多重解析度模塑技術已經廣泛的應用在地形展示、飛行模擬、科學視覺化、及電腦遊戲上。目前在繪製一個3D埸景時，大部分的應用程式都使用了很多的三角形來構成複雜的3D埸景，因而使得繪圖效能受到埸景中三角形數目的影響而下降。多重解析度模塑技術是一種在繪製複雜3D埸景時可以維持繪圖效能的技術。然而這個技術在低解析度的情形下並無法完整保存3D埸景的模型的形狀及其外觀屬性。
在這篇論文中，我們修改了一個以二次式誤差 (Quadric error metrics)為準則的多重解析度模塑技術加入了模型的外觀屬性，如顏色、法向量、及貼圖座標資訊，使得簡化後的模型有著高品質的多重解析度模形外，還能保持和原始模型相似的外觀。
視點相關展示技術是一種可以更進一步改善多重解析度模形展示效能的方法。在我們的研究中，我們也加入了視點相關展示技術，根據視點參數，使多重解析度模形能夠在相同展示效能下，展示更精細的模型或在相同展示品質的模型下，提供更好的展示效能。

Multiresolution modeling techniques have been applied in terrain visualization, military simulation, flight simulation, and other simulations for many years. The number of triangles of models influences the 3D rendering performance significantly and most applications generally use a large amount of triangles to render the simulation environment. Using the multiresolution technique is one way to archive the real-time rendering for the large-scale environment; however, most multiresolution techniques did not consider the appearance of the environment, then the shapes of the models and environment are degraded during lower-resolution rendering.
In this paper, we presented a multiresolution modeling algorithm using quadric error metrics and provide the error metrics with the appearance attributes of a model such as color, normal and texture coordinates to rapidly obtain multiresolution models with high qualities.
The view-dependent technique is one way to further improve the rendering performance of multiresolution models. In this study, we also provide the view-dependent technique for automatically deciding the proper resolution and model structure based on the view parameters to archive a real-time visualization.

[1] Bajaj, C. L, V. Pascucci, and G. Zhuang, “Progressive compression and transmission of arbitrary triangular meshes,” in Proc. Visualization’99, San Francisco, CA, Oct.24-29, 1999, pp.307-316.
[2] Cignoni, P., C. Mantani, C. Rocchini, and R. Scopigno, “A general method for preserving attribute values on simplified meshes,” in Proc. Visualization‘98, Research Triangle Park, NC, Oct.18-23, 1998, pp.59-66.
[3] Cohen, J., A. Varshney, D. Manocha, G. turk, H. Weber, P. Agawal, F. Brooks, and W. Wright, “Simplification envelops,” in Proc. SIGGRAPG’96, New Orleans, LA, Aug.4-9, 1996, pp.119-128.
[4] Cohen, J., M. Olano, and D. Manocha, “Appearance-preserving simplification,” in Proc. SIGGRAPH‘98, Orlando, FL, Jul.19-24, 1998, pp.115-122.
[5] Cohen-Or, D., D. Levin, and O. Remez, “Progressive compression of arbitrary triangular meshes,” in Proc. Visualization’99, San Francisco, CA, Oct.24-29, 1999, pp.67-72.
[6] Desbrun M., M. Meyer, P. Schroder, and A. H. Barr, “Implicit fairing of irregular meshes using diffusion and curvature flow,” in Proc. SIGGRAPH’99, Los Angeles, CA, Aug.8-13, 1999, pp.317-324.
[7] Eck, M., T. DeRose, T. Duchamp, H. Hoppe, T. Lounsbery, and W. Stuetzle. “Multiresolution analysis of arbitrary meshes,” in Proc. SIGGRAPH’95, Los Angeles, CA, Aug.6-11, 1995, pp.173-182.
[8] El-Sana, J., E. Azanli, and A. Varshney, “Skip strips: maintaining triangle strips for view-dependent rendering,” in Proc. Visualization’99, San Francisco, CA, Oct.24-29, 1999, pp.131-518.
