Acquiring accurate scattering properties is important for rendering translucent materials. In particular, the phase function, which determines the distribution of scattering directions, plays a significant role in the appearance of a material. We propose a distinctive scattering theory that approximates the effect of single scattering to acquire the non-parametric phase function from a single image. Furthermore, in various experiments, we measured the phase functions from several real diluted media and rendered images of these materials to evaluate the effectiveness of our theory.

Abstract Fast realistic rendering of objects in scattering media is still a challenging topic in computer graphics. In presence of participating media, a light beam is repeatedly scattered by media particles, changing direction and getting spread out. Explicitly evaluating this beam distribution would enable efficient simulation of multiple scattering events without involving costly stochastic methods. Narrow beam theory provides explicit equations that approximate light propagation in a narrow incident beam. Based on this theory, we propose a closed‐form distribution function for scattered beams. We successfully apply it to the image synthesis of scenes in which scattering occurs, and show that our proposed estimation method is more accurate than those based on the Wentzel‐Kramers‐Brillouin (WKB) theory.

Tai Chi Chuan is a popular Chinese martial art, practiced all over the world. Practitioners have to memorize complicated forms of motion, which is the first hurdle for beginners. We applied CG and VR technologies to self-study video materials and demonstrated that these cyber technologies can improve practices of this traditional martial art.

When synthesizing images of fine objects like hair, we usually adopt sub-pixel drawing techniques to improve the image quality. For this paper, we analyzed the statistical features of images of thin lines and found that the distributions of the pixel values tended to be Gaussian. A psychophysical experiment showed that images of stripes with the appropriate Gaussian noise added are perceived to be finer than the original ones. We applied this perceptional property to hair rendering and developed a fast fine hair drawing algorithm.

Spring-mass simulations are widely used in the computer animation of soft objects. Although such systems can be numerically solved by either explicit or implicit methods, it has been difficult to obtain stable results from the explicit methods. This work presents an easy way to stabilize explicit methods in spring-mass simulations. The simulation procedures are modeled as a linear digital system, and system stability is mathematically defined. This allows us to develop theories of simulation stability. The application of these theories to explicit methods allows them to become as stable as implicit methods.

Periodic motion is an important class of motion to synthesize, but it is not easy to compute it robustly and efficiently. In this paper we propose a simple, robust and efficient method to compute periodic motion from linear equation systems. The method first calculates the response of the system when an external periodic force is applied during one period, and then sums up the periodically shifted versions of the system response to provide the periodic solution. It is also shown that Fourier decomposition is very effective to compress the motion data without a drop in visual fidelity. © 1998 John Wiley & Sons, Ltd.

Anti-aliasing is generally an expensive process because it requires super-sampling or sophisticated rendering.This paper presents a new type of anti-aliasing filter for animation sequences, the pixeltracing filter, that does not require any additional sample nor additional calculation in the rendering phase.The filter uses animation information to calculate correlation among the images, and sub-pixel information is extracted from the sequence based on the correlation.Theoretical studies prove that the filter becomes an ideal antialiasing filter when the filter size is infinite.The algorithm is simple image processing implemented as postfiltering.The computational cost is independent of the complexity of the scene.Experiments demonstrate the efficiency of the filter.Almost complete anti-aliasing was achieved at the rate of about 30 seconds per frame for very complex scenes at a resolution of 256x256 pixels.The pixel tracing filter provides effective antialiasing for animation sequences at a very modest computational cost.

Abstract Stochastic approaches are very effective for modelling natural phenomena. This paper presents a motion model based on a stochastic process as well as physics, and proposes motion synthesis techniques for stochastic motion—motion under the influence of wind. The motion synthesis process is modelled by a cascade system of three components: wind model, dynamic model, and deformation model. Wind models produce spatio‐temporal wind velocity fields using the power spectrum and auto‐correlation of wind, just like fractal geometry. Dynamic models describe the dynamic response of the systems, using equation systems or response functions. Deformation models produce deformed shapes of objects according to the geometric models of the objects and the results of the dynamic systems. The biggest advantage of the model is its generality and consistency. The model is applicable to most of the existing trees and grass models, including structural models, particle systems, impressionist models, and 3D texture. It is demonstrated that the coupling of stochastic approaches and physically‐based approaches can synthesize realistic motion of trees, grass and snow with modest computational cost.

Abstract Interference detection is a useful technique, but it is also generally time‐consuming. In this paper, a new type of interference detection algorithm is proposed for real‐time interference detection. The algorithm first rasterizes the projection of the target objects and calculates the z‐values, just as done by the z‐buffer visible surface algorithm. For interference detection, all z‐values and pointers to the corresponding faces of objects are saved in a z‐list for each pixel. Sorting the z‐list against the z‐values allows the detection of overlapping objects in the z‐direction at each pixel position and, thus, finds interfering faces by referring to the face pointers in the z‐list. The algorithm is simple and easy to implement. Its computational complexity is directly proportional to the number of polygons, and, in addition, standard graphics hardware can be used to greatly accelerate execution. Another advantage is that the algorithm can be applied to all ‘ray‐traceable’ objects, including algebraic surfaces, and procedurally defined objects; traditionally these were not suitable subjects for interference detection. The algorithm is implemented on a graphics workstation using a standard graphics library. Interference detection at a practical interaction speed is achieved for complicated objects such as polyhedra with thousands of polygons. The algorithm can be used in two ways: for inexpensive interference detection, and as an efficient culling method for more precise collision/interference detection algorithms.

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 system matrix) that provides the basis for pencil tracing and a variety of ray tracing techniques, such as beam tracing, ray tracing with cones, ray-object intersection tolerance, and a lighting model for reflection and refraction. In the error analysis, functions that estimate approximation errors and determine a constraint on the spread angle of a pencil are given.The theory results in the following fast ray tracing algorithms; ray tracing using a system matrix, ray interpolation, and extended 'beam tracing' using a 'generalized perspective transform'. Some experiments are described to show their advantages. A lighting model is also developed to calculate the illuminance for refracted and reflected light.