计算机图形学算法可视化教学研究与实现
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摘要
可视化是理解复杂现象和大规模数据的重要工具,在自然科学领域得到了广泛应用。自1986年可视化概念提出以来,可视化技术的研究已经取得了可喜的进展。目前,可视化教学已经引起教育界的关注。国外,许多研究者已经肯定了可视化在教学方面的作用和地位;国内,研究者也开始了在可视化教学方面的研究。
本文在研究国内外关于可视化理论的基础上,深入探讨了当前引入可视化教学的意义,针对目前计算机图形学教学内容,确定了可视化教学内容及目标,开展了计算机图形学算法可视化教学的研究和实践。利用可视化编程工具VB 6.0对基本图元的生成、多边形填充、直线段裁剪、曲线生成及分形算法进行可视化设计与实现。同时给出了实现过程中发现的问题及解决方法。通过分析,认为采用可视化教学法,对于改变教师的教授方式,帮助学生理解计算机图形学算法有着积极的作用和影响。在教学过程中,学生通过观察、猜想、验证,提高了领悟、探索、发现和创造能力。
此外,本文在可视化实现椭圆生成算法时,查阅相关文献资料,对已有的椭圆生成算法进行深入研究后,提出了一种双点生成椭圆弧的算法。与同类算法相比,该算法判别式构造简单,具有递推性,且只有整数加减和移位运算。比较结果表明,该算法比现有其他算法具有更快的执行速度。文中算法便于硬件实现。
Visualization is an important tool to understand complicated phenomenons and the large-scale data. Since the concept was brought up in 1986, the research on visualization technology has already got gratifying progress. At present, visualization instruction has been attracted the eyes of researchers in education. At abroad, a lot of researchers have agreed with the role and position of visualization instruction. And at home, the researchers have also begun to study visualization instruction.
Based on the study on the theory of visualization, this paper deeply discusses the significance of visualization instruction. Concerning with the content of computer graphics curriculum, the paper establishes the content and target for visualization instruction and carries out the research and realization on algorithm visualization instruction for computer graphics. This paper carries out visualization design and realization with VB6.0 for computer graphics algorithm. It includes generation of line, circle and curve, polygon filling, line clip and fractals. At the same time the paper gives the problems and solutions that in the process of realization. By analysis, the paper believes that adopting the method of visualization instruction will make great help to change the teaching way and help students understand the algorithm. It also arouse students’learning interests, strengthen students’learning motivation, improve the ability of comprehension, exploration, discovery and creativity.
Besides, This paper presented a double-step ellipse drawing algorithm. Compared with other analogous algorithms, the discriminators of algorithm obey a simple recurrence formula which may be evaluated by only integer arithmetic and binary shifts. The comparision result shows that its speed is higher than the existing ellipse drawing algrithms. The algorithm is easy to be realized by hardware.
本文在研究国内外关于可视化理论的基础上,深入探讨了当前引入可视化教学的意义,针对目前计算机图形学教学内容,确定了可视化教学内容及目标,开展了计算机图形学算法可视化教学的研究和实践。利用可视化编程工具VB 6.0对基本图元的生成、多边形填充、直线段裁剪、曲线生成及分形算法进行可视化设计与实现。同时给出了实现过程中发现的问题及解决方法。通过分析,认为采用可视化教学法,对于改变教师的教授方式,帮助学生理解计算机图形学算法有着积极的作用和影响。在教学过程中,学生通过观察、猜想、验证,提高了领悟、探索、发现和创造能力。
此外,本文在可视化实现椭圆生成算法时,查阅相关文献资料,对已有的椭圆生成算法进行深入研究后,提出了一种双点生成椭圆弧的算法。与同类算法相比,该算法判别式构造简单,具有递推性,且只有整数加减和移位运算。比较结果表明,该算法比现有其他算法具有更快的执行速度。文中算法便于硬件实现。
Visualization is an important tool to understand complicated phenomenons and the large-scale data. Since the concept was brought up in 1986, the research on visualization technology has already got gratifying progress. At present, visualization instruction has been attracted the eyes of researchers in education. At abroad, a lot of researchers have agreed with the role and position of visualization instruction. And at home, the researchers have also begun to study visualization instruction.
