John L. Lowther

A tool for teaching curve design

This paper describes a tool for teaching curve design. This tool is a component of the software tools to be used in a computing with geometry course [3, 4] that is being developed under the support of National Science Foundation. Curve design is important in computer graphics, animation, and computer aided design. Unfortunately, curve design requires very involved mathematics even though many curve design concepts are intuitive. As a result, it has been a challenging job for instructors teaching curves and surfaces in computer graphics, computer aided design, and other related courses. During past years, there have not been very many efforts dedicated to curve design tool development. Yen [7] produced a well-received video program explaining important concepts of B-spline curves and surfaces and Rockwood and Chambers [6] published a multimedia tutorial on computer aided geometric design. The former only provides a one-way communication, while the latter restricts users to a predefined environment with very limited interaction for users to carry out experiments. To fill this gap, our tool provides students with a fully interactive environment in which they are free to design, modify, and manipulate curved objects and perform experiments without constraints.In the following, Section 2 presents design issues, Section 3 discusses general features, Section 4 enumerates basic elements, Section 5 covers advanced topics, and Section 6 is our conclusion. Interested readers should consult [1, 2, 5] for mathematical background details.

Teaching surface design made easy

All popular computer graphics textbooks have chapters on curves and surfaces [1, 5, 6, 7]. Teaching these chapters could be one of the most challenging tasks in a computer graphics course because of the involved mathematics and the difficulty of visualizing the anticipated effects of the theoretical results. We certainly can skip these chapters and only rely on the polyhedron world, because Gouraud’s or Phong’s shading algorithms could make polyhedra objects appear as realistic curvilinear ones. Unfortunately, real world applications such as ship hull and car body design are usually curvilinear and may only be approximated using polyhedron models. Thus, to address this problem and to make teaching surface design easier, we have designed a pedagogical tool as part of our NSF supported project [8]. One of our goals is to provide the students with an interactive environment which is used to visualize, experiment and verify important and fundamental concepts and algorithms. While there are good textbooks on curve and surface design [3, 4, 9], we can only find two pedagogical aids. Yen’s video program [11] only provides one way information flow. Rockwood and Chambers [10] describe a multimedia tutorial on computer aided geometric design which runs on Windows. It is basically a tutorial that introduces concepts using some animation but lacks a

Computing with geometry as an undergraduate course: a three-year experience

Computing with geometry is a rapidly evolving interdisciplinary field involving computer science, engineering and mathematics. It has relationships to many other areas within computer science (e.g., computational geometry, graphics, information/scientific visualization and computer vision) and serves as a vehicle for engineering students to approach product design and manufacturing processes. Moreover, this is a geometric world! Unfortunately, in a typical computer science curriculum, computing with geometry is virtually missing in spite of its impact on computer science and other fields, and its importance to increase students’ employability. Furthermore, many educators still believe computing with geometry, especially curves, surfaces and solids, belongs to engineering and is not part of computer science curricula, despite the need in graphics and computer-aided design for software engineers and programmers.

If you know b-splines well, you also nnow NURBS!

This paper presents our attempt in designing intuitive and interesting materials for teaching NURBS in an undergraduate course with the help of our tool DesignMentor. This approach does not require tedious mathematics and is based on learning-by-doing and visualization. Our approach was classroom tested and used world-wide in the last seven years.

Curve and surface interpolation and approximation: knowledge unit and software tool

This paper describes a knowledge unit and the use of a software tool, DesignMentor, for teaching a very challenging topic in computer graphics and visualization, namely: curve and surface interpolation and approximation. Topics include global and local interpolation, global approximation, and curve network interpolation. For the past six years, a junior-level course has successfully used this approach.

CSE Graphics and Visualization

We have enjoyed an explosion of developments and applications in computer graphics in the past decade without seeing their inclusion in a typical graphics course. Moreover, computer graphics is interdisciplinary in nature and has relationships with many other areas such as scientific/data visualization, geometric modeling, human computer interaction, computer-aided design, and GIS systems. This special issue is dedicated to the exploration of innovative approaches in teaching computer graphics and related courses. The papers of this special issue cover a range of topics from using computer graphics in a pre-CS1 course, the role of art in a computer graphics curriculum, the use of art and graphics design for computer science majors, and interactive visualization tools. ‘‘Using Animated 3D Graphics to Prepare Novices for CS1’’ by S. Cooper, W. Dann, and R. Pausch, provides an innovative way to teach 3D interactive animation, provide problem solving and logical reasoning skills, learn programming language constructs, and design and implementation of algorithms. While their experimental course is a pre-CS1 course, these concepts will perhaps be in CS1 courses using Alice, Java 3D, or some other programming language that supports 3D interactive graphics. The paper by Wolfe et al., ‘‘Curricular Considerations for Supporting Careers in Computer Graphics’’, describes the importance of creating an interdisciplinary undergraduate computer graphics degree. This paper surveys