the lesser-known dual construction. In both cases, the weights can be computed by adding the contributions of individual tetrahedra to an edge. The resulting two different discrete Laplacians for tetrahedral meshes only retain some of the properties of their two-dimensional counterpart. In particular, while both constructions have linear precision, only the primal construction is positive semi-definite and only the dual construction generates positive weights and provides a maximum principle for Delaunay meshes. We perform a range of numerical experiments that highlight the benefits and limitations of the two constructions for different problems and meshes.},
	keywords = {computer graphics, geometry processing, laplacian},
	pubstate = {published},
	tppubtype = {article}