Tobias Djuren

@article{DJUREN2025104316,
title = {Interpolating splines over triangulated surfaces by blending vertex-centric local geometries},
journal = {Computers & Graphics},
volume = {131},
pages = {104316},
year = {2025},
issn = {0097-8493},
doi = {https://doi.org/10.1016/j.cag.2025.104316},
url = {https://www.sciencedirect.com/science/article/pii/S0097849325001578},
author = {Tobias Djuren and Ugo Finnendahl and Maximilian Kohlbrenner and Markus Worchel and Marc Alexa},
keywords = {Rational interpolation, Splines, Local control},
abstract = {We investigate the construction of visually smooth spline surfaces that interpolate the vertices of triangulations by blending local patches. Each triangle star carries a locally interpolating surface patch. The patches are only required to interpolate the vertex, whereas in previous methods the patches are often defined per edge, imposing multiple constraints on local approximations. We adopt simple rational blend functions for the triangular domains, that are constructed so that they retain the interpolation and tangent behavior on the patch boundaries. Decoupling local approximation from blending facilitates the exploration of visually pleasing constructions, while controlling the complexity.}
}

@article{10.1145/3618383,
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 = {https://doi.org/10.1145/3618383},
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}
}

@article{Kohlbrenner2021,
	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 = {https://cybertron.cg.tu-berlin.de/projects/gaussStylization/},
	doi = {https://doi.org/10.1111/cgf.14355},
	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}
}