03242nam a2200409 4500 20260817171317.0 280898 th eng .b1011113x AIT Thesis no.CS-89-11 Chuang, Chen-chang Beta-spline curves : properties and computations Bangkok : Asian Institute of Technology, 1989 77, [56] p. + 1 online resource A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering Thesis (M.Eng.) - Asian Institute of Technology, 1989 The Beta-spline developed by Barsky is to combine uniform cubic B-splines with geometric continuity using the unit tangent vector and curvature vector. Two shape parameters called bias and tension respectively were introduced to take care of the geometric continuity constraints. The effects of these two parameters on the shape of the curve have been studied. Uniformly-shaped Ý-spline has fixed shape parameters which affect the curve over the whole length. For a more 2local3 sense, continuous-shaped Ý-spline is formed by introducing quintic interpolating polynomial between the distinct Ý values at each knot. Some 2kinks3 is created in case of wildly varying adjacent Ý values. This is not a desired situation in Computer Aided Geometric Modeling. Later, Goodman gave a general definition of Ý -splines. The basic properties of convex hull and variation diminishing have been shown. An explicit formula for cubic Ý-splines has been given. Starting from this definition and the explicit formula, a B- Ý spline concept was suggested for computational efficiency thanks to its recurrence relation. The computation scheme and implementation were also given. Analogous to Ý-splines, discrete Ý-splines with the technique of subdivision and the knots insertion on the Ý-spline curves have been studied, based on the above general definition of B-spline. A computation scheme of the above two methods was discussed. Computer-aided design Huynh, Ngoc Phien, Chairperson Bohez, Erik L.J., Examination Committee Phan, Minh Dung, Examination Committee Goverment of R.O.C., Scholarship donor Asian Institute of Technology. Thesis ; no. CS-89-11 Full-Text http://203.159.5.9/ait-thesis/detail.php?q=B17645 .b1011113x mnait x 240411 2 951012 m a x 0 mnait mnarc mnait 22 40 20 Barcode : 30050120677397 CREATED : 2014-02-18 RECORD # : i12766021 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 Barcode : 30050120373369 CREATED : 2016-08-06 RECORD # : i13023809 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 Barcode : 30050121008311 CREATED : 2021-08-02 RECORD # : i13322540 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 11712 11712 0 0 0 0 MAIN MAIN mnait 2026-08-17 50.00 0 AIT Thesis no.CS-89-11 30050120677397 2026-08-17 17:13:17 3 2026-08-17 22 0 0 0 0 MAIN MAIN mnarc 2026-08-17 0 AIT Thesis no.CS-89-11 30050120373369 2026-08-17 17:13:17 2026-08-17 40 0 0 0 0 MAIN MAIN mnait 2026-08-17 0 AIT Thesis no.CS-89-11 30050121008311 2026-08-17 17:13:18 1 2026-08-17 20