Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of des...Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of descriptive geometry, math and computer algorithm. Firstly, geometric elements in general position are transformed to a special position in new coordinate system. Then a 3D problem is projected to new coordinate planes. Finally, according to 2D/3D correspondence principle in descriptive geometry, the solution is constructed computerized drawing process with ruler and compasses. In order to make this method a regular operation, a two-level pattern is established. Basic Layer is a set algebraic packaged function including about ten Primary Geometric Functions （PGF） and one projection transformation. In Application Layer, a proper coordinate is established and a sequence of PGFs is sought for to get the final results. Examples illustrate the advantages of our method on dimension reduction, regulatory and visual computing and robustness.展开更多
Graphic science is the subject which teaches geometry and graphics, and is taught in early undergraduate curricula at many Japanese universities as a liberal arts subject or as a basic subject for design and drawing. ...Graphic science is the subject which teaches geometry and graphics, and is taught in early undergraduate curricula at many Japanese universities as a liberal arts subject or as a basic subject for design and drawing. In traditional graphic science courses, de-scriptive geometry based on hand drawings was taught. However, in recent years, there continues to be a rapid spread in the use of 3D-CAD in the field of engineering design and drawing, and there is also increasing use of CG in many fields such as for visualiza-tion of computer simulation results in science, and for image display in the movie and game entertainment fields. So there is a need for graphic presentation education including the competence in the use of 3D-CAD/CG, or ＂graphics literacy （or visual literacy） education＂ for a wide range of students. In order to realize graphics literacy education, from 2007, a new graphic science curriculum has been started at the College of Arts and Sciences of the University of Tokyo. The main part of the curriculum consists of Graphic Science I and Graphic Science II. With Graphic Science I, as before, traditional descriptive geometry is taught with hand drawing as the base. With Graphic Science II, commercial graphic processing software can be experienced. In this course, by introducing geo- metric problems as examples and assignments, it is designed to mutually complement with descriptive geometry education （Graphic Science I）. With the spread of 3D-CAD/CG, some people say that there is no longer any need for descriptive geometry, but for the following reasons, it has been decided to teach descriptive geometry. 1） Traditional descriptive geometry is an excellent method in teaching and learning geometry of projection and of three-dimensional objects, and concepts and/or procedures in descriptive geome-try can be applied in solving geometric design problems by the use of 3D-CAD/CG. 2） Even in this age of 3D-CAD/CG, hand draw-ing is still being used （especially for free-hand sketches）. 3） Hand drawing is an effective method of developing spatial ability of students. However, with the spread of 3D-CAD/CG, the descriptive geometry techniques in analyzing shapes and forms of three-dimensional objects are now loosing their earlier practical importance. So emphasis is not being placed on the education of practical techniques, but is being placed on teaching the theory behind the techniques, i.e., geometry of projection and of three-dimensional objects. This paper reports specific examples of classes in order to describe the importance of descriptive geometry education, and the need to switch from education focused on techniques to education on the theory behind the techniques.展开更多
基金National Natural Science Foundation of China（No.61073986）
文摘Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of descriptive geometry, math and computer algorithm. Firstly, geometric elements in general position are transformed to a special position in new coordinate system. Then a 3D problem is projected to new coordinate planes. Finally, according to 2D/3D correspondence principle in descriptive geometry, the solution is constructed computerized drawing process with ruler and compasses. In order to make this method a regular operation, a two-level pattern is established. Basic Layer is a set algebraic packaged function including about ten Primary Geometric Functions （PGF） and one projection transformation. In Application Layer, a proper coordinate is established and a sequence of PGFs is sought for to get the final results. Examples illustrate the advantages of our method on dimension reduction, regulatory and visual computing and robustness.
文摘Graphic science is the subject which teaches geometry and graphics, and is taught in early undergraduate curricula at many Japanese universities as a liberal arts subject or as a basic subject for design and drawing. In traditional graphic science courses, de-scriptive geometry based on hand drawings was taught. However, in recent years, there continues to be a rapid spread in the use of 3D-CAD in the field of engineering design and drawing, and there is also increasing use of CG in many fields such as for visualiza-tion of computer simulation results in science, and for image display in the movie and game entertainment fields. So there is a need for graphic presentation education including the competence in the use of 3D-CAD/CG, or ＂graphics literacy （or visual literacy） education＂ for a wide range of students. In order to realize graphics literacy education, from 2007, a new graphic science curriculum has been started at the College of Arts and Sciences of the University of Tokyo. The main part of the curriculum consists of Graphic Science I and Graphic Science II. With Graphic Science I, as before, traditional descriptive geometry is taught with hand drawing as the base. With Graphic Science II, commercial graphic processing software can be experienced. In this course, by introducing geo- metric problems as examples and assignments, it is designed to mutually complement with descriptive geometry education （Graphic Science I）. With the spread of 3D-CAD/CG, some people say that there is no longer any need for descriptive geometry, but for the following reasons, it has been decided to teach descriptive geometry. 1） Traditional descriptive geometry is an excellent method in teaching and learning geometry of projection and of three-dimensional objects, and concepts and/or procedures in descriptive geome-try can be applied in solving geometric design problems by the use of 3D-CAD/CG. 2） Even in this age of 3D-CAD/CG, hand draw-ing is still being used （especially for free-hand sketches）. 3） Hand drawing is an effective method of developing spatial ability of students. However, with the spread of 3D-CAD/CG, the descriptive geometry techniques in analyzing shapes and forms of three-dimensional objects are now loosing their earlier practical importance. So emphasis is not being placed on the education of practical techniques, but is being placed on teaching the theory behind the techniques, i.e., geometry of projection and of three-dimensional objects. This paper reports specific examples of classes in order to describe the importance of descriptive geometry education, and the need to switch from education focused on techniques to education on the theory behind the techniques.
