Hans-Peter Schröcker

Publications on MathSciNet, zbMATH, arXiv, Google Scholar, ORCID, Scopus.

In Review

1. J. Frischauf, N. Lubbes, and H.-P. Schröcker. Bivariate quaternionic factorizations and surfaces that decompose into two circles. Submitted for publication, 2023.
2.  Z. Li, H.-P. Schröcker, M. Skopenkov, and D. F. Scharler. Motion Polynomials Admitting a Factorization with Linear Factors. Submitted for publication, 2022. [ arXiv ]

Journal Articles

1. Z. Li, H.-P. Schröcker, and J. Siegele. A Geometric Algorithm for the Factorization of Spinor Polynomials.  J. Symbolic Computation, 128:102388, 2025. [ DOI| arXiv ]

2. H.-P. Schröcker and Z. Šír. Three Paths to Rational Curves with Rational Arc Length. Appl. Math. Comput., 478:128842, 2024. [ DOI | arXiv ]

3. H.-P. Schröcker and Z. Šír. Optimal interpolation with spatial rational Pythagorean hodograph curves. Appl. Math. Comput., 458:128214, 2023. [ DOI | MR | arXiv ]

4. H.-P. Schröcker and Z. Šír. Partial fraction decomposition for rational Pythagorean hodograph curves. J. Comput. Appl. Math. , 428:115196, 2023. [ DOI | MR | ZBL | arXiv ]

