Helmut Pottmann
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Austrian mathematician
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Helmut Pottmannmathematics Degrees
Mathematics
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Geometry
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Measure Theory
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Mathematics
Why Is Helmut Pottmann Influential?
(Suggest an Edit or Addition)Helmut Pottmann's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Robust global registration (2005) (662)
- Geometric modeling with conical meshes and developable surfaces (2006) (439)
- Discovering structural regularity in 3D geometry (2008) (403)
- Reassembling fractured objects by geometric matching (2006) (359)
- Computational Line Geometry (2001) (350)
- Architectural geometry (2007) (335)
- Fitting B-spline curves to point clouds by curvature-based squared distance minimization (2006) (325)
- Registration of point cloud data from a geometric optimization perspective (2004) (312)
- Geometric modeling in shape space (2007) (306)
- Integral invariants for robust geometry processing (2009) (246)
- Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes (2006) (233)
- Rational curves and surfaces with rational offsets (1995) (232)
- Geometry of multi-layer freeform structures for architecture (2007) (225)
- Freeform surfaces from single curved panels (2008) (198)
- Curved folding (2008) (187)
- Paneling architectural freeform surfaces (2010) (182)
- Registration without ICP (2004) (179)
- Energy-minimizing splines in manifolds (2004) (167)
- Approximation algorithms for developable surfaces (1999) (160)
- Applications of Laguerre geometry in CAGD (1998) (146)
- Design of self-supporting surfaces (2012) (146)
- Computing Rational Parametrizations of Canal Surfaces (1997) (143)
- Developable rational Bézier and B-spline surfaces (1995) (142)
- Dynamic geometry registration (2007) (133)
- A Laguerre geometric approach to rational offsets (1998) (133)
- The geometry of Tchebycheffian splines (1993) (132)
- Approximation with active B-spline curves and surfaces (2002) (130)
- Interactive Design of Developable Surfaces (2016) (120)
- Geometry of the Squared Distance Function to Curves and Surfaces (2002) (120)
- Robust Feature Classification and Editing (2007) (113)
- Robust principal curvatures on multiple scales (2006) (106)
- An introduction to line geometry with applications (1999) (106)
- Shape space exploration of constrained meshes (2011) (105)
- Locally optimal cutting positions for 5-axis sculptured surface machining (2003) (104)
- A concept for parametric surface fitting which avoids the parametrization problem (2003) (103)
- Industrial geometry: recent advances and applications in CAD (2005) (97)
- Principal curvatures from the integral invariant viewpoint (2007) (91)
- A curvature theory for discrete surfaces based on mesh parallelity (2009) (90)
- The focal geometry of circular and conical meshes (2008) (85)
- On Surface Approximation Using Developable Surfaces (1999) (84)
- Rotational and helical surface approximation for reverse engineering (1998) (81)
- Laguerre minimal surfaces, isotropic geometry and linear elasticity (2009) (80)
- Form-finding with polyhedral meshes made simple (2015) (79)
- Packing circles and spheres on surfaces (2009) (77)
- On the computational geometry of ruled surfaces (1999) (76)
- Form-finding with polyhedral meshes made simple (2014) (74)
- Rational Ruled Surfaces and Their Offsets (1996) (73)
- Fitting B-Spline Curves to Point Clouds by Squared Distance Minimization (2006) (71)
- Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution (2016) (70)
- Curvature continuous triangular interpolants (1989) (68)
- Geodesic patterns (2010) (65)
- Ruled Surfaces for Rationalization and Design in Architecture (2010) (65)
- A variational approach to spline curves on surfaces (2005) (63)
- Approximation of developable surfaces with cone spline surfaces (1998) (63)
- Curve design with rational Pythagorean-hodograph curves (1995) (62)
- Circular arc structures (2011) (62)
- Precise gouging-free tool orientations for 5-axis CNC machining (2015) (62)
- Approximation by ruled surfaces (1999) (61)
- The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces (2004) (60)
- Helix splines as an example of affine Tchebycheffian splines (1994) (58)
- Darboux cyclides and webs from circles (2011) (58)
- Modified multiquadric methods for scattered data interpolation over a sphere (1990) (56)
