AI SearchInterpolation methods in curve and surface modelling
Xu, Jiang
Interpolation methods in curve and surface modelling - Bangkok : Asian Institute of Technology, 1991 - 112 p. - Thesis ; no. CS-91-15 . - Asian Institute of Technology. Thesis ; no. CS-91-15 .
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineeerin and Technology
Thesis (M.Eng.) - Asian Institute of Technology, 1991
Two independent C2 cubic interpolatary spline modelling methods have been investigated in this study. They are piecewise Bezier form and B-spline form methods which are both suitable for generating plane and space C2 interpolation curves. A theoretical analysis of geometric continuity and Frenet Frame continuity of the C2 space piecewise cubic Bezier interpolation curve has been carried out. A necessary and sufficient condition for a C2 curve to be G3 was also proposed and proved here. Meanwhile two programs, for 2D and 3D curves interpolating respectively, were developed using the above modelling methods, and each method was considered to support open and closed curves. General B-spline Hermite interpolation curves' methods have also been investigated. An implementation of the method in case of 2D C1 cubic curves has been done for numerical experiments. The work also dealts with surface interpotation methods, and a program for C1 composite bicubic Bezier interpolation surface modelling was developed based on the theory presented.
Curves, Cubic
Computer-aided design
Interpolation methods in curve and surface modelling - Bangkok : Asian Institute of Technology, 1991 - 112 p. - Thesis ; no. CS-91-15 . - Asian Institute of Technology. Thesis ; no. CS-91-15 .
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineeerin and Technology
Thesis (M.Eng.) - Asian Institute of Technology, 1991
Two independent C2 cubic interpolatary spline modelling methods have been investigated in this study. They are piecewise Bezier form and B-spline form methods which are both suitable for generating plane and space C2 interpolation curves. A theoretical analysis of geometric continuity and Frenet Frame continuity of the C2 space piecewise cubic Bezier interpolation curve has been carried out. A necessary and sufficient condition for a C2 curve to be G3 was also proposed and proved here. Meanwhile two programs, for 2D and 3D curves interpolating respectively, were developed using the above modelling methods, and each method was considered to support open and closed curves. General B-spline Hermite interpolation curves' methods have also been investigated. An implementation of the method in case of 2D C1 cubic curves has been done for numerical experiments. The work also dealts with surface interpotation methods, and a program for C1 composite bicubic Bezier interpolation surface modelling was developed based on the theory presented.
Curves, Cubic
Computer-aided design