NDLI: Geometric Hermite Interpolation for Planar Pythagorean-hodograph Cubics

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Geometric Hermite Interpolation for Planar Pythagorean-hodograph Cubics

Content Provider	Semantic Scholar
Author	Lee, Hyun Chol Lee, Sunhong
Copyright Year	2013
Abstract	Abstract. We solve the geometric Hermite interpolation problem withplanar Pythagorean-hodograph cubics. For every Hermite data, we de-termine the exact number of the geometric Hermite interpolants and rep-resent the interpolants explicitly. We also present a simple criterion fordetermining whether the interpolants have a loop or not. 1. IntroductionIn computer-aided geometric design, curves are usually represented by poly-nomial/rational parameterizations. But the derived objects, such as their o setcurves, are not generally represented by rational parameterizations. To over-come this barrier, Farouki and Sakkalis (1990, 1994) introduced Pythagorean-hodograph (PH) curves, which are a special class of polynomial curves withpolynomials as their speed functions. PH curves have many computationallyattractive features, so that we can compute their arc lengths and bending en-ergies and o set curves in an exact manner. For successively abundant resultsobtained by many researchers, see Farouki (2008) and references therein.Hermite interpolation by PH curves are one of the main subjects in the soci-ety of these research. (For more details see for example Farouki and Ne , 1995;Albrecht and Farouki, 1996; Juttler and Maurer, 1999; Juttler, 2001; Faroukiet al., 2002; Pelosi et al., 2005; �S��r et al., 2010.) In this paper, we presentthe G
Starting Page	53
Ending Page	68
Page Count	16
File Format	PDF HTM / HTML
Volume Number	29
Alternate Webpage(s)	http://ocean.kisti.re.kr/downfile/volume/bgms/E1BGBB/2013/v29n1/E1BGBB_2013_v29n1_53.pdf
Alternate Webpage(s)	https://doi.org/10.7858/eamj.2013.005
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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