- Intrinsic subdivision with smooth limits for graphics and animation (2006) (54)
- Discrete Surfaces for Architectural Design (2007) (54)
- Case Studies in Cost-Optimized Paneling of Architectural Freeform Surfaces (2010) (53)
- Constrained 3D shape reconstruction using a combination of surface fitting and registration (2006) (52)
- 3D shape recognition and reconstruction based on line element geometry (2005) (51)
- Collision-free 3-axis milling and selection of cutting tools (1999) (49)
- Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces (1994) (48)
- Designing NURBS Cam Profiles Using Trigonometric Splines (1998) (46)
- Interpolation on surfaces using minimum norm networks (1992) (44)
- SIMULTANEOUS REGISTRATION OF MULTIPLE VIEWS OF A 3 D OBJECT (2002) (42)
- Polyhedral patterns (2015) (42)
- Fat surfaces: a trivariate approach to triangle-based interpolation on surfaces (1992) (41)
- Pipe surfaces with rational spine curve are rational (1996) (40)
- Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining (2017) (39)
- Freeform Honeycomb Structures (2014) (39)
- Interactive Modeling of Architectural Freeform Structures: Combining Geometry with Fabrication and Statics (2014) (39)
- Architectural Geometry and Fabrication-Aware Design (2013) (39)
- Line Geometry for 3D Shape Understanding and Reconstruction (2004) (39)
- Discrete Surfaces in Isotropic Geometry (2007) (37)
- Geometry of architectural freeform structures (2008) (37)
- From curve design algorithms to the design of rigid body motions (2004) (36)
- Cell packing structures (2015) (36)
- Approximation in Line Space — Applications in Robot Kinematics and Surface Reconstruction (1998) (36)
- Scattered data interpolation based upon generalized minimum norm networks (1991) (35)
- On piecewise linear approximation of quadratic functions. (2000) (35)
- Visualizing functions on a surface (1991) (34)
- Error propagation in geometric constructions (2000) (33)
- Architectural Geometry as Design Knowledge (2010) (33)
- Functional webs for freeform architecture (2011) (33)
- Contributions to Motion Based Surface Design (1998) (33)
- Geometric computing for freeform architecture (2011) (32)
- Detection and reconstruction of freeform sweeps (2014) (32)
- Swept Volumes (2004) (32)
- General offset surfaces (1997) (32)
- Geometric Criteria for Gouge-Free Three-Axis Milling of Sculptured Surfaces (1999) (31)
- Surface fitting based on a feature sensitive parametrization (2006) (31)
- Self-Intersections of Offset Curves and Surfaces (2001) (31)
- Infinitesimally flexible meshes and discrete minimal surfaces (2008) (30)
- Geometric Computing in Shape Space (2007) (29)
- Material-minimizing forms and structures (2017) (29)
- Polynomial and Rational Pythagorean-Hodograph Curves Reconciled (1994) (28)
- Exact Minkowski Products of N Complex Disks (2002) (27)
- Design and construction of curved support structures with repetitive parameters (2018) (27)
- Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces (2018) (27)
- Quad-mesh based isometric mappings and developable surfaces (2020) (27)
- Circular Arc Snakes and Kinematic Surface Generation (2013) (26)
- Optimal slicing of free-form surfaces (2002) (25)
- Rational blending surfaces between quadrics (1997) (25)
- Discrete Line Congruences for Shading and Lighting (2013) (23)
- The d2-Tree: A Hierarchical Representation of the Squared Distance Function (2003) (23)
- Analysis and design of curved support structures (2016) (22)
- Generalized penetration depth computation based on kinematical geometry (2009) (22)
- Computing the Minkowski sum of ruled surfaces (2003) (22)
- Ruled Free Forms (2012) (21)
- Intuitive Design Exploration of Constrained Meshes (2012) (21)
- Discrete geodesic parallel coordinates (2019) (20)
- Equiform kinematics and the geometry of line elements. (2006) (20)
- Edge offset meshes in Laguerre geometry (2010) (19)
- Piecewise optimal triangulation for the approximation of scattered data in the plane (2000) (17)
- Locally controllable conic splines with curvature continuity (1991) (17)
- Curve-pleated structures (2019) (16)
- Discretizations of Surfaces with Constant Ratio of Principal Curvatures (2019) (16)
- Aligning principal stress and curvature directions (2018) (15)
- Checkerboard patterns with black rectangles (2019) (15)
- Tiling Freeform Shapes With Straight Panels: Algorithmic Methods (2010) (15)
- Designing patterns using triangle-quad hybrid meshes (2018) (14)
