C1 Surface Interpolation Using Quartic Rational Triangular Patches

Nur Nabilah Che Draman; Samsul Ariffin Abdul Karim; Ishak Hashim

doi:10.1007/978-981-15-8606-4_6

C¹ Surface Interpolation Using Quartic Rational Triangular Patches

Nur Nabilah Che Draman
, Samsul Ariffin Abdul Karim
, Ishak Hashim

Universiti Teknologi Petronas
Universiti Kebangsaan Malaysia

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

A version of quartic rational triangular patches is used to C¹ construct a surface comprising two composite triangles. Like previous scheme such as cubic Ball and cubic Bézier, they have no free parameter that can be adjusted for surface interpolant. Thus, our proposed method has three free shape parameters, α, β, and γ. This study shows the comparison of the three methods—quartic rational, cubic Ball and cubic Bézier triangular patches. To validate the performances, the error measurement used are root mean square errors (RMSE), maximum error and Central Processing Unit (CPU) times. Besides that, we also made a comparison between C¹ and G¹ continuity. Based on the results, the proposed scheme is better than the three previous schemes in terms of a smaller value of RMSE, and maximum error. Meanwhile, G¹ continuity gives less computation rather than C¹.

Original language	English
Title of host publication	Studies in Systems, Decision and Control
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	89-99
Number of pages	11
DOIs	https://doi.org/10.1007/978-981-15-8606-4_6
State	Published - 2021
Externally published	Yes

Publication series

Name	Studies in Systems, Decision and Control
Volume	320
ISSN (Print)	2198-4182
ISSN (Electronic)	2198-4190

Keywords

C continuity
Computation
Error
G continuity
Rational quartic triangular patches

Access to Document

10.1007/978-981-15-8606-4_6

Cite this

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title = "C1 Surface Interpolation Using Quartic Rational Triangular Patches",

abstract = "A version of quartic rational triangular patches is used to C1 construct a surface comprising two composite triangles. Like previous scheme such as cubic Ball and cubic B{\'e}zier, they have no free parameter that can be adjusted for surface interpolant. Thus, our proposed method has three free shape parameters, α, β, and γ. This study shows the comparison of the three methods—quartic rational, cubic Ball and cubic B{\'e}zier triangular patches. To validate the performances, the error measurement used are root mean square errors (RMSE), maximum error and Central Processing Unit (CPU) times. Besides that, we also made a comparison between C1 and G1 continuity. Based on the results, the proposed scheme is better than the three previous schemes in terms of a smaller value of RMSE, and maximum error. Meanwhile, G1 continuity gives less computation rather than C1.",

keywords = "C continuity, Computation, Error, G continuity, Rational quartic triangular patches",

author = "Draman, \{Nur Nabilah Che\} and Karim, \{Samsul Ariffin Abdul\} and Ishak Hashim",

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C¹ Surface Interpolation Using Quartic Rational Triangular Patches. / Draman, Nur Nabilah Che; Karim, Samsul Ariffin Abdul; Hashim, Ishak.
Studies in Systems, Decision and Control. Springer Science and Business Media Deutschland GmbH, 2021. p. 89-99 (Studies in Systems, Decision and Control; Vol. 320).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - C1 Surface Interpolation Using Quartic Rational Triangular Patches

AU - Draman, Nur Nabilah Che

AU - Karim, Samsul Ariffin Abdul

AU - Hashim, Ishak

PY - 2021

Y1 - 2021

N2 - A version of quartic rational triangular patches is used to C1 construct a surface comprising two composite triangles. Like previous scheme such as cubic Ball and cubic Bézier, they have no free parameter that can be adjusted for surface interpolant. Thus, our proposed method has three free shape parameters, α, β, and γ. This study shows the comparison of the three methods—quartic rational, cubic Ball and cubic Bézier triangular patches. To validate the performances, the error measurement used are root mean square errors (RMSE), maximum error and Central Processing Unit (CPU) times. Besides that, we also made a comparison between C1 and G1 continuity. Based on the results, the proposed scheme is better than the three previous schemes in terms of a smaller value of RMSE, and maximum error. Meanwhile, G1 continuity gives less computation rather than C1.

AB - A version of quartic rational triangular patches is used to C1 construct a surface comprising two composite triangles. Like previous scheme such as cubic Ball and cubic Bézier, they have no free parameter that can be adjusted for surface interpolant. Thus, our proposed method has three free shape parameters, α, β, and γ. This study shows the comparison of the three methods—quartic rational, cubic Ball and cubic Bézier triangular patches. To validate the performances, the error measurement used are root mean square errors (RMSE), maximum error and Central Processing Unit (CPU) times. Besides that, we also made a comparison between C1 and G1 continuity. Based on the results, the proposed scheme is better than the three previous schemes in terms of a smaller value of RMSE, and maximum error. Meanwhile, G1 continuity gives less computation rather than C1.

KW - C continuity

KW - Computation

KW - Error

KW - G continuity

KW - Rational quartic triangular patches

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