5. J. Lercher, D. F. Scharler, H.-P. Schröcker, and J. Siegele Factorization of quaternionic polynomials of bi-degree (n,1). Beitr. Algebra Geom., 64:209-232, 2023. [ DOI | MR | arXiv ]
6. J. Frischauf, M. Pfurner, D. F. Scharler, and H.-P. Schröcker. A multi-Bennett 8R mechanism obtained from factorization of bivariate motion polynomials. Mech. Mach. Theory, 180:105143, 2023. [ DOI | arXiv ]
7. J. Lercher and H.-P. Schröcker. A multiplication technique for the factorization of bivariate quaternionic polynomials. Adv. Appl. Clifford Algebras, 32, 2022. [ DOI | MR | ZBL | arXiv]
8. B. Kalkan, D. F. Scharler, H.-P. Schröcker, and Z. Šír. Rational framing motions and spatial rational Pythagorean hodograph curves. Comput. Aided Geom. Design, 99:102160, 2022. [ DOI | MR | arXiv ]
9. B. Kalkan, Z. Li, H.-P. Schröcker, and J. Siegele. The Study variety of conformal kinematics. Adv. Appl. Clifford Algebras, 32, 2022. [ DOI | MR | ZBL | arXiv]
10. J. Siegele, M. Pfurner, and H.-P. Schröcker. Space kinematics and projective differential geometry over the ring of dual numbers. J. Geom. Graphics, 25(1):19-31, 2021. [ MR | ZBL | arXiv | www ]
11. J. Siegele, M. Pfurner, and H.-P. Schröcker. Factorization of dual quaternion polynomials without Study's condition. Adv. Appl. Clifford Algebras, 33, 2021. [ DOI | MR | ZBL | arXiv ]
12. D. F. Scharler and H.-P. Schröcker. An algorithm for the factorization of split quaternion polynomials. Adv. Appl. Clifford Algebras, 31, 2021. [ DOI | MR | ZBL | arXiv ]
13. J. Siegele, D. F. Scharler, and H.-P. Schröcker. Rational motions with generic trajectories of low degree. Comput. Aided Geom. Design, 76:101793, 2020. [ DOI | MR | ZBL | arXiv ]
14. D. F. Scharler, J. Siegele, and H.-P. Schröcker. Quadratic split quaternion polynomials: Factorization and geometry. Adv. Appl. Clifford Algebras, 30(11), 2020. [ DOI | MR | ZBL | arXiv ]
15. Z. Li, J. Schicho, and H.-P. Schröcker. Factorization of motion polynomials. J. Symbolic Comput., 92:190-202, 2019. [ DOI | MR | ZBL | arXiv ]
16. Z. Li, D. F. Scharler, and H.-P. Schröcker. Factorization results for left polynomials in some associative real algebras: State of the art, applications, and open questions. J. Comput. Appl. Math., 349:508-522, 2019. [ DOI| MR | ZBL | arXiv ]
17. Z. Li, J. Schicho, and H.-P. Schröcker. Kempe's universality theorem for rational space curves. Found. Comput. Math., 18(2):509-536, 2018. [ DOI | MR | ZBL | arXiv ]
18. Z. Li, J. Schicho, and H.-P. Schröcker. A survey on the theory of bonds. IMA J. Math. Control Inform., 35(1):279-295, 2018. [ DOI | MR | ZBL | arXiv ]
19. Tudor-Dan Rad, D. F. Scharler, and H.-P. Schröcker. The kinematic image of RR, PR, and RP dyads. Robotica, 36(10):1477-1492, 2018. [ DOI | arXiv ]
20. H.-P. Schröcker. From A to B: New methods to interpolate two poses. J. Geom. Graphics, 22(1):87-98, 2018. [ MR | ZBL | arXiv ]
21. H.-P. Schröcker. Singular Frégier conics in non-Euclidean geometry. J. Geom. Graphics, 21(2):201-208, 2017. [ MR | ZBL | arXiv | www ]
22. Z. Li, J. Schicho, and H.-P. Schröcker. The rational motion of minimal dual quaternion degree with prescribed trajectory. Comput. Aided Geom. Design, 41:1-9, 2016. [ DOI | MR | ZBL | arXiv ]
23. G. Hegedüs, J. Schicho, and H.-P. Schröcker. Four-pose synthesis of angle-symmetric 6R linkages. ASME J. Mech. Robot., 7(4), 2015. [ DOI | arXiv ]
24. G. Hegedüs, Z. Li, J. Schicho, and H.-P. Schröcker. The theory of bonds II: Closed 6R linkages with maximal genus. J. Symbolic Comput., 68(2):167-180, 2015. [ DOI | MR | ZBL | arXiv ]
25. Z. Li, J. Schicho, and H.-P. Schröcker. Spatial straight-line linkages by factorization of motion polynomials. ASME J. Mech. Robot., 8(2), 2015. [ DOI | arXiv ]
26. H.-P. Schröcker and M. J. Weber. Guaranteed collision detection with toleranced motions. Comput. Aided Geom. Design, 31(7-8):602-612, 2014. [ DOI | MR | ZBL | arXiv ]
27. J. Schadlbauer and H.-P. Schröcker. Orthogonality relations for tetrahedra in elliptic and hyperbolic spaces. J. Geom. Graphics, 18(1):97-104, 2014. [ MR | ZBL | www ]
28. M. J. Weber and H.-P. Schröcker. Minimal area ellipses in the hyperbolic plane. Beitr. Algebra Geom., 54(1):181-200, 2013. [ DOI | MR | ZBL | arXiv ]
29. G. Hegedüs, J. Schicho, and H.-P. Schröcker. Factorization of rational curves in the Study quadric and revolute linkages. Mech. Mach. Theory, 69(1):142-152, 2013. [ DOI | arXiv ]
30. G. Hegedüs, J. Schicho, and H.-P. Schröcker. The theory of bonds: A new method for the analysis of linkages. Mech. Mach. Theory, 70:407-424, 2013. [ DOI | arXiv ]
31. M. J. Weber and H.-P. Schröcker. Minimal area conics in the elliptic plane. Advances in Geom., 12(4):665-684, 2012. [ DOI | MR | ZBL | arXiv ]
32. H.-P. Schröcker. Discrete Laplace cycles of period four. Central European J. Mathematics, 10(2):426-439, 2012. [ DOI | MR | ZBL | arXiv ]
33. M. J. Weber and H.-P. Schröcker. Davis' convexity theorem and extremal ellipsoids. Beitr. Algebra Geom., 51(1):263-274, 2010. [ MR | ZBL | arXiv | www ]
34. H.-P. Schröcker. Discrete gliding along principal curves. J. Geom. Graphics, 14(2):171-180, 2010. [ MR | ZBL | www ]
35. H.-P. Schröcker. Orthologic tetrahedra with intersecting edges. KoG, 13:13-18, 2009. [ MR | ZBL | arXiv | www ]
36. H.-P. Schröcker. Uniqueness results for minimal enclosing ellipsoids. Comput. Aided Geom. Design, 25(9):756-762, 2008. [ DOI | MR | ZBL ]
37. H.-P. Schröcker. Double tangent circles and focal properties of sphero-conics. J. Geom. Graphics, 12(2):161-169, 2008. [ MR | ZBL | www ]
38. M. Husty, M. Pfurner, and H.-P. Schröcker. A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator. Mech. Mach. Theory, 42(1):66-81, 2007. [ DOI | MR | ZBL ]
39. M. Husty, M. Pfurner, H.-P. Schröcker, and K. Brunnthaler. Algebraic methods in mechanism analysis and synthesis. Robotica, 25(6):661-675, 2007. [ DOI ]
40. Ch. Niederegger, C. Bruschek, M. Koppi, H.-P. Schröcker, and D. Wagner. Verbesserung von Frisch- und Festbetoneigenschaften durch Mischung der Haufwerksporosität von Bindemitteln mittels Approximation der Fuller-Kurve durch Mischen von Kornfraktionen. Beton, 5:220-222, 2007.
41. H.-P. Schröcker, M. Husty, and J. M. McCarthy. Kinematic mapping based assembly mode evaluation of planar four-bar mechanisms. ASME J. Mech. Design, 129(9):924-929, 2007. [ DOI ]
42. H.-P. Schröcker. Minimal enclosing hyperbolas of line sets. Beitr. Algebra Geom., 48(2):367-381, 2007. [ MR | ZBL | www ]
43. H.-P. Schröcker and J. Wallner. Geometric constructions with discretized random variables. Reliab. Comput./Nadezhn. Vychisl., 12(3):206-223, 2006. [ DOI | MR | ZBL ]
44. H.-P. Schröcker and J. Wallner. Curvatures and tolerances in the Euclidean motion group. Results Math., 47:132-146, 2005. [ DOI | MR | ZBL ]
45. H.-P. Schröcker. The geometry of rational parameterized representations. J. Geom., 82:171-187, 2005. [ DOI | MR | ZBL ]
46. H.-P. Schröcker. Conic sections in space defined by intersection conditions. Beitr. Algebra Geom., 46(2):301-309, 2005. [ MR | ZBL | www ]
47. H.-P. Schröcker. The intersection conics of six straight lines. Beitr. Algebra Geom., 46(2):435-446, 2005. [ MR | ZBL | www ]
48. E. Tsutsumi, H.-P. Schröcker, H. Stachel, and G. Weiß. Evaluation of student's spatial abilities in Austria and Germany. J. Geom. Graphics, 9(1):107-117, 2005. [ ZBL | www ]
49. J. Wallner, H.-P. Schröcker, and Shi-Min Hu. Tolerances in geometric constraint problems. Reliab. Comput./Nadezhn. Vychisl., 11(3):235-251, 2005. [ DOI | MR | ZBL ]
50. H.-P. Schröcker. The manifold of planes that intersect four straight lines in points of a circle. J. Geom. Graphics, 8(1):59-68, 2004. [ MR | ZBL | www ]
51. H.-P. Schröcker. Semi-Darboux motions of rational curves with equivalent trajectories. Abh. Math. Sem. Univ. Hamburg, 73:271-279, 2003. [ DOI | MR | ZBL ]
52. H.-P. Schröcker. Generatrices of rational curves. J. Geom., 73:134-147, 2002. [ DOI | MR | ZBL ]
53. H.-P. Schröcker. A family of conics and three special ruled surfaces. Beitr. Algebra Geom., 42(2):531-545, 2001. [ MR | ZBL | www ]
54. G. Glaeser and H.-P. Schröcker. Reflections on refractions. J. Geom. Graphics, 4(1):1-18, 2000. [ MR | ZBL | www ]
55. J. Lang and H.-P. Schröcker. Edge-orthogonal patches trough a given rational Bézier-curve. J. Geom. Graphics, 2(2):109-121, 1998. [ MR | ZBL | www ]

