We examined how well we can recover surface-reflectance properties from shading patterns under changes in surface shape. The stimulus we used was a square surface modulated in depth by a low-pass-filtered random field and rendered by the Phong illumination model [Commun. ACM 18, 311 (1975)]. Two different surface images (target and match) were presented side by side, with either the viewing direction or the surface-normal direction rotating around the horizontal axis. The target shape was manipulated by changing the spatial spectrum, and the target reflectance was manipulated by changing the diffuse-reflection coefficient and the specular-reflection exponent (shininess) of the Phong model. The shape parameters of the match stimulus were fixed, but its reflectance parameters were under the control of subjects, who had to make the apparent reflectance of the two surfaces as similar as possible. The results showed that the constant error (difference between simulated and matched values) was large except when the two surfaces had the same shape parameters or when they differed only in scale. The pattern of the constant errors and response variabilities suggests that the judgments of the subjects were based on the similarity of the luminance histogram of the surface image. Our results demonstrate a limitation of surface-reflectance constancy for changes in shape and the importance of image-based information in reflectance judgments. The results are discussed in relation to previous studies that showed effects of spatial layout on surface-reflectance perception.

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.

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 approximation 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.

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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.