Based on the study on the theory of visualization, this paper deeply discusses the significance of visualization instruction. Concerning with the content of computer graphics curriculum, the paper establishes the content and target for visualization instruction and carries out the research and realization on algorithm visualization instruction for computer graphics. This paper carries out visualization design and realization with VB6.0 for computer graphics algorithm. It includes generation of line, circle and curve, polygon filling, line clip and fractals. At the same time the paper gives the problems and solutions that in the process of realization. By analysis, the paper believes that adopting the method of visualization instruction will make great help to change the teaching way and help students understand the algorithm. It also arouse students’learning interests, strengthen students’learning motivation, improve the ability of comprehension, exploration, discovery and creativity.
Besides, This paper presented a double-step ellipse drawing algorithm. Compared with other analogous algorithms, the discriminators of algorithm obey a simple recurrence formula which may be evaluated by only integer arithmetic and binary shifts. The comparision result shows that its speed is higher than the existing ellipse drawing algrithms. The algorithm is easy to be realized by hardware.
引文
[1] Gitta domik. Visualization Viewpoints: Do We NeedFormal Education in Visualization? IEEE Computer Graphics and Applications. 2000(July/August)
[2] Brain John Foley.Visualization Tools: Models, Representations and Knowledge Integration. Dissertation for Doctor Degree,University of California,Berkeley 1999
[3] J.T.Stasko. Tango: A framework and system for algorithm animation. IEEE Computer, 23(9) :27~39, November 1990
[4] Tao Chen, Tarek Sobh. A Tool for Data Structure Visualization and User-Defined Algorithm Animation. 31th ASEE/IEEE Frontiers in Education Conference,2001(TID)
[5] Hermann Hartel, Michael Ludke: 3D Simulations of Interacting Particles. Computing in Science&Engineering,2000(July/August)
[6] Byrne, M.D. , Catrambone, R. and Stasko, J.T. . Do Algorithm Animations Aid Learning? Technical Report GIT-GVU-96-18, Georgia Tech Graphics, Visualization, and Usability Center,1996.
[7] McCormick, B.H. , DeFantim T.A. and Brown, M.D. : Visualization in scientific. computing:Definition,domain,andrecommendations , Computer Graphics 1987,21:3~13
[8] 李晓梅,黄朝晖,等. 科学计算可视化导论. 北京:国防科技大学出版社,1996
[9] 张恩成. 计算机多媒体教学实况评析. 电化教育研究,1999 (5) :52~55
[10] 谢维,沈大林. 关于多媒体 CAI 课件设计的分析与思考. 教育科学研究,2002, (5) :40~42
[11] Tomasz Müldner and Elhadi Shakshuki. A New Approach to Learning Algorithms. Proceedings of the International Conferencd on Information Technology: Coding and Computing(ITCC‘04)IEEE
[12] 张庆林. 当代认知心理学在教学中的应用. 西南师范大学出版社,1996.04