Book

1. G. Glaeser and H.-P. Schröcker. Handbook of Geometric Programming Using Open Geometry GL. Springer, New York, 2002. [ ZBL | www ]

Chapters or pages in books (reviewed)

1. D. Huczala, J. Siegele, D. A. Thimm, M. Pfurner, H.-P. Schröcker. Rational Linkages: From Poses to 3D-printed Prototypes. In J. Lenarčič, M. Husty, Advances in Robot Kinematics 2024, Springer, 2024. [ DOI | arXiv]
2. J. Lercher, D. F. Scharler, and H.-P. Schröcker. A remarkable 8R-mechanism. In W. Holderbaum and J. M. Selig, editors, 2nd IMA Conference on Mathematics of Robotics. IMA 2020., number 21 in Springer Proceedings in Advanced Robotics, pages 107-114. Springer, Cham, 2022. [ DOI | ZBL ]
3. H.-P. Schröcker, M. Pfurner, and J. Siegele. Space kinematics and projective differential geometry over the ring of dual numbers. In Liang-Yee Cheng, editor, ICGG 2020 - Proceedings of the 19th International Conference on Geometry and Graphics, chapter Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers, pages 15-24. Springer, 2021. An extended version of this article has been published, after additional reviewing, in J. Geom. Graph. [ DOI | MR | ZBL ]
4. M. Pfurner and H.-P. Schröcker. M. Husty: A short biography of his scientific life. In Tadeusz Uhl, editor, Advances in Mechanism and Machine Science, pages 409-417. Springer International Publishing, Cham, 2019. [ DOI ]
5. H.-P. Schröcker, M. Pfurner, and J. Schadlbauer. Constraint varieties in mechanism science. In Meera Sitharam, Audrey St. John, and Jessica Sidman, editors, Handbook of Geometric Constraint Systems Principles, Discrete Mathematics and Its Applications. Chapman and Hall/CRC, 2018. [ MR | ZBL ]
6. Tudor-Dan Rad and H.-P. Schröcker. Optimal synthesis of overconstrained 6R linkages by curve evolution. In Saïd Zeghloul, Lotfi Romdhane, and Med Amine Laribi, editors, Computational Kinematics. Springer, 2017. [ DOI | arXiv ]
7. G. Hegedüs, J. Schicho, and H.-P. Schröcker. Construction of overconstrained linkages by factorization of rational motions. In J. Lenarčič and M. Husty, editors, Latest Advances in Robot Kinematics, pages 213-220. Springer, 2012. [ DOI ]
8. G. Hegedüs, J. Schicho, and H.-P. Schröcker. Bond theory and closed 5R linkages. In J. Lenarčič and M. Husty, editors, Latest Advances in Robot Kinematics, pages 221-228. Springer, 2012. [ DOI ]
9. M. Husty and H.-P. Schröcker. Kinematics and algebraic geometry. In J. M. McCarthy, editor, 21st Century Kinematics. The 2012 NSF Workshop, pages 85-123. Springer, London, 2012.
10. M. Husty and H.-P. Schröcker. A proposal for a new definition of the degree of freedom of a mechanism. In Andrés Kecskeméthy, Veljko Potkonjak, and Andreas Müller, editors, Interdisciplinary Applications of Kinematics, pages 109-117. Springer, 2011. [ DOI ]
11. M. Husty and H.-P. Schröcker. Algebraic geometry and kinematics. In Ioannis Z. Emiris, Frank Sottile, and Thorsten Theobald, editors, Nonlinear Computational Geometry, volume 151 of The IMA Volumes in Mathematics and its Applications, chapter Algebraic Geometry and Kinematics, pages 85-107. Springer, 2010. [ DOI | MR | ZBL ]
12. H.-P. Schröcker. Contributions to four-positions theory with relative rotations. In D. L. Pisla, M. Ceccarelli, M. Husty, and Corves. B. J., editors, New Trends in Mechanism Science. Analysis and Design, volume 5 of Mechanism and Machine Science, pages 21-28. Springer, 2010. [ DOI | arXiv ]
13. H.-P. Schröcker, B. Jüttler, and M. Aigner. Evolving four-bars for optimal synthesis. In Marco Ceccarelli, editor, Proceedings of EUCOMES 08, pages 109-116. Springer, 2009. [ DOI | ZBL ]
14. H.-P. Schröcker and B. Jüttler. Motion interpolation with Bennett biarcs. In Andres Kecskeméthy and Andreas Müller, editors, Proceedings of Computational Kinematics (CK 2009), pages 101-108. Springer, 2009. [ DOI ]
15. [K. Brunnthaler, H.-P. Schröcker, and M. Husty. Synthesis of spherical four-bar mechanisms using spherical kinematic mapping. In J. Lenarčič and B. Roth, editors, Advances in Robot Kinematics, pages 377-384. Springer, 2006. [ DOI | ZBL ]

