Caustics are patterns of light formed by reflection or refraction of light from objects, and several methods have been developed to render caustics because of their visually beautiful patterns. This paper proposes a method for the rapid rendering of caustics formed by refracted light through transparent objects. First, a preprocess is used to generate sampling rays incident on each vertex of the object, and, taking refraction into account, to trace the rays until they leave the object. The position and direction of each ray that finally leaves the transparent object are obtained and stored in a lookup table. Next, in the rendering process, when the object is illuminated, the position and direction of the rays leaving the object are calculated using the lookup table. This makes it possible to render refractive caustics due to transparent objects at interactive frame rates even if the direction of the light changes and the object is translated or rotated.

The importance of informal communication on the Internet has been increasing in recent years. Several systems for informal communication are currently available to the public. These systems, however, require a particular server and/or specialized 3D content. In this paper, we propose a system for informal communication in a 3D virtual environment. The system makes 3D virtual worlds from existing common 2D HTML documents. Browsers communicate in a peer-to-peer manner. Construction and management of the system can be achieved with ease and at low cost in contrast with existing 3D virtual communication systems. Our results show that users shared interests by gaze awareness.

A picture is one of important research subjects in order to make our life spiritually rich. Most studies on pictures, however, only propose some substitute functions of actual drawing or painting materials. There is no system that evaluates pictures drawn by users and gives advice about them. We propose a learning support system for basic techniques in beginner's pencil drawing. The proposed system receives a subject (motif) data set and an image of user's sketch and returns advice to the user. The system is composed of the four subsystems: feature extraction of motifs, feature extraction of sketches, error identification, and generation and presentation of advice. We developed and experimented a prototype system limited to treat a basic motif and some principal advice. As a result, the validity of the proposed system was confirmed.

In a pencil drawing class, a teacher explains often the differences between a drawing and a motif by many ways; even so, it is difficult for most learners to understand the existence of errors in his/her drawing. When a learner watches the 3D model of his/her drawing from appropriate viewpoints, he/she is immediately aware of the errors. This paper describes the technique of error visualization from a learner's erroneous drawing. We developed a drawing advice system that consists of a 3D model converter from a 2D image and an evaluation function to estimate the effect of the 3D model. We designed a geometrical formula that expresses the relation between the geometrical feature and the error expression in the teacher's advice.

This paper reports on the clinical application of a system for recovering the time-varying three-dimensional (3-D) left-ventricular (LV) shape from multiview X-ray cineangiocardiograms. Considering that X-ray cineangiocardiography is still commonly employed in clinical cardiology and computational costs for 3-D recovery and visualization are rapidly decreasing, it is meaningful to develop a clinically applicable system for 3-D LV shape recovery from X-ray cineangiocardiograms. The system is based on a previously reported closed-surface method of shape recovery from two-dimensional occluding contours with multiple views. To apply the method to "real" LV cineangiocardiograms, user-interactive systems were implemented for preprocessing, including detection of LV contours, calibration of the imaging geometry, and setting of the LV model coordinate system. The results for three real LV angiographic image sequences are presented, two with fixed multiple views (using supplementary angiography) and one with rotating views. 3-D reconstructions utilizing different numbers of views were compared and evaluated in terms of contours manually traced by an experienced radiologist. The performance of the preprocesses was also evaluated, and the effects of variations in user-specified parameters on the final 3-D reconstruction results were shown to be sufficiently small. These experimental results demonstrate the potential usefulness of combining multiple views for 3-D recovery from "real" LV cineangiocardiograms.

Generally, in the field of industrial design, the measurement data of a clay model are faired, and a 3D model is made in CAD. However, it is a problem that this fairing work takes a long time and requires a great deal of labor. We propose an automatic curve fairing system for the application to reverse engineering technology. The system is constructed by the following five steps. (1) Key-line data are extracted from a clay model by a 3D digitizer. (2) The extracted key-line data are approximated by a spline with a genetic algorithm. (3) The spline curve (key-line) is divided into curves of monotone curvature. (4) The "characteristic" of the curve is analyzed for each monotone-curvature curve. (5) Each monotone-curvature curve is substituted by a visual language based on the result of the analysis mentioned above, and each key-line is reconstructed by the visual language. By using this system, we can easily obtain an aesthetic curve, as intended by a designer, in a short time.

In order to obtain a good spline model from many measurement data, frequently we have to deal with bets as variables. Then the problem to be solved becomes a continuous nonlinear and multivariate optimization problem with many local optima. Therefore, it is difficult to obtain a global optimum. We propose a new method to convert the original problem into a discrete combinatorial optimization problem and solve the converted problem by a genetic algorithm. We construct individuals by considering candidates of the locations of knots as genes, and convert the continuous problem into a discrete problem. We search for the best model among the candidate models by using H. Akaike's (1974) Information Criterion (AIC). Our method can determine appropriate number and locations of knots automatically and simultaneously. We don't need any subjective parameters such as error tolerance or a smoothing factor, and good initial location of knots for iterative search. Numerical examples are given to show the effectiveness of our method.

A method is described for fitting a piecewise cubic polynomial to a sequence of data by a onepass method.The polynomial pieces are calculated as the data is scanned only once from left to right.The algorithm is shown to be stable when a piecewise cubic polynomial is used which is continuous with its first derivative, while it becomes unstable if the polynomial is made continuous up to the second derivative.The knots of the approximating function are determined successively using a criterion by Powell.