Approximation of Dupin cyclide patches by ringed surfaces and its application towards curvature-adapted 5-axis CNC machining

Alena Lindauerová; Michal Bizzarri; Pengbo Bo; Rimvydas Krasauskas; Michael Bartoň

doi:10.1016/j.cagd.2026.102559

Approximation of Dupin cyclide patches by ringed surfaces and its application towards curvature-adapted 5-axis CNC machining

Alena Lindauerová
, Michal Bizzarri^*
, Pengbo Bo
, Rimvydas Krasauskas
, Michael Bartoň

^*Corresponding author for this work

University of West Bohemia
School of Computer Science and Technology (School of Software), Harbin Institute of Technology Weihai
Faculty of Mathematics and Informatics
Basque Center for Applied Mathematics
Ikerbasque Basque Foundation for Science

Research output: Contribution to journal › Article › peer-review

Abstract

We propose an algorithm for approximating a Dupin cyclide patch using a union of motions of circular (flat-end) and/or toroidal cutters. The method employs an adapted curvature-matched tilt function designed to achieve both high approximation accuracy and gouging-free contact between the cutter and the target cyclide. We derive closed-form formulas for second-order line contact along arbitrary tangent directions on a cyclide and introduce an automatic tool-selection procedure that identifies the largest possible cutter admitting gouging-free motion over the entire patch. The algorithm is validated on individual Dupin cyclide patches as well as on free-form Dupin cyclide spline surfaces.

Original language	English
Article number	102559
Journal	Computer Aided Geometric Design
Volume	127
DOIs	https://doi.org/10.1016/j.cagd.2026.102559
State	Published - Jun 2026
Externally published	Yes

Keywords

5-axis CNC machining
Curvature matching
Dupin cyclide
Free-form surface
Gouging-free position
Higher-order contact
Toroidal milling tool

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10.1016/j.cagd.2026.102559

Cite this

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title = "Approximation of Dupin cyclide patches by ringed surfaces and its application towards curvature-adapted 5-axis CNC machining",

abstract = "We propose an algorithm for approximating a Dupin cyclide patch using a union of motions of circular (flat-end) and/or toroidal cutters. The method employs an adapted curvature-matched tilt function designed to achieve both high approximation accuracy and gouging-free contact between the cutter and the target cyclide. We derive closed-form formulas for second-order line contact along arbitrary tangent directions on a cyclide and introduce an automatic tool-selection procedure that identifies the largest possible cutter admitting gouging-free motion over the entire patch. The algorithm is validated on individual Dupin cyclide patches as well as on free-form Dupin cyclide spline surfaces.",

keywords = "5-axis CNC machining, Curvature matching, Dupin cyclide, Free-form surface, Gouging-free position, Higher-order contact, Toroidal milling tool",

author = "Alena Lindauerov{\'a} and Michal Bizzarri and Pengbo Bo and Rimvydas Krasauskas and Michael Barto{\v n}",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.",

year = "2026",

month = jun,

doi = "10.1016/j.cagd.2026.102559",

language = "英语",

volume = "127",

journal = "Computer Aided Geometric Design",

issn = "0167-8396",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Approximation of Dupin cyclide patches by ringed surfaces and its application towards curvature-adapted 5-axis CNC machining

AU - Lindauerová, Alena

AU - Bizzarri, Michal

AU - Bo, Pengbo

AU - Krasauskas, Rimvydas

AU - Bartoň, Michael

PY - 2026/6

Y1 - 2026/6

N2 - We propose an algorithm for approximating a Dupin cyclide patch using a union of motions of circular (flat-end) and/or toroidal cutters. The method employs an adapted curvature-matched tilt function designed to achieve both high approximation accuracy and gouging-free contact between the cutter and the target cyclide. We derive closed-form formulas for second-order line contact along arbitrary tangent directions on a cyclide and introduce an automatic tool-selection procedure that identifies the largest possible cutter admitting gouging-free motion over the entire patch. The algorithm is validated on individual Dupin cyclide patches as well as on free-form Dupin cyclide spline surfaces.

AB - We propose an algorithm for approximating a Dupin cyclide patch using a union of motions of circular (flat-end) and/or toroidal cutters. The method employs an adapted curvature-matched tilt function designed to achieve both high approximation accuracy and gouging-free contact between the cutter and the target cyclide. We derive closed-form formulas for second-order line contact along arbitrary tangent directions on a cyclide and introduce an automatic tool-selection procedure that identifies the largest possible cutter admitting gouging-free motion over the entire patch. The algorithm is validated on individual Dupin cyclide patches as well as on free-form Dupin cyclide spline surfaces.

KW - 5-axis CNC machining

KW - Curvature matching

KW - Dupin cyclide

KW - Free-form surface

KW - Gouging-free position

KW - Higher-order contact

KW - Toroidal milling tool

UR - https://www.scopus.com/pages/publications/105036808638

U2 - 10.1016/j.cagd.2026.102559

DO - 10.1016/j.cagd.2026.102559

M3 - 文章

AN - SCOPUS:105036808638

SN - 0167-8396

VL - 127

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

M1 - 102559

ER -

Approximation of Dupin cyclide patches by ringed surfaces and its application towards curvature-adapted 5-axis CNC machining

Abstract

Keywords

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