我們提出一個可以建造多個網格模型間一致性規則四角化網格的方法，提出這個方法的原因有三點：第一點，普遍得到的網格模型都不是規則分部的，在幾何的處理上，規則網格比不規則網格容易處理，因此如何以規則網格表示不規則網格在電腦圖學的應用上是很有幫助的一個題目；第二點，在電腦圖學的應用上，大部分的網格都是以三角形構成，所以大多的研究也是建立在以三角形為基礎的處理上，但是某些應用中四角形網格較能有較良好的效果，例如流體力學或是貼圖的應用上等等；第三點，在現今的研究中，有越來越多的研究不只是專注在處理單一網格模型，而是希望在多個網格模型間找到更有趣的應用，但是多個網格模型間的應用絕大部分需要仰賴一致性的網格模型。有鑒於以上三種需要，我們設計一個方法，可以在多個非genus 0的網格模型間找出對應的四角化參數空間，用以建造一致性網格。

We propose a novel approach to build consistent regular and quadrilateral meshes among many input mesh models. The major contributions of this thesis are described as follows. First, the general mesh models are always not regular. However, it is well-known that the regular meshes are much easier to manipulate than the irregular meshes. So, the conversion from an irregular mesh to a regular mesh is very useful in today digital geometry processing. Second, most of mesh models are comprised of triangles in computer graphics. In contrast, the quadrilateral mesh models can facilitate many important applications such as PDEs, fluid dynamic, texturing and etc. Finally, many people are concentrated on manipulating multi-models, so a common consistent mesh model is required. In this thesis, we design a novel method to create consistent quadrangulation among input irregular meshes. In particular, this novel cross-surface quadrangulation method is not limited by the genus of input models.

[1]. ALEXA, M.
Merging Polyhedral Shapes with Scattered Features.
The Visual Computer 16, 26-37. 2000.
[2]. ALEXA, M.
Recent Advances in Mesh Morphing.
Computer Graphics Forum, 21, 2, 173-196. 2002.
[3]. ASPERT, N., SANTA-CRUZ, D., and EBRAHIMI, T.
MESH: Measuring Errors between Surfaces using the Hausdorff Distance.
In IEEE Multimedia, 705--708. 2002.
[4]. ALLIEZ, P., UCELLI, G., GOTSMAN, C., AND ATTENE, M.
Recent advances in remeshing of surfaces.
2005.
[5]. BERN, M. W., AND EPPSTEIN, D.
Mesh generation and optimal triangulation.
In Computing in Euclidean Geometry, Lecture Notes on Computing #4. World Scientific, 47–123. 1995.
[6]. CHRISTINASEN, H. N., SEDERBERG, T. W.
Conversion of complex contour line definitions into polygonal element mosaics.
ACM SIGGRAPH Computer Graphics, v.12 n.3, p.187-192, August 1978.
[7]. Dong, S., KIRCHER, S., Garland, M.
Harmonic functions for quadrilateral remeshing of arbitrary manifolds.
Computer Aided Geometric Design, v.22 n.5, p.392-423, July 2005.
[8]. Dong S., Bremer P.-T., Garland M., PASCUCCI, V., Hart J. C.
Spectral surface quadrangulation.
ACM SIGGRAPH ’06, July 2006.
[9]. ECK, M., DEROSE, T. D., DUCHAMP, T., HOPPE, H., LOUNSBERY, M., AND STUETZLE, W.
Multiresolution analysis of arbitrary meshes.
ACM SIGGRAPH, 173–182. 1995.
[10]. EVERITT, C.
Interactive order-independent transparency.
Tech. rep., NVIDIA Corporation. 2001.
[11]. FOLEY J. D., VAN DAM A., FEINER S. K., HUGHES J. F., PHILLIPS, R.
Introduction to Computer Graphics.
Addison-Wesley, 1993.
[12]. FLOATER, M. S.
Mean value coordinates.
Computer Aided Geometric Design 20, 1 (Mar.), 19–27. 2003.
[13]. FLOATER, M. S., AND HORMANN, K.
Surface parameterization: A tutorial and survey.
In Multiresolution in Geometric Modeling. 2004.
[14]. GARLAND, M.
Multiresolution modeling: Survey & future opportunities.
In State of the Art Report, Eurographics, 111–131. 1999.
[15]. GUSKOV, I., VIDIMCE, K., SWELDENS, W., AND SCHR¨O DER, P.
Normal meshes.
ACM SIGGRAPH, 95–102. 2000.
[16]. GU, X., GORTLER, S. J., AND HOPPE, H.
Geometry Images.
ACM Transactions on Graphics. v.21, n.3, 355–361. 2002.
[17]. GOTSMAN, C., GU, X., AND SHEFFER, A.
Fundamentals of spherical parameterization for 3D meshes.
ACM Transactions on Graphics, 22, 3, 358-363. 2003.
[18]. KHODAKOVSKY, A., LITKE, N., AND SCHR¨ODER, P.
Globally smooth parameterizations with low distortion.
TOG 22, 3, 350–357. (ACM SIGGRAPH). 2003.
[19]. KRAEVOY, V., SHEFFER, A.
Cross-parameterization and compatible remeshing of 3D models.
ACM Transactions on Graphics. v.23 n.3, 2004.
[20]. LEE, A. W. F., SWELDENS, W., SCHR¨ODER, P., COWSAR, L., AND DOBKIN, D.
MAPS: Multiresolution adaptive parameterization of surfaces.
ACM SIGGRAPH, 95–104. 1998.
[21]. MEYERS, D., Skinner, S. and SLOANK.
Surfaces from contours: the correspondence and branching problems.
Graphics Inter. face '91, 246-254. 1991.
[22]. PRAUN, E., HOPPE, H.
Spherical parameterization and remeshing.
ACM Transactions on Graphics 22, 3, 340-349. 2003.
[23]. REQUICHA, A. A. G.
Representations for rigid solids: theory, methods and systems.
Computing Surveys 12, 4, 437–464. 1980.
[24]. SANDER, P., Snyder, J., GORTLER, S., Hoppe, H.
Texture mapping progressive meshes.
ACM SIGGRAPH ’01, pp. 409–416. ACM Press, New York, 2001.
[25]. SANDER, P. V., WOOD, Z. J., GORTLER, S. J., SNYDER, J., AND HOPPE, H.
Multi-chart geometry images.
Eurographics Symposium on Geometry Processing, 146–155. 2003.
[26]. SCHREINER, J., ASIRVATHAM, A., PRAUN, E., Hoppe, H.
Inter-surface mapping.
ACM Transactions on Graphics. v.23 n.3, 2004.
[27]. SORKINE, O., AND COHEN-OR, D.
Least-squares meshes.
Shape Modeling International, 191–199. 2004.
[28]. TARINI, M., HORMANN, K., CIGNONI, P., MONTANI, C.
PolyCube-Maps.
ACM Transactions on Graphics (TOG), v.23 n.3, 2004.
[29]. YOON, S.H., KIM, M.S.
Sweep-based Freeform Deformations.
ACM SIGGRAPH ’06. 2006.