Conference Proceedings (reviewed)

1. Z. Li, H.-P. Schröcker, J. Siegele, and D. A. Thimm. Quadratic Spinor Polynomials with Infinitely Many Factorizations. In K. Takenouchi, editor, Proceedings of the the 21st International Conference on Geometry and Graphics, ICGG 2024. Lecture Notes on Data Engineering and Communications Technologies, vol 216. Springer, Cham. [DOI | arXiv]

2. M. Pfurner, H.-P. Schröcker, and M. Husty. Path planning in kinematic image space without the Study condition. In J. Lenarčič and Jean-Pierre Merlet, editors, Proceedings of Advances in Robot Kinematics, 2016. [ MR | www ]

3. Z. Li, Tudor-Dan Rad, J. Schicho, and H.-P. Schröcker. Factorization of rational motions: A survey with examples and applications. In Shuo-Hung Chang, editor, Proceedings of the 14th IFToMM World Congress, 2015. [ DOI | arXiv ]
4. Z. Li, J. Schicho, and H.-P. Schröcker. 7R Darboux linkages by factorization of motion polynomials. In Shuo-Hung Chang, editor, Proceedings of the 14th IFToMM World Congress, 2015. [ DOI | arXiv ]
5. Tudor-Dan Rad and H.-P. Schröcker. The kinematic image of 2R dyads and exact synthesis of 5R linkages. In Proceedings of the IMA Conference on Mathematics of Robotics , 2015. [ arXiv ]
6. M. Rabl, L. Gonzalez-Vega, B. Jüttler, and H.-P. Schröcker. Oriented bounding surfaces with at most six common normals. In A. Bicchi, editor, IEEE Conference on Robotics and Automation. Kobe, 5 2009. CD-Rom.
7. H.-P. Schröcker and M. Husty. Kinematic mapping based assembly mode evaluation of spherical four-bar mechanisms. In Jean-Pierre Merlet and Marc Dahan, editors, Proceedings of IFToMM 2007, Besançon, France, 2007.
8. H.-P. Schröcker and K. Suzuki. A comparison of solution strategies to applied geometric design problems by descriptive geometry and 3D-CAD. In Proceedings of the 8th China-Japan Joint Conference on Graphics Education, pages 20-25, Suzhou, 2007. Beijing Institute of Technology Press.
9. M. Husty, M. Pfurner, and H.-P. Schröcker. A new and efficient algorithm for the inverse kinematics of a general serial 6R. In Proceedings of ASME 2005 29th Mechanism and Robotics Conference, Long Beach, 2005.
10. K. Brunnthaler, H.-P. Schröcker, and M. Husty. A new method for the synthesis of Bennett mechanisms. In Proceedings of CK 2005, International Workshop on Computational Kinematics, Cassino, 2005.
11. H.-P. Schröcker, M. Husty, and J. M. McCarthy. Kinematic mapping based evaluation of assembly modes for planar four-bar synthesis. In Proceedings of ASME 2005 29th Mechanism and Robotics Conference, Long Beach, 2005.

Conference Proceedings (not reviewed)

1. D. F. Scharler and H.-P. Schröcker. New Trends in Analysis and Geometry, chapter Motion Factorization and Bond Theory in Hyperbolic Kinematics, pages 193-217. Cambridge Scholars Publishing, 2020.
2. Z. Li, J. Schicho, and H.-P. Schröcker. The geometry of quadratic quaternion polynomials in Euclidean and non-Euclidean planes. In Luigi Cocchiarella, editor, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics, pages 298-309, Cham, 2019. Springer International Publishing. [ ZBL | arXiv ]
3. H.-P. Schröcker. From A to B: New methods to interpolate two poses. In Hirotaka Suzuki, Naomi Ando, and Yasushi Yamaguchi, editors, Proceedings of the 11th Asian Forum on Graphic Science, Tokyo, 2017. Re-published after additional reviewing in J. Geom. Graph. [ arXiv ]
4. H.-P. Schröcker. Singular Frégier conics in non-Euclidean geometry. In Proceedings of the 17th International Conference on Geometry and Graphics, Beijing, 2016. Re-published after additional reviewing in J. Geom. Graph.
5. M. Pfurner, J. Schadlbauer, and H.-P. Schröcker. A recyclable Möbius strip. In H.-P. Schröcker and M. Husty, editors, Proceedings of the 16th International Conference on Geometry and Graphics, pages 1024-1030. Innsbruck University Press, 2014.
6. H.-P. Schröcker. The shapes of Walter Wunderlich. In Günther H. Filz, Rupert Maleczek, and Christian Scheiber, editors, FORM - RULE | RULE - FORM 2013, pages 109-117. innsbruck university press, 2014.
7. G. Hegedüs, J. Schicho, and H.-P. Schröcker. A non-unique factorization theorem and its engineering applications. In Anita Cerić and Stjepan Lukušić, editors, Proceedings of Future Trends in Civil Engineering, pages 123-140. University of Zagreb, Faculty of Civil Engineering, 2014.
8. H.-P. Schröcker. The axodes of rotation quadrilaterals. In Paul Zsombor-Murray, Aaron Sprecher, and Bruno Angeles, editors, Proceedings of the 15th International Conference on Geometry and Graphics, pages 675-681, Montréal, 2012.
9. J. Schadlbauer and H.-P. Schröcker. Orthogonality relations for tetrahedra in elliptic and hyperbolic spaces. In Paul Zsombor-Murray, Aaron Sprecher, and Bruno Angeles, editors, Proceedings of the 15th International Conference on Geometry and Graphics, pages 668-674, Montréal, 2012. Re-published after additional reviewing in J. Geom. Graph.
10. H.-P. Schröcker. Discrete gliding along principal curves. In Naomi Ando, Takashi Kanai, Jun Mitani, Aya Saito, and Yasushi Yamaguchi, editors, Proceedings of the 14th International Conference on Geometry and Graphics, pages 37-46, Kyoto, 2010. Re-published after additional reviewing in J. Geom. Graph. [ arXiv ]
11. H.-P. Schröcker. Double tangent circles and focal properties of sphero-conics. In Proceedings of the 13th International Conference on Geometry and Graphics (ICGG 2008), Dresden, Germany, 2008. Re-published after additional reviewing in J. Geom. Graph. [ ZBL ]
12. K. Suzuki and H.-P. Schröcker. Application of descriptive geometry procedures in solving spatial problems with feature and parametric modelling 3D-CAD. In Proceedings of the 13th International Conference on Geometry and Graphics (ICGG 2008), Dresden, Germany, 2008. [ ZBL ]
13. Ch. Niederegger and H.-P. Schröcker. Eine Möglichkeit der Kornbandoptimierung im Feinteilbereich - neue Separationstechniken. In Jürgen Feix and Andreas Andreatta, editors, Innsbrucker Bautage 2008, Innsbruck - Massivbau und Brückenbau, pages 65-74. Innsbruck University Press, 2008.
14. H.-P. Schröcker and K. Suzuki. A comparison of solution strategies to applied geometry problems between descriptive geometry and 3D-CAD. In Proceedings of the Annual Meeting of the Japan Society for Graphic Science, volume 40. Japan Society for Graphic Science, 12 2007. In Japanese.
15. H.-P. Schröcker. Geometrisches Freihandzeichnen an der Universität für Angewandte Kunst in Wien. In Proceedings Dresden Symposium Geometrie, pages 289-296. TU Dresden, 2003.
16. H.-P. Schröcker. Das Erzeugnis dreier projektiv gekoppelter Kegelschnitte. In H. Stachel and J. Wallner, editors, Proceedings 25. Süddt. Differentialgeometrie-Kolloquium, pages 79-94. TU Wien, 2001. [ MR | ZBL ]

