02063nas|a2200253 i 450000500170000000800410001703500150005810000300007324500670010326000520017030000110022249000270023350001360026050200570039652010190045365000260147265000230149870000360152170000480155770000440160571000360164981000590168585600650174420260818175909.0020510s2001    th  uzm rtt  00|  a1eng d  a.b118536941 aAmirthalingam, Sathasivam10aRelationships between Bernstein, Chebyshev and Legendre models  aBangkok :bAsian Institute of Technology,c2001  a113 p.1 aThesis ;vno. IM-01-12  aA thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, School of Advanced Technoologies  aThesis (M.Sc.) - Asian Institute of Technology, 2001  aThis 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.   0aComputer-aided design 0aCurves on surfaces1 aHuynh, Ngoc Phien,eChairperson1 aBatanov, Dentcho N.,eExamination Committee1 aTien, Hoang Le, eExamination committee2 aWorld Bank, eScholarship donor2 aAsian Institute of Technology.tThesis ;vno. IM-01-12  3Full-Textuhttp://203.159.5.9/ait-thesis/detail.php?q=B08574