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Relationships between BERNSTEIN, CHEBYSHEV and LEGENDRE models

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dc.contributor.advisor Prof. Huynh Ngoc Phien (Chairman) en_US
dc.contributor.advisor Dr.D.N. Batanov (Member) en_US
dc.contributor.advisor Dr. Hoang Le Tien (Member) en_US
dc.contributor.author Sathasivam Amirthalingam en_US
dc.date.accessioned 2015-01-12T10:44:38Z
dc.date.available 2015-01-12T10:44:38Z
dc.date.issued 2001 en_US
dc.identifier.other AIT Thesis no.IM0112 en_US
dc.identifier.uri http://www.cs.ait.ac.th/xmlui/handle/123456789/526
dc.description 127 p. en_US
dc.description.abstract This study was carried out with the main objective of establishing the relationships between Bezier, Chebyshev and Legendre curves. These relationships are obtained using the polar form approach with mathematical derivations. They can serve as convenient ways to convert a curve in a given form into the other two remaining forms. It was found that - the control points of a curve given in one of the forms Bezier, Chebyshev and Legendre, can be expressed as affine combinations of the control points of in each of the remaining forms for the rational case. This result is not true for non-rational curves. - the control points of a Chebyshev or Legendre curve do not provide any hint about the shape of the curve defined by them. This is completely different from the case of Bezier curves. In view of these results, it seems that when a curve is given in the Chebyshev’s or Legendre’s form, it should be converted into the Bezier form so that its shape can be roughly figured out before any drawing is carried out. en_US
dc.description.sponsorship World Bank en_US
dc.language.iso en en_US
dc.publisher Asian Institute of Technology en_US
dc.relation.ispartofseries AIT Publications; en_US
dc.subject bernstein en_US
dc.subject Chebyshev en_US
dc.subject Legendre en_US
dc.title Relationships between BERNSTEIN, CHEBYSHEV and LEGENDRE models en_US
dc.type Thesis en_US


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