04348nam a2200433 4500 20260818115018.0 280898 th eng .b10303339 AIT Thesis no. CS-91-4 Setiabudi, Djoni Haryadi Generation of circular and elliptical arcs Bangkok : Asian Institute of Technology, 1991 138 p. Thesis ; no. CS-91-4 A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering School of Engineering and Technology Thesis (M.Eng.) - Asian Institute of Technology, 1991 Ten important algorithms of circle generation and six algorithms of ellipse generation were analyzed both analytically and experimentally in this study. The methods considered were: Bresenham, Kappel, Double-step, DDA (Digital Differential Analyzer), Difference and NURBS (Nonuniform Rational B-Spline). The main criteria used in comparing the algorithms concerned were the speed and accuracy. The implementation of drawing arcs on the screen was based on the eight-way symmetry concept for circle and four-way symmetry for ellipse. Furthermore, the problem in accuracy of intersection between a circle and a straight line and between two circles was also considered using a unified representation. There are two formulations of the intersection between a straight line and a circle. The first formulation uses an initial point of the line outside the circle, the second formulation uses the midpoint of the line between the intersection points as the initial point. For circle-circle intersection, there are three formulations. The first formulation uses the radical axis intersecting with one of the two circles. The second formulation uses the radical axis intersecting with the orthogonal circle obtained by adding the weighting equations of the two circles. The third formulation uses the radical axis intersecting with the orthogonal circle obtained by adding the equations of the two circles. From the study, the following conclusions can be made : 1. The datatype used for the methods is the main role of the speed performance. The Kappel algorithm for generating ellipse can be improved significantly by changing the datatype from real to integer. 2. The time spent for generating the points of the arcs is much shorter than the time for displaying the pixels on the screen. 3. NURBS methods give the best visual looking appearance. 4. Incremental methods have the highest speed performance among all of the three categories, incremental, parametric and approximation. 5. For the rounding error the Bresenham method gives the least errors, but for the real error the NURBS gives the least errors. 6. From the two formulations of the intersection between a straight line and a circle, the first formulation requires less numerical calculations. 7. From the three formulations of the intersection between two circles, the first and the third formulations give higher accuracy and the second formulation is more efficient. Computer graphics Computer-aided design Huynh, Ngoc Phien, Chairperson Bohez, Erik L.J., Examination Committee Zhao, Ming, Examination committee Petra Christian University Surabaya, Indonesia, Scholarship donor Asian Institute of Technology. Thesis ; no. CS-91-4 Full-Text http://203.159.5.9/ait-thesis/detail.php?q=B17326 .b10303339 mnait x 240402 2 951012 m a x 0 mnait mnait mnarc 22 40 20 Barcode : 30050120677181 CREATED : 1995-10-14 RECORD # : i10375454 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 Barcode : 30050120372957 CREATED : 2016-08-06 RECORD # : i13025867 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 Barcode : 30050121000623 CREATED : 2021-03-03 RECORD # : i13330202 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 49382 49382 0 0 0 0 MAIN MAIN mnait 2026-08-18 0 AIT Thesis no. CS-91-4 30050120677181 2026-08-18 11:50:18 3 2026-08-18 22 0 0 0 0 MAIN MAIN mnarc 2026-08-18 0 AIT Thesis no. CS-91-4 30050120372957 2026-08-18 11:50:18 2026-08-18 40 0 0 0 0 MAIN MAIN mnait 2026-08-18 0 AIT Thesis no. CS-91-4 30050121000623 2026-08-18 11:50:18 1 2026-08-18 20