- Visualizing Curvature Discontinuities of Free-Form Surfaces (1989) (14)
- New Strategies and Developments in Transparent Free-Form Design: From Facetted to Nearly Smooth Envelopes (2010) (14)
- Smooth surfaces from bilinear patches: Discrete affine minimal surfaces☆ (2013) (14)
- Freeform quad-based kirigami (2020) (14)
- Computational design of cold bent glass façades (2020) (14)
- Applications of the dual Be´zier representation of rational curves and surfaces (1994) (13)
- On optimal tolerancing in computer-aided design (2000) (13)
- Approximation by Profile Surfaces (2000) (13)
- Fair webs (2006) (12)
- Singularities of motions constrained by contacting surfaces (2000) (12)
- Principal symmetric meshes (2020) (11)
- Smooth curves under tension (1990) (11)
- Hough Transform and Laguerre Geometry for the Recognition and Reconstruction of Special 3 D Shapes (2003) (11)
- Geometric design of motions constrained by a contacting surface pair (2003) (11)
- Ruled Laguerre minimal surfaces (2010) (11)
- Spline Orbifolds (1997) (10)
- RECOGNITION AND RECONSTRUCTION OF SPECIAL SURFACES FROM POINT CLOUDS (2002) (10)
- Classification using normal curves (1992) (10)
- Fair Surface Reconstruction Using Quadratic Functionals (1995) (10)
- Developable Surfaces with Curved Creases (2008) (10)
- Approximation in the space of planes-Applications to geometric modeling and reverse engineering (2002) (10)
- Geometry and tool motion planning for curvature adapted CNC machining (2021) (10)
- Multi-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles (2018) (9)
- Inverse Problems of Integral Invariants and Shape Signatures (2007) (9)
- Dissertation Constrained Matching of Point Clouds and Surfaces (2010) (9)
- Smooth surfaces from rational bilinear patches (2014) (9)
- Geometries for CAGD (2002) (8)
- Proceedings of the third Eurographics symposium on Geometry processing (2005) (8)
- Subdivision Algorithms for Motion Design Based on Homologous Points (2002) (8)
- Spline Orbifolds Curves and Surfaces with Applications in Cagd 445 (2007) (8)
- Visual smoothness of polyhedral surfaces (2019) (8)
- Computational design of weingarten surfaces (2021) (8)
- Computing shortest paths on polyhedra: applications in geometric modeling and scientific visualization (1994) (8)
- Fast model based segmentation of ultrasound data using an active image (2002) (7)
- Characterizing envelopes of moving rotational cones and applications in CNC machining (2020) (7)
- SCATTERED DATA APPROXIMATION WITH KINEMATIC SURFACES (1999) (7)
- Smooth polyhedral surfaces (2017) (7)
- Approximating Boundary-Triangulated Objects with Balls (2007) (7)
- MEASURING CORTICAL THICKNESS FROM VOLUMETRIC MRI DATA (2006) (7)
- Geometry and freeform architecture (2016) (7)
- Reconstruction of Kinematic Surfaces from Scattered Data (1998) (7)
- Form Finding of Shell Bridges Using the Pneumatic Forming of Hardened Concrete Construction Principle (2018) (7)
- Symmetric Tchebycheffian B-spline schemes (1994) (6)
- Subdivision schemes for the fair discretization of the spherical motion group (2008) (6)
- ALGORITHMS FOR CONSTRAINED MINIMIZATION OF QUADRATIC FUNCTIONS – GEOMETRY AND CONVERGENCE ANALYSIS (6)
- Interpolating Functions on Lines in 3-Space (2000) (6)
- On Approximation in Spaces of Geometric Objects (2000) (6)
- Using isometries for computational design and fabrication (2021) (6)
- VARIATIONAL MOTION DESIGN (2004) (6)
- MEASURING AND CONTROLLING FAIRNESS OF TRIANGULATIONS (2016) (5)
- Geometric Contribution to 3-axis Milling of Sculptured Surfaces (1998) (5)
- SMI 2012: Keynote Speaker: Freeform architecture and fabrication-aware design (2012) (5)
- Vertex Normals and Face Curvatures of Triangle Meshes (2016) (5)
- Computational Mechanical Modelling of Wood—From Microstructural Characteristics Over Wood-Based Products to Advanced Timber Structures (2019) (5)
- Projectively invariant classes of geometric continuity for CAGD (1989) (5)
- Freeform Shading and Lighting Systems from Planar Quads (2013) (5)
- Geometry and tool motion planning for curvature adapted CNC machining (2021) (5)
- Architectural freeform structures from single curved panels (2008) (5)
- Inflections of planar surface curves (1997) (4)
- Computational design of weingarten surfaces (2021) (4)
- Fair curve networks in nonlinear geometries (2005) (4)
- From curve de-sign algorithms to motion design (2002) (4)
- Characteristic parameterizations of surfaces with a constant ratio of principal curvatures (2022) (4)