Editorial Work

1. Miroslav Lávička, Maria Lucia Sampoli, and H.-P. Schröcker. New progress in geometry for applications (editorial). Comput. Aided Geom. Design, 2018. [ DOI | MR ]
2. H.-P. Schröcker and M. Husty, editors. Proceedings of the 16th International Conference on Geometry and Graphics. Innsbruck University Press, 2014. [ www ]
3. M. Husty and H.-P. Schröcker, editors. Proceedings of EuCoMeS, the First European Conference on Mechanism Science. Innsbruck University Press, 2006. [ www ]

Didactic Articles

1. H.-P. Schröcker. Selbstkorrigierende Aufgaben am Tetreader. Inf. Bl. Geom., 30(2):27-29, 2011.
2. H.-P. Schröcker and K. Suzuki. Ein Vergleich von Lösungsstrategien für eine anspruchsvolle Modellieraufgabe. Inf. Bl. Geom., 26(1):23-25, 2007.
3. H.-P. Schröcker. Geometry and CAD education at the University of Innsbruck. J. Graphic Science Japan, 40(4):17-26, 2006.
4. P. Taschwer and H.-P. Schröcker. Parametrische Erzeugung von Flächen in Rhinoceros am Beispiel von Schnecken und Muscheln. Inf. Bl. Geom., 24(2):39-42, 2005. [ PDF ]
5. H.-P. Schröcker and G. Glaeser. Geometrisches Freihandzeichnen - Anregungen, Gedanken, Beispiele. Inf. Bl. Geom., 23(1):16-20, 2004. [ PDF ]

Theses

1. H.-P. Schröcker. Die von drei projektiv gekoppelten Kegelschnitten erzeugte Ebenenmenge. PhD thesis, Technische Universität Graz, 2000.
2. H.-P. Schröcker. Die Konstruktion orthogonaler Fortsetzungen von Bézier-Kurven und -Flächen. Master's thesis, Technische Universität Graz, 1998.

Technical Reports

1. M. Rabl, L. Gonzalez-Vega, B. Jüttler, and H.-P. Schröcker. Oriented bounding surfaces with at most six common normals. Technical Report 77, FSP Industrial Geometry, 2009.
2. H.-P. Schröcker, B. Jüttler, and M. Aigner. Evolving four-bars for optimal synthesis. Technical Report 67, FSP Industrial Geometry, 2008.

Miscellaneous

1. G. Hegedüs, Z. Li, J. Schicho, and H.-P. Schröcker. From the fundamental theorem of algebra to Kempe's universality theorem. Internat. Math. Nachrichten, 229:13-26, 2015. [ ZBL | arXiv ]
2. H.-P. Schröcker. Elegante Bewegungsschule. Konstruktion für Elektronik und Maschinenbau, (12):20-21, 2011.
3. H.-P. Schröcker. The Bäcklund transform of principal contact element nets, 2010. [ arXiv ]