[9] Evans, F., S. Skiena, and A. Varshney, “Optimizing triangle strips for fast rendering,” in Proc. Visualization’96, San Francisco, CA, Oct.27-Nov.1, 1996, pp.319-326.
[10] Finkelstein, A. and D. H. Salesin, “Multiresolution curves,” in Proc. SIGGRAPH ’94, Orlando, Florida, Jul. 24-29, 1994, pp.261-268.
[11] Forsey, D. R. and R. H. Bartels, “Hierarchical B-spline refinement,” Computer Graphics, vol.22, no.4, pp.205-212, 1988.
[12] Garland, M. and P. S. Heckbert, Fast Polygonal Approximation of Terrains and Height Fields, Technical Report CMU-CS-95-181, School of Computer Science, Carnegie Mellon Univ., Sep. 1995.
[13] Garland, M. and P. S. Heckbert, “Surface simplification using quadric error metrics,” in Proc. SIGGRAPH''97, Los Angeles, CA, Aug.3-8, 1997, pp.209-216.
[14] Garland, M. and P. S. Heckbert, “Simplifying surfaces with color and texture using quadric error metrics,” in Proc. IEEE Visualization‘98, Research Triangle Park, NC, Oct.18-23, 1998, pp.263-269.
[15] Garland, M., Quadric-Based Polygonal Surface Simplification, Ph.D. Thesis, School of Computer Science, Carnegie Mellon Univ., Pittsburgh, PA, May 1999.
[16] Heckbert, P. S. and M. Garland, Survey of Polygonal Surface Simplification Algorithms, Tutorial Course, SIGGRAPH’97, Los Angeles, CA, Aug.3-8, 1997.
[17] Heckbert, P. S. and M. Garland, “Optimal triangulation and quadric-based surface simplification,” Journal of Computational Geometry: Theory and Applications, vol.14, no.1-3, pp.49-65, 1999.
[18] Hong, B.-S., Interactive Multiresolution Editing on Arbitrary Triangulated Models, Master’s thesis, Inst. of Computer Science and Information Engineering, National Central Univ., Chung-li, Taiwan, 2001.
[19] Hoppe, H., T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Mesh optimization,” in Proc. SIGGRAPH’93, Anaheim, CA, Aug.1-6, 1993, pp.19-26.
[20] Hoppe, H., “Progressive meshes,” in Proc. SIGGRAPH‘96, New Orleans, LA, Aug.4-9, 1996, pp.99-108.
[21] Hoppe, H., “View-dependent refinement of progressive meshes,” in Proc. SIGGRAPH’97, Los Angeles, CA, Aug.3-8, 1997, pp.189-198.
[22] Hoppe, H., Efficient Implementation of Progressive Meshes, Tech. Report of Microsoft Research, MSR-TR-98-02, Microsoft Corporation, Jan. 1998.
[23] Hoppe, H., “Smooth view-dependent level-of-detail control and its application to terrain rendering,” in Proc. IEEE Visualization ‘98, Research Triangle Park, NC, Oct.18-23, 1998, pp.35-42.
[24] Hoppe, H. “New quadric metric for simplifying meshes with appearance attributes,” in Proc. IEEE Visualization‘99, San Francisco, LA, Oct.24-29, 1999, pp.59-66.
[25] Hoppe, H. and S. Marschner, Efficient Minimization of New Quadric Metric for Simplifying Meshes with Appearance Attributes, Tech. Report of Microsoft Research, MSR-TR-2000-64, Microsoft Corporation, June 2000.
[26] Huang, C.-C., View-dependent Progressive-mesh Terrain Browsing with Dynamic Loading, Master’s thesis, Inst. of Computer Science and Information Engineering, National Central Univ., Chung-li, Taiwan, 1999.
[27] Huang, W.-K., A Tactical Simulation System with Dynamic-loading Multiresolution Terrain Modeling, Master’s thesis, Inst. of Computer Science and Information Engineering, National Central Univ., Chung-li, Taiwan, 2001.
