本文由五個計算曲率的方法：1.座標轉換法(Coordinate Transformation Method )、2. 直角移動法(Orthogonal Walking Method)、3. 交叉路徑法(The Cross Patch Method)、4.三角形近似法(Surface Triangulation Method)、5. 烏龜移動法(Turtle Walking Method)之優缺點來找出比較適合的方法，進而改善之並做為本文計算曲率之方法的理論基礎。
在本文中提出了三個方法去計算一曲面的曲率。方法一和三都是由座標轉換法去改良而成的。而方法二主要是藉由旋轉和移動去找到適合的橢圓，使我們所要計算曲率的曲面能貼在橢圓表面上，再藉由橢圓找到其曲面的曲率。而方法一和方法二雖然都遇到了需要去克服的困難處，但是在方法三終於可以簡單的把橢圓球的曲率計算出來，而且和正確值幾乎一樣。雖然我們用來印證的橢圓球是軸對稱的，但是相信只要是給定適當的曲面，就算不是軸對稱的曲面，方法三一樣可以將曲率計算出來。
經由本文的研究，不僅對於三維曲面的曲率有了進一步的了解，而且不用侷限於軸對稱的條件下，如此一來便可以應用在三維氣泡曲率的計算，進而研究在三維時曲率之變化對流場的影響。甚至可以利用曲率將曲面的形狀找到。

參考文獻
[1] Takemura, F., Takagi, S., Magnaudet, J., et al., “Drag and lift forces on a bubble rising near a vertical wall in a viscous liquid,” J. Fluid Mech., 461, pp. 277-300, 2002.
[2] Zun, I., “The transverse migration of bubbles influenced by wall in vertical bubbly flow,” Int. J. Multiphase Flow., Vol. 6, pp. 583-588, 1980.
[3] Wu, M., Gharib, M., “Experimental studies on the shape and path of small air bubbles rising in clean water,” Physics of Fluids, 14, pp. L49-L52, 2002.
[4] 張元榕, “微小氣泡於小口徑垂直方管內浮升之研究”, 國立清華大學動機系碩士論文, 2005.
[5] Ernest M. S. and, Shang Y. W., “Surface Parameter and Curvature Measurement of Arbitrary 3-D Objects: Five Practical Methods”,IEEE Transactions on Pattern Analysis and Machine intelligence 14(8),833-839, 1992.
[6] Sander P. T. and Zucker S. W., “Tracing surfaces for surfacing traces,” in Proc. 1st Int. Conf. Comput. Vision (London), June 8-11, pp. 231-240, 1987.
[7] Foley J. D. and Dam A.V., Fundamentals of Interactive Computer Graphics, Reading, MA: Addison-Wesley, 1984.
[8] Hsiung C. C., A First Course in Differential Geometry. New York: Wiley, 1981.

[9] Paul J. Besl and Ramesh C. Jain, “Invariant surface characteristics for 3-D object recognition in range images,” Comput. Vision Graphics Image Processing, vol.33, pp. 33-80, 1986.
[10] Mortenson M. E., Geometric Modeling. New York: Wiley, 1985.
[11] Rosenfeld A. and Kak A., Digital Picture Processing, vol. 2. London: Academic Press, 1982.
[12] Lin C. and Perry M. J., “Shape description using surface triangulation,” in Proc. IEEE Workshop Comput. Vision: Repres. Contr. (Rindge, NH), pp. 38-43, Aug. 1982.
[13] Moise E. E., Geometric Topology in Dimension 2and 3. New York: Springer-Verlag, 1977.
[14] Abelson H. and diSessa A. A., Turtle Geometry. Cambridge, MA:MIT Press, 1986.