02923nas|a2200433 i 4500 20260818175909.0 020510s2001 th uzm rtt 00| a1eng d .b11853694 AIT Thesis no.IM-01-12 Amirthalingam, Sathasivam Relationships between Bernstein, Chebyshev and Legendre models Bangkok : Asian Institute of Technology, 2001 113 p. Thesis ; no. IM-01-12 A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, School of Advanced Technoologies Thesis (M.Sc.) - Asian Institute of Technology, 2001 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. Computer-aided design Curves on surfaces Huynh, Ngoc Phien, Chairperson Batanov, Dentcho N., Examination Committee Tien, Hoang Le, Examination committee World Bank, Scholarship donor Asian Institute of Technology. Thesis ; no. IM-01-12 Full-Text http://203.159.5.9/ait-thesis/detail.php?q=B08574 .b11853694 mnait u 240329 0 020510 m a u 0 mnait mnait mnarc 20 22 40 Barcode : 30050120701619 CREATED : 2013-01-10 RECORD # : i12743264 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 Barcode : 30050120701601 CREATED : 2014-03-21 RECORD # : i12777936 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 Barcode : 30050160073606 CREATED : 2016-04-26 RECORD # : i12953258 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 99092 99092 0 0 0 0 MAIN MAIN mnait 2026-08-18 50.00 0 AIT Thesis no.IM-01-12 30050120701619 2026-08-18 17:59:09 3 2026-08-18 20 0 0 0 0 MAIN MAIN mnait 2026-08-18 50.00 0 AIT Thesis no.IM-01-12 30050120701601 2026-08-18 17:59:09 4 2026-08-18 22 0 0 0 0 MAIN MAIN mnarc 2026-08-18 0 AIT Thesis no.IM-01-12 30050160073606 2026-08-18 17:59:10 1 2026-08-18 40