Invited or plenary talks

1. H.-P. Schröcker. Mechanisms from Motions – Rational and Algebraic. Topical Day: Mechanism Design and Computer Algebra, Institut Henri Poincaré, Paris, 10, 2023.
2. H.-P. Schröcker. Conformal Kinematics at Infinity. 23rd Scientific-Professional Colloquium on Geometry and Graphics, Vinkovci, 9/2023.
3. H.-P. Schröcker. Nested bases for rational PH-curves. 4th International Conference on Pure and Applied Mathematics, Van, 6/2022. Online.
4. H.-P. Schröcker. From the factorization of motions to the factorization of Darboux cyclides. 19th International Geometry Symposium, Edirne, 6/2022.
5. H.-P. Schröcker. Rational kinematics. 3rd International Conference on Pure and Applied Mathematics, Van, 9/2020. Online.
6. H.-P. Schröcker. Rational motions: Algebra and geometry inseparable. Czech-Slovak Conference on Geometry and Graphics, Pardubice, 9/2020.
7. H.-P. Schröcker. Bond theory and motion factorization in hyperbolic geometry. First International Conference of Mathematics and its Applications, Abha, 3/2018.
8. H.-P. Schröcker. Factorization of dual quaternion polynomials. State of the art and applications to computational kinematics and mechanism science. Second Conference on Subdivision, Geometric and Algebraic Methods, Isogeometric Analysis and Refinability in Italy, Gaeta, 9/2017.
9. H.-P. Schröcker. A non-unique factorization theorem and its engineering applications. Scientific Symposium Future Trends in Civil Engineering, Zagreb, 2/2014.
10. H.-P. Schröcker. Discrete gliding along principal curves. 14th International Conference on Geometry and Graphics, Kyoto, 8/2010.
11. H.-P. Schröcker. Der Spezialfall n=3 - Die Beziehung von Geometrie und Mathematik. Tag der Geometrie, Graz, 4/2009.
12. H.-P. Schröcker. Pairs of tetrahedra with orthogonal edges. 14th Scientific-Professional Colloquium on Geometry and Graphics, Velika, 9/2009.
13. H.-P. Schröcker. Uniqueness results for minimal enclosing quadrics. Conference on Geometry: Theory and Applications, Vorau, 6/2007.

Registered talks

1. H.-P. Schröcker, Quo Vadis DG? Visionen für einen modernen Geometrieunterricht. 43. Fortbildungstagung für Geometrie, Strobl, 11/2024.
2. H.-P. Schröcker, Quadratic Spinor Polynomials with Infinitely Many Factorizations. The 21st International Conference on Geometry and Graphics, Kitakyushu, 08/2024.
3. H.-P. Schröcker, Three Ways to Compute Rational Curves with Rational Arc Length. SIAM Conference on Computational Geometric Design, Genoa, 07/2023.
4. H.-P. Schröcker. A Linear Algebra Approach to Rational PH Curves. SMART 2022 – Third International Conference on Subdivision, Geometric and Algebraic Methods, Isogeometric Analysis and Refinability in Italy, Rimini, 09/2022.
5. H.-P. Schröcker. Die COVID-19 Pandemie und der universitäre Geometrieunterricht. 41. Fortbildungstagung für Geometrie, Strobl, 05/2022.
6. H.-P. Schröcker. Space kinematics and projective differential geometry over the ring of dual numbers. 19th International Conference on Geometry and Graphics, Online, 1/2021.
7. H.-P. Schröcker. A remarkable 8R-mechanism. 2nd IMA Conference on Mathematics of Robotics, Online, 9/2021.
8. H.-P. Schröcker. Geometry of split quaternion factorization. 21st Scientific-Professional Colloquium on Geometry and Graphics, Sisak, 9/2019.
9. H.-P. Schröcker. The geometry of quadratic quaternion polynomials in Euclidean and non-Euclidean planes. 18th International Conference on Geometry and Graphics, Milano, 8/2018.
10. H.-P. Schröcker. Uniqueness of minimal motions. Conference on Geometry: Theory and Applications, Plzeň, 6/2017.
11. H.-P. Schröcker. Algebraic geometry and mechanism science. Recent results and open problems. SIAM Conference on Applied Algebraic Geometry, Atlanta, 8/2017.
12. H.-P. Schröcker. From A to B. New methods to interpolate two poses. 11th Asian Forum on Graphic Science, Tokyo, 8/2017.
13. H.-P. Schröcker. Singular Frégier conics in non-Euclidean geometry. 17th International Conference on Geometry and Graphics, Beijing, 8/2016.
14. H.-P. Schröcker. Rational ruled surfaces as trajectories of minimal degree rational motions. 19th Scientific-Professional Colloquium on Geometry and Graphics, Starigrad-Paklenica, 9/2016.
15. H.-P. Schröcker. The rational motion of minimal dual quaternion degree with prescribed trajectory. Conference on Geometry: Theory and Applications, Kefermarkt, 6/2015.
16. H.-P. Schröcker. The kinematic image of 2R dyads and exact synthesis of 5R linkages. IMA Conference on Mathematics of Robotics, Oxford, 9/2015.
17. H.-P. Schröcker. Factorization of rational motions: A survey with examples and applications. The 14th IFToMM World Congress, Taipei, 10/2015.
18. H.-P. Schröcker. Four-pose synthesis of 5R- and 6R-linkages with rational coupler motion. Conference on Geometry: Theory and Applications, Ljubljana, 6/2013.
19. H.-P. Schröcker. Spatial linkages with a straight line trajectory. 18th ÖMG Congress and Annual DMV Meeting, Innsbruck, 9/2013.
20. H.-P. Schröcker. The axodes of rotation quadrilaterals. 15th International Conference on Geometry and Graphics, Montréal, 8/2012.
21. H.-P. Schröcker. Selbstkorrigierende Aufgaben am Tetraeder. 33. Fortbildungstagung für Geometrie, Strobl, 11/2012.
22. H.-P. Schröcker. Discrete Laplace cycles of period four. Conference on Geometry: Theory and Applications, Vorau, 6/2011.
23. H.-P. Schröcker. Remarks on the local geometry of a discrete Bäcklund configuration. 15th Scientific-Professional Colloquium on Geometry and Graphics, Tuheljske Toplice, 9/2011.
24. H.-P. Schröcker. A kinematic approach to Bäcklund transforms of pseudospherical principal contact element nets. 2nd Croatian Conference on Geometry and Graphics, Šibenik, 9/2010.
25. H.-P. Schröcker. Contributions to four-positions theory with relative rotations. 3rd European Conference on Mechanism Science, Cluj-Napoca, 9/2010.
26. H.-P. Schröcker and Bert Jüttler. Motion interpolation with Bennett biarcs. Computational Kinematics 2009, Duisburg, 5/2009.
27. H.-P. Schröcker. The simplest truly spatial motion. Conference on Geometry: Theory and Applications, Plzeň, 6/2009.
28. H.-P. Schröcker. A line-based discretization of curvature lines. 17. ÖMG-Kongress - Jahrestagung der DMV, Graz, 9/2009.
29. Ch. Niederegger and H.-P. Schröcker. Eine Möglichkeit der Kornbandoptimierung im Feinteilbereich - neue Separationstechniken. Innsbrucker Bautage 2008, 1/2008.
30. H.-P. Schröcker. Double tangent circles and focal properties of sphero-conics. 13th International Conference on Geometry and Graphics, Dresden, 8/2008.
31. H.-P. Schröcker. Evolving four-bars for optimal synthesis. 2nd European Conference on Mechanism Science, Cassino, 9/2008.
32. H.-P. Schröcker. 100 Tage Japan - “Graphic Science” an einer Eliteuniversität. 29. Fortbildungstagung für Geometrie, Strobl, 11/2008.
33. H.-P. Schröcker. Kinematic mapping based assembly mode evaluation for spherical four-bar mechanisms. IFToMM 2007, The 12th World Congress in Mechanism and Machine Science, Besançon, (France), 6/2007.
34. H.-P. Schröcker. Geometrische Konstruktionen mit diskretisierten Zufallsvariablen. 16. Internationalen Kongress der Österreichischen Mathematischen Gesellschaft, Klagenfurt, 9/2005.
35. H.-P. Schröcker. Curvatures and tolerances in the Euclidean motion group. Mathematical Methods for Curves and Surfaces, Tromsø, 6/2004.
36. H.-P. Schröcker. Toleranzanalyse für Graphen geometrischer Relationen. Geometrie-Tagung, Vorau, 6/2004.
37. H.-P. Schröcker. Geometrisches Freihandzeichnen an der Angewandten. Dresden Symposium Geometrie, 2/2003.
38. H.-P. Schröcker. Das Erzeugnis dreier projektiv gekoppelter Kegelschnitte. 25. Süddt. Differentialgeometrie-Kolloquium, Wien, 6/2002.