[13] Jessica M. Gowey. Orjola Kajo. Using Algorithm Visualization to Improve Students‘ Understanding of Parameter Passing Methods. at the 37th Annual Midwest Instruction and Computing. Symposium April 16~17th,2004
[14] Steven Hansen,N. Hari Narayanan,Mary Hegarty: Designing Educationally Effective Algorithm Visualizations.Journal. of Visual Languages and Computing,2002,13(2) : 291~317
[15] 陆枫,陈传波等.基于建构主义的教学内容可视化研究.高等教育研究学,2003,26(1)
[16] Marc H.Brown and John Hershberger. Zeus: A system for Algorithm Animation.Proc. IEEE 1991 Workshop on Visual Languages,4~9
[17] 沈翼之,张益民,等. 算法可视化技术及其实现. 计算机辅助工程,1996, 3
[18] R??ling, G. ,Naps,TL. A Testbed for Pedagogical Requirements in Algorithm Visualizations.7thAnnual SIGCSE/SIGCUE Conference on Innovation and Technology in Computer Science Education (ITiCSE‘ 02) , Aarhus, Denmark (June 2002)
[19] Jon L.Bentley and Brian W.Kernighan. A system for algorithm animation. Computing Systems, Winter 1991,4(1),5~30
[20] 张仁津,邓静. 可视化计算机教学的研究. 贵州师范大学学报,2004,22(1)
[21](美)赫恩(Hearn, D.)等著;蔡士杰等译. 计算机图形学(第二版).北京:电子工业出版社,2002
[22] 陈传波等. 计算机图形学基础. 北京:电子工业出版社,2002
[23] 陆润民,李学志. 计算机绘图. 高等教育出版社,1999
[24] 陈庆章,何文秀等. 国外可视化数据结构教学软件及其比较. 计算机教育,2005,2
[25] 陈丽娟. 算法执行过程的可视化在CAI中的应用. 计算机工程,1999,9
[26] 臧玉琴,腾跃. Visual Basic 界面、多媒体与操作系统程序设计. 北京:人民邮电出版社,2003
[27] 龚沛曾. Visual Basic 程序设计教程(第二版) . 北京:高等教育出版社,2003
[28] 何斌,王运坚. Visual Basic 6.0 应用指南. 北京:人民邮电出版社,2002
[29] 高春艳,李俊民,刘彬彬. Visual Basic 程序开发范例宝典. 北京:人民邮电出版社,2006
[30] 杨树林. 算法演示软件的设计思路、实现方法及技术. 北京印刷学院学报,2003, 11(3)
[31] Educationally Effective Algorithm Visualizations. Journal of Visual Languages and Computing, 2002, 13(2) : 291~317
[32] Judith S. Gurka and Wayne Citrin. Testing effectiveness of algorithm animation. Proceedings of the 1996 IEEE Symposium on Visual Languages, 1996,9 : 182~189
[33] 孙博文.分形算法与程序设计——Visual Basic 实现.北京:科学出版社,2004
[34] 孙家广,杨长贵. 计算机图形学. 北京:清华大学出版社,1998.165~178
[35] 唐泽胜等. 计算机图形学基础. 北京:清华大学出版社,1998.63~72
[36] 唐棣,孙岩.一种高效的整数型椭圆生成算法. 计算机辅助设计与图形学学报,2002,14(1):14~16
[37] XiaolinWu, JonGRokne .Double-step generation of ellipses.IEEE Computer Graphics & Application, 1989.9(5) :56~69
[38] 刘凯,侯伯亨,吴成柯. 椭圆双步增量生成算法及其硬件实现. 计算机辅助设计与图形学学报,2003,4(15):393~396
[2] Brain John Foley.Visualization Tools: Models, Representations and Knowledge Integration. Dissertation for Doctor Degree,University of California,Berkeley 1999
[3] J.T.Stasko. Tango: A framework and system for algorithm animation. IEEE Computer, 23(9) :27~39, November 1990
[4] Tao Chen, Tarek Sobh. A Tool for Data Structure Visualization and User-Defined Algorithm Animation. 31th ASEE/IEEE Frontiers in Education Conference,2001(TID)
[5] Hermann Hartel, Michael Ludke: 3D Simulations of Interacting Particles. Computing in Science&Engineering,2000(July/August)
[6] Byrne, M.D. , Catrambone, R. and Stasko, J.T. . Do Algorithm Animations Aid Learning? Technical Report GIT-GVU-96-18, Georgia Tech Graphics, Visualization, and Usability Center,1996.
