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Papers by Helmut Pottmann

ACM Transactions on Graphics, 2008

Proceedings of the 2008 ACM symposium on Solid and physical modeling - SPM '08, 2008

Handbook of Computer Aided Geometric Design, 2002

In the reconstruction process of geometric objects from several three-dimensional images (clouds ... more In the reconstruction process of geometric objects from several three-dimensional images (clouds of measurement points) it is crucial to align the point sets of the different views, such that errors in the overlapping regions are minimized. We present an iterative algorithm which simultaneously registers all 3D image views. It can also be used for the solution of related positioning problems

Mathematics and Visualization, 2003

Computer-aided Design, 2000

Given a solid 3 S R ⊂ with a piecewise smooth boundary, we compute an approximation of the bounda... more Given a solid 3 S R ⊂ with a piecewise smooth boundary, we compute an approximation of the boundary surface of the volume which is swept by S under a smooth one-parameter motion. Using knowledge from kinematical and elementary differential geometry, the algorithm computes a set of points plus surface normals from the envelope surface. A study of the evolution

Lecture Notes in Computer Science, 2004

Fascinating and elegant shapes may be folded from a single planar sheet of material without stret... more Fascinating and elegant shapes may be folded from a single planar sheet of material without stretching, tearing or cutting, if one incor- porates curved folds into the design. We present an optimization- based computational framework for design and digital reconstruc- tion of surfaces which can be produced by curved folding. Our work not only contributes to applications in architecture and

Lecture Notes in Computer Science, 2004

European Workshop on Computational Geometry, 2000

We compute a set of balls that approximates a given 3D object, and we derive small additive bound... more We compute a set of balls that approximates a given 3D object, and we derive small additive bounds for the overhead in balls with respect to the minimal so- lution with the same quality. The algorithm has been implemented and tested using the CGAL library (7).

Proceedings Geometric Modeling and Processing 2000. Theory and Applications, 2000

Mathematics and Visualization, 2009

Developable surfaces are surfaces in Euclidean space which ‘can be made of a piece of paper’, i.e... more Developable surfaces are surfaces in Euclidean space which ‘can be made of a piece of paper’, i.e., are isometric to part of the Euclidean plane, at least locally. If we do not assume sufficient smoothness, the class of such surfaces is too large to be useful — if includes all possible aways of arranging crumpled paper in space. For C 2 surfaces, however, developability is characterized by vanishing Gaussian curvature, and by being made of pieces of torsal ruled surfaces. We will here use ‘developable’ and ‘torsal ruled’ as synonyms, because we are most interested in the ruled surface which carries a developable surface patch. We first have a look at the Euclidean differential geometry of developable surfaces, and then study developables as envelopes of their tangent planes. This view-point identifies the curves in dual projective space with the torsal ruled surfaces. We describe some fields of applications where the concept of developable surface arises naturally and knowledge of the theory leads to geometric insights. These include developables of constant slope, the cyclographic mapping, medial axis computations, geometrical optics, rational curves with rational offsets, geometric tolerancing, and the use of developable surfaces in industrial processes.

ACM Transactions on Graphics, 2008

Proceedings of the 2008 ACM symposium on Solid and physical modeling - SPM '08, 2008

Handbook of Computer Aided Geometric Design, 2002

In the reconstruction process of geometric objects from several three-dimensional images (clouds ... more In the reconstruction process of geometric objects from several three-dimensional images (clouds of measurement points) it is crucial to align the point sets of the different views, such that errors in the overlapping regions are minimized. We present an iterative algorithm which simultaneously registers all 3D image views. It can also be used for the solution of related positioning problems

Mathematics and Visualization, 2003

Computer-aided Design, 2000

Given a solid 3 S R ⊂ with a piecewise smooth boundary, we compute an approximation of the bounda... more Given a solid 3 S R ⊂ with a piecewise smooth boundary, we compute an approximation of the boundary surface of the volume which is swept by S under a smooth one-parameter motion. Using knowledge from kinematical and elementary differential geometry, the algorithm computes a set of points plus surface normals from the envelope surface. A study of the evolution

Lecture Notes in Computer Science, 2004

Fascinating and elegant shapes may be folded from a single planar sheet of material without stret... more Fascinating and elegant shapes may be folded from a single planar sheet of material without stretching, tearing or cutting, if one incor- porates curved folds into the design. We present an optimization- based computational framework for design and digital reconstruc- tion of surfaces which can be produced by curved folding. Our work not only contributes to applications in architecture and

Lecture Notes in Computer Science, 2004

European Workshop on Computational Geometry, 2000

We compute a set of balls that approximates a given 3D object, and we derive small additive bound... more We compute a set of balls that approximates a given 3D object, and we derive small additive bounds for the overhead in balls with respect to the minimal so- lution with the same quality. The algorithm has been implemented and tested using the CGAL library (7).

Proceedings Geometric Modeling and Processing 2000. Theory and Applications, 2000

Mathematics and Visualization, 2009

Developable surfaces are surfaces in Euclidean space which ‘can be made of a piece of paper’, i.e... more Developable surfaces are surfaces in Euclidean space which ‘can be made of a piece of paper’, i.e., are isometric to part of the Euclidean plane, at least locally. If we do not assume sufficient smoothness, the class of such surfaces is too large to be useful — if includes all possible aways of arranging crumpled paper in space. For C 2 surfaces, however, developability is characterized by vanishing Gaussian curvature, and by being made of pieces of torsal ruled surfaces. We will here use ‘developable’ and ‘torsal ruled’ as synonyms, because we are most interested in the ruled surface which carries a developable surface patch. We first have a look at the Euclidean differential geometry of developable surfaces, and then study developables as envelopes of their tangent planes. This view-point identifies the curves in dual projective space with the torsal ruled surfaces. We describe some fields of applications where the concept of developable surface arises naturally and knowledge of the theory leads to geometric insights. These include developables of constant slope, the cyclographic mapping, medial axis computations, geometrical optics, rational curves with rational offsets, geometric tolerancing, and the use of developable surfaces in industrial processes.