[28] Isenburg, M., S. Gumhold, and C. Gotsman, “Connectivity shapes,” in Proc. Visualization 2001. San Diego, CA, Oct.21-26, 2001, pp.135-142.
[29] Kahler, K., C. Rossl, R. Schneider, J. Vorsatz, and H.-P. Seidel, “Efficient processing of large 3D meshes,” in Proc. Shape Modeling and Applications 2001, Genova, Italy, May.7-11, 2001, pp.228-237.
[30] Krus, M., P. Bourdot, F. Guisnel, and G. Thibault, “Levels of detail and polygonal simplification,” ACM Crossroads, vol.3.4, summer 1997.
[31] Lee, A. W. F., W. Sweldens, P. Schroder, L. Cowsar, and D. Dobkin, “MAPS: Multiresolution adaptive parameterization of surfaces,” in Proc. SIGGRAPH‘98, Orlando, FL, Jul.19-24, 1998, pp.95-104.
[32] Lee, A., H. Moreton, and H. Hoppe, “Displaced subdivision surface,” in Proc. SIGGRAPH 2000, New Orleans, LA, Jul.23-28, 2000, pp.85-94.
[33] Lindstrom, P., D. Koller, W. Ribarsky, L. F. Hodges, N. Faust, and G. A. Turner, “Real-time, continues level of detail rendering of height fields,” in Proc. SIGGRAPH’96, New Orleans, LA, Aug.4-9, 1996, pp.109-118.
[34] Lindstrom, P. and G. Turk, “Fast and memory efficient polygonal simplification,” in Proc. IEEE Visualization’98, Research Triangle Park, NC, Oct.18-23, 1998, pp.279-286.
[35] Lindstrom, P. and G. Turk, “Evaluation of memoryless simplification,” IEEE Trans. on Visualization and Computer Graphics, vol.5, no.2, pp.98-115, 1999.
[36] Lindstrom, P., “Out-of-core simplification of large polygonal models,” in Proc. SIGGRAPH 2000, New Orleans, LA, July 23-28, 2000, pp.259-262.
[37] Liu, S.-C., View-dependent Multiresolution Modeling with Appearance Attributes Using Quadric Error Metrics, Master’s thesis, Inst. of Computer Science and Information Engineering, National Central Univ., Chung-li, Taiwan, 2001.
[38] Pajarola, R. and J. Rossignac “Compressed progressive meshes,” IEEE Trans. Visualization and Computer Graphics, vol.6, no.1, pp.79-93, 2000.
[39] Pajarola, R., “FastMesh: Efficient view-dependent meshing,” in Proc. Computer Graphics and Applications, 2001, Tokyo, Japan, Oct.16-18, 2001, pp.22-30.
[40] Sander, P. V., J. Snyder, S. J. Gortler, and H. Hoppe, “Texture mapping progressive meshes,” in Proc. SIGGRAPH 2001, Los Angeles, CA, Aug.12-17, 2001, pp.409-416.
[41] Shaffer, E. and M. Garland, “Efficient adaptive simplification of massive meshes,” in Proc. Visualization 2001, San Diego, CA, Oct.21-26, 2001, pp.127-134.
[42] Xia, J. C. and A. Varshney, “Dynamic view-dependent simplification for polygonal models,” in Proc. Visualization’96, San Francisco, CA, Oct.27-Nov.1, 1996, pp.327-334.
[43] Xia, J. C., J. El-Sana, and A. Varshney, “Adaptive real-time level-of-detail-based rendering for polygonal models,” IEEE Trans. on Visualization and Computer Graphics, vol.3, no.2, pp.171-183, 1997.
[44] Yang, T.-S., Dynamic-loading Multiresolution Terrain Modeling in A Flight Simulation System, Master’s thesis, Inst. of Computer Science and Information Engineering, National Central Univ., Chung-li, Taiwan, 2000.