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Pencil tracing, a new approach to ray tracing, is introduced for faster image synthesis with more physical fidelity. The paraxial approximation theory for efficiently tracing a pencil of rays is described and analysis of its errors is conducted to insure the accuracy required for pencil tracing. The paraxial approimation is formulated from a 4x4 matrix (a(More)
A new method for easily and rapidly generating three-dimensional shapes from two-dimensional line-drawings is presented. This method is based on the generalized symmetry constraint. Generalized symmetry is an extended concept of threedimensional symmetry and its axis is a 3D smooth curve. This paper first develops the definition and constraint of(More)
We propose a web-based training system and courseware for advanced computer graphics for undergraduate students. By using the system, the students have no temporal and spatial limitations for learning computer graphics technologies. Once they can connect to the Internet, they can study for as much time as they wish and in any place. We have designed more(More)
A still image extracted from a 3D animation sequence does not contain any information about the motions of 3D objects. In order to represent fast-moving 3D objects in a still image, the motion blur technique has been used. However, it cannot easily depict other kinds of motions. Several non-photorealistic rendering approaches [1] [2] have been proposed to(More)