[7] McCormick, B.H. , DeFantim T.A. and Brown, M.D. : Visualization in scientific. computing:Definition,domain,andrecommendations , Computer Graphics 1987,21:3~13
[8] 李晓梅,黄朝晖,等. 科学计算可视化导论. 北京:国防科技大学出版社,1996
[9] 张恩成. 计算机多媒体教学实况评析. 电化教育研究,1999 (5) :52~55
[10] 谢维,沈大林. 关于多媒体 CAI 课件设计的分析与思考. 教育科学研究,2002, (5) :40~42
[11] Tomasz Müldner and Elhadi Shakshuki. A New Approach to Learning Algorithms. Proceedings of the International Conferencd on Information Technology: Coding and Computing(ITCC‘04)IEEE
[12] 张庆林. 当代认知心理学在教学中的应用. 西南师范大学出版社,1996.04
[13] Jessica M. Gowey. Orjola Kajo. Using Algorithm Visualization to Improve Students‘ Understanding of Parameter Passing Methods. at the 37th Annual Midwest Instruction and Computing. Symposium April 16~17th,2004
[14] Steven Hansen,N. Hari Narayanan,Mary Hegarty: Designing Educationally Effective Algorithm Visualizations.Journal. of Visual Languages and Computing,2002,13(2) : 291~317
[15] 陆枫,陈传波等.基于建构主义的教学内容可视化研究.高等教育研究学,2003,26(1)
[16] Marc H.Brown and John Hershberger. Zeus: A system for Algorithm Animation.Proc. IEEE 1991 Workshop on Visual Languages,4~9
[17] 沈翼之,张益民,等. 算法可视化技术及其实现. 计算机辅助工程,1996, 3
[18] R??ling, G. ,Naps,TL. A Testbed for Pedagogical Requirements in Algorithm Visualizations.7thAnnual SIGCSE/SIGCUE Conference on Innovation and Technology in Computer Science Education (ITiCSE‘ 02) , Aarhus, Denmark (June 2002)
[19] Jon L.Bentley and Brian W.Kernighan. A system for algorithm animation. Computing Systems, Winter 1991,4(1),5~30
[20] 张仁津,邓静. 可视化计算机教学的研究. 贵州师范大学学报,2004,22(1)
[21](美)赫恩(Hearn, D.)等著;蔡士杰等译. 计算机图形学(第二版).北京:电子工业出版社,2002
[22] 陈传波等. 计算机图形学基础. 北京:电子工业出版社,2002
[23] 陆润民,李学志. 计算机绘图. 高等教育出版社,1999
[24] 陈庆章,何文秀等. 国外可视化数据结构教学软件及其比较. 计算机教育,2005,2
[25] 陈丽娟. 算法执行过程的可视化在CAI中的应用. 计算机工程,1999,9
[26] 臧玉琴,腾跃. Visual Basic 界面、多媒体与操作系统程序设计. 北京:人民邮电出版社,2003
[27] 龚沛曾. Visual Basic 程序设计教程(第二版) . 北京:高等教育出版社,2003
[28] 何斌,王运坚. Visual Basic 6.0 应用指南. 北京:人民邮电出版社,2002
[29] 高春艳,李俊民,刘彬彬. Visual Basic 程序开发范例宝典. 北京:人民邮电出版社,2006
[30] 杨树林. 算法演示软件的设计思路、实现方法及技术. 北京印刷学院学报,2003, 11(3)
[31] Educationally Effective Algorithm Visualizations. Journal of Visual Languages and Computing, 2002, 13(2) : 291~317
[32] Judith S. Gurka and Wayne Citrin. Testing effectiveness of algorithm animation. Proceedings of the 1996 IEEE Symposium on Visual Languages, 1996,9 : 182~189
[33] 孙博文.分形算法与程序设计——Visual Basic 实现.北京:科学出版社,2004
[34] 孙家广,杨长贵. 计算机图形学. 北京:清华大学出版社,1998.165~178
[35] 唐泽胜等. 计算机图形学基础. 北京:清华大学出版社,1998.63~72
[36] 唐棣,孙岩.一种高效的整数型椭圆生成算法. 计算机辅助设计与图形学学报,2002,14(1):14~16
[37] XiaolinWu, JonGRokne .Double-step generation of ellipses.IEEE Computer Graphics & Application, 1989.9(5) :56~69
[38] 刘凯,侯伯亨,吴成柯. 椭圆双步增量生成算法及其硬件实现. 计算机辅助设计与图形学学报,2003,4(15):393~396