Guest lectures

1. H.-P. Schröcker. Factorization of Polynomials Over Clifford Algebras, Charles University, 4/2024.
2. H.-P. Schröcker. Mechanisms from Motions: The First Decade of Motion Factorization, Universität Graz, 5/2023.

3. H.-P. Schröcker. Devil in paradise II: Recent results in motion factorization. Colloquium at the Occasion of Hellmuth Stachel's 80th Birthday, 11/2022. Vienna University of Technology. [ PDF ]

4. H.-P. Schröcker. Curves, surfaces, and motions. Geometrisches Kolloquium, Technical University Graz, 8/2021.

5. H.-P. Schröcker. Neue Resultate zu Rationalen Bewegungsvorgängen. Geometry Colloquium at the Occasion of Otto Röschel's 60th Birthday, Graz University of Technology, 7/2014.
6. H.-P. Schröcker. Geometry and CAD education at Innsbruck University. CSGG subject meeting, Zagreb, 2/2012.
7. H.-P. Schröcker. New results in algebraic kinematics: Mechanism science, algebra, and discrete mathematics. Université Laval, Départment de génie mécanique, 7/2012.
8. H.-P. Schröcker. New results in algebraic kinematics: Mechanism science, algebra, and discrete mathematics. McGill University, Mechanical Engineering - Robotic Mechanical Systems and Mathematics Seminar, 7/2012.
9. H.-P. Schröcker. Bianchis Vertauschungssatz für pseudosphärische Hauptberührelementnetze. Fakultät für Mathematik und Naturwissenschaften, Technische Universität Dresden, 5/2011. [ PDF]
10. H.-P. Schröcker. Devil in paradise or how to factor a rational motion. Special Colloquium Celebrating the Retirement of Hellmuth Stachel, Vienna University of Technology, 11/2011. [ PDF]
11. H.-P. Schröcker. Diskret drehende Bewegungsvorgänge. Dresdner Mathematisches Seminar, Fakultät für Mathematik und Naturwissenschaften, Technische Universität Dresden, 4/2010. [ PDF]
12. H.-P. Schröcker. Das Kontrollnetz von Zyklidenstücken. Institut für Geometrie, Technische Universität Dresden, 6/2009. [ PDF]
13. H.-P. Schröcker. Contributions to four-positions theory with relative rotations. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, 11/2009. [ PDF]
14. H.-P. Schröcker. Double tangent circles and focal properties of sphero-conics. Institute of Applied Geometry, University Linz, 11/2007.
15. H.-P. Schröcker. Graphics science education at Innsbruck University - geometry and CAD. Graphic Science Educational Board Meeting of the Japanese Society for Graphic Science (JSGS), Tokyo, 9/2006.
16. H.-P. Schröcker. Open Geometry - a geometric programming system. Graphic Science Educational Board Meeting of the Japanese Society for Graphic Science (JSGS), Tokyo, 8/2000.

