臺灣博碩士論文加值系統

找出Enneper'sminamal surface 的control point,以此建立局部曲面並貼出一些有用的曲面,另外整理了一些二維標準圖形的bezier patch 的畫法

In this paper, we collect construction of standard surfaces and attempt to design surfaces by patches constructed from Enneper’s minimal surface.

1. Introduction -------------------------------------------------------1
2. Computer Aided Geometry Design
2.1 Rational Bezier Representation -------------------------------- 1
2.2 Tensor Patch -------------------------------------------------- 3
2.3 Triangular Patch .--------------------------------------------- 3

3. Construct Standard Curves and Patches
3.1 Ellipse , Parabola , Hyperbola -------------------------------- 4
3.2 Torus .-------------------------------------------------------- 7
3.3 Sphere -------------------------------------------------------- 9
3.4 Set of Methods to Draw the Ellipse, Hyperbola and Parabola------- 10

4. Minimal Surface
4.1 Construction of Control Points of Enneper’s Minimal Surface--- 13
4.2 Classification Each Kind of Tensor Patches
of Enneper’s Minimal Surface. --------------------------------------- 16
4.3 Surfaces Design by Minimal Patches------------------------------- 18

5. Reference---------------------------------------------------------- 24

[1] Eugene T.Y. Lee, The Rational Bezier Representation for Conics,
Boeing Document, Boeing, Seattle, Wash., 1983.
[2] Piegl L., The Sphere as a Retional Bezier Surface, 1986 CAGD 3 45-52.
[3] Farin G., The Octant of a Sphere as Nondegenerate Triangular Bezier Patch,
1987 CAGD 4 329-332.
[4] Ang Swee Wen, Siti Mariyam Hj. Shamsuddin, Yahya Samian:
Ship Hull Fitting Using NURBS. 2005 CGIV: 431-436.