- Variational Interpolation of Subsets (2004) (3)
- Computational design and optimization of quad meshes based on diagonal meshes (2020) (3)
- Planar Panels and Planar Supporting Beams in Architectural Structures (2022) (3)
- Steering of form - New integrative approaches to architectural design and modeling (2015) (3)
- Surface Reconstruction Based Upon (2007) (3)
- Using isometries for computational design and fabrication (2021) (3)
- Dual Focal Splines and Rational Curves with Rational Offsets (1997) (3)
- Shape-morphing mechanical metamaterials (2021) (3)
- Freeform honeycomb structures and lobel frames (2015) (2)
- Laguerre geometry in space forms and incircular nets (2019) (2)
- Non-Euclidean Laguerre Geometry and Incircular Nets (2020) (2)
- Designing Energy-Minimizing Rigid Body Motions in the Presence of Obstacles (2005) (2)
- Geometric Motion Design (1994) (2)
- Approximation by Pro le Surfaces (1998) (2)
- Freeform Architecture and Discrete Differential Geometry (2017) (2)
- Models of Line Space (2010) (1)
- 3. Lamella Flock (2017) (1)
- Special section on geometric modeling and processing (2005) (1)
- Technical Perspective: Linking form, function, and fabrication (2017) (1)
- Chapter 2. Computational Geometry for SSM Geometric Contributions to 3-Axis Milling of Sculptured Surfaces (1999) (1)
- Fitting B-Spline Curves to Point Clouds in the Presence of Obstacles ausgeführt am (2005) (1)
- Geometry and Statics of Optimal Freeform Gridshells (2020) (1)
- Discrete and Computational Differential Geometry for Functional Pattern Design (2019) (1)
- Designing Asymptotic Geodesic Hybrid Gridshells (2022) (1)
- Discrete geometric structures for architecture (2010) (1)
- Special issue on geometric modeling and processing (2004) (1)
- Segmentation and modeling of approximately rotationally symmetric objects in 3D ultrasound (2003) (1)
- Checkerboard Incircular Nets (2021) (1)
- Approximation in Line Space (2010) (1)
- 15. Realizing Formal and Funcional Complexity for Structurally Dynamic Systems in Rapid Computational Means (2017) (0)
- Line Congruences and Line Complexes (2010) (0)
- Developable Quad Meshes (2022) (0)
- Optimizing shapes and structures for freeform architecture (2020) (0)
- Curved support structures and meshes with spherical vertex stars (2018) (0)
- Architectural Structures from Quad Meshes with Planar Parameter Lines (2022) (0)
- Lie Geometry (2021) (0)
- Principal Symmetric Structures (2021) (0)
- Ruled Laguerre minimal surfaces (2011) (0)
- Non-Euclidean Laguerre Geometry (2021) (0)
- UrbanFlow: Designing Comfortable Outdoor Areas (2022) (0)
- Voronoi Diagrams for Oriented Spheres (2007) (0)
- Programme on “ Infinite-dimensional Riemannian geometry with applications to image matching and shape analysis (2015) (0)
- Quadrics in Projective Space (2021) (0)
- Helical surfaces with a constant ratio of principal curvatures (2022) (0)
- AD Structuring in Architecture (2010) (0)
- Multi-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles (2019) (0)
- Geometry and Computational Design (2015) (0)
- Architectural Geometry and Fabrication-Aware Design (2013) (0)
- 10. Wiggled Brick Bond (2017) (0)
- Geometry and computational design of equilibrium structures (2019) (0)
- Generalization of the Orthodiagonal Involutive Type of Kokotsakis Flexible Polyhedra (2023) (0)
- The Visual Computer ( to appear 2007 ) (2006) (0)
- Garcia Geometry and New and Future Spatial Patterns (2009) (0)
- Geometry and Interactive Design of Curved Creases (2017) (0)
- 14. Geometry of Structural Form (2017) (0)
- Two-Dimensional Laguerre Geometry (2021) (0)
- 9. Architectural Acoustics for Practioners (2017) (0)
- Third Eurographics Symposium on Geometry Processing, Vienna, Austria, July 4-6, 2005 (2005) (0)
- Approximation by Profile Surfaces 1 (2000) (0)
- Variational and PDE level set methods (2007) (0)
- Rationalization and Design with Cylindrical Strip Models (2014) (0)
- und mathematische Modellierung Discrete surfaces for architectural design (2008) (0)
- Research Group for Geometric Modelling and Industrial Geometry (2015) (0)
- Linear Line Mappings — Computational Kinematics (2010) (0)
- Editorial to: Industrial Geometry (2004) (0)
- Central Projection of Quadrics and Möbius Geometry (2021) (0)
- Discretizations of Surfaces with Constant Ratio of Principal Curvatures (2019) (0)
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What Schools Are Affiliated With Helmut Pottmann?
Helmut Pottmann is affiliated with the following schools:
