TY  - SER
AU  - Amirthalingam,Sathasivam
AU  - Huynh,Ngoc Phien
AU  - Batanov,Dentcho N.
AU  - Tien,Hoang Le
ED  - World Bank, 
TI  - Relationships between Bernstein, Chebyshev and Legendre models
T2  - Thesis
PY  - 2001///
CY  - Bangkok
PB  - Asian Institute of Technology
KW  - Computer-aided design
KW  - Curves on surfaces
N1  - 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
N2  - 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.
UR  - http://203.159.5.9/ait-thesis/detail.php?q=B08574
ER  -