Workshop talks

1. H.-P. Schröcker. Basics of Differential Geometry for Robotics II – Quaternions as a Riemannian Manifold. Part of the workshop “Riemann and Gauss meet Asimov – A Tutorial on Geometric Methods in Robot Learning, Optimization and Control”, IROS 2022 (online).
2. H.-P. Schröcker. A plea for non-Euclidean geometry in mechanism science. Applied Algebraic Geometry, 7/2019. Loughborough University. [ PDF]
3. H.-P. Schröcker. Kempe's universality theorem for rational space curves. ICMS Workshop: Geometric Rigidity Theory and Applications, Edinburgh, May/June 2016. [ PDF]
4. H.-P. Schröcker. The shapes of Walter Wunderlich. Form-Rule [13], Innsbruck, 1/2013.
5. H.-P. Schröcker. New results in algebraic kinematics. Workshop on Rigidity Theory: Progress, Applications and Key Open Problems, Banff, 7/2012.
6. H.-P. Schröcker. Optimal evolution based synthesis of planar four-bar mechanisms. 5th FSP Workshop Industrial Geometry, Strobl, 3/2008.
7. H.-P. Schröcker. Kinematics and algebraic geometry. Workshop on Computational Methods for Algebraic Spline Surfaces, Strobl, 9/2007. [ PDF]

Teacher Eduation Seminars or Workshops

1. H.-P. Schröcker. Solving spatial problems using Rhinoceros. CSGG subject meeting, Zagreb, 2/2012.
2. H.-P. Schröcker. Selbstkorrigierende Aufgaben am Tetraeder. 33. Fortbildungstagung für Geometrie, Strobl, 11/2012.
3. H.-P. Schröcker. Geometrisches Freihandzeichnen. Seminar der Pädagogischen Hochschule Tirol, Tramin, 3/2010.
4. H.-P. Schröcker. Geometrisches Freihandzeichnen. Seminar der Pädagogischen Hochschule Oberösterreich, Linz, 4/2009.
5. H.-P. Schröcker. Geometrieunterricht mit Hilfe des Computers - Auf der Suche nach den guten Beispielen. Fortbildungsseminar der Arbeitsgemeinschaft DG/GZ Steiermark, St. Peter im Sulmtal, 4/2008.
6. H.-P. Schröcker. Geometrisches Freihandzeichnen. Seminar des Pädagogischen Instituts Tirol, Lienz, 3/2006.
7. H.-P. Schröcker. Geometrisch-technisches Freihandzeichnen. Seminar des Pädagogischen Instituts des Bundes für Niederösterreich, Mödling, 5/2005.
8. H.-P. Schröcker. Geometrisches Freihandzeichnen. Seminar des Pädagogischen Instituts des Bundes für Wien, 4/2004.
9. H.-P. Schröcker. Geometrisches Freihandzeichnen. Workshop, 24. Fortbildungstagung für Geometrie, Strobl, 11/2003.

Miscellaneous

1. H.-P. Schröcker. Die Geometrie der Bewegung eines Roboters. PI-DAY, Freie Universität Bozen, 3/2019.
2. H.-P. Schröcker. Elliptische Kugeln und hyperbolische Bierdeckel. Eine Einführung in die nichteuklidische Geometrie. uni.com - Wissen für alle, Volkshochschule Innsbruck, 5/2013.

Research Areas

• Computational Kinematics
• Clifford Algebras
• Mechanism Science
• Computer-Aided Geometric Design
• Non-Euclidean Geometry
• Robotics
• Convex Geometry
• Didactics of Geometry and CAD

Recent Funded Projects

Collision-Free Design of Rational Single-Loop Linkages
Horizon Europe – MSCA Postdoctoral Fellowship
Project Leader (Host)
Duration: 2023–2025
Amount: 183 600.96 €

Rotor Polynomials: Algebra and Geometry of Conformal Motions
FWF Austrian Science Fund
Principal Investigator (100%)
Duration: 2021–2024
Amount: 123 511.50 €

The Algebra of Motions in 3-Space
FWF Austrian Science Fund
Co-Applicant (30%)
Duration: 2018–2021
Amount: 368 985.75 €

Algebraic Methods in Kinematics: Motion Factorization and Bond Theory
FWF Austrian Science Fund
Co-Applicant (33%)
Duration: 2014–2017
Amount: 335 358.45 €

Algebraic Methods in Collision Detection and Path Planning
FWF Austrian Science Fund
Principal Investigator (100%)
Duration: 2011–2014
Amount: 191 037,00 €

ExQuad – Uniqueness Results for Extremal Quadrics
FWF Austrian Science Fund
Principal Investigator (100%)
Duration: 2008–2011
Amount: 99 760,50 €

Doctoral theses

Supervised theses

Matthias Weber: Uniqueness Results for Extremal Quadrics, University of Innsbruck, 2012.

Tudor-Dan Rad: Factorization of Motion Polynomials and its Application in Mechanism Science, University of Innsbruck, 2018.

Daniel Scharler: Factorization of Polynomials over Quaternion Algebras and Applications to Kinematics, 2022.

Johanna Frischauf: Factorizations of Bivariate Quaternionic Polynomials and Applications in Kinematics, 2023.

Second or external reviewer

Brian Moore: Dynamic Balancing of Linkages by Algebraic Methods, PhD Thesis, Johannes Kepler University Linz, 2009.

Ali Alkhaldi: The Parabola in Universal Hyperbolic Geometry, PhD Thesis, University of New South Wales, 2014.

Rupert W. Maleczek: Linear Folded Stripes, PhD Thesis, University of Innsbruck, 2014.

Zijia Li: Closed Linkages with Six Revolute Joints, PhD Thesis, Johannes Kepler University Linz, 2016.

Arvin Rasoulzadeh: Design and Path Optimization of LInear Pentapods Based on the Geometry of Their Singularity Varieties, Technische Universität Wien, 2020

Mirja Rotzoll: Algebraic Input-output Equations of Four-bar Kinematic Chains: Planar; Spherical; Spatial, Carleton University, 2023.