Method and apparatus for displaying three-dimensional image by use of tensor rendering

Abstract

In order to visually display a spatial distribution of a multi-value function represented by nine components of a two-order, three-dimensional tensor, a distribution function of an anisotropic fine face distribution is set to have a form of a second-order curved surface of an anisotropic ellipsoid associated with discrete sampling points, the intensity of the scattering light is calculated from a contribution of a bisector-direction vector between a light-source-directed vector and a line of sight vector (in a reflection light intensity calculating part to simulate the light scattering. With respect to each calculation point having a tensor, the intensity of the scattering light is integrated according to a rendering light beam equation with a light transmittance weighted (in a light beam integration part). As a result, since the correlation between the light integration effect and the angle dependency based on a scattering distribution function associated with the tensor components is displayed, multi-value information in a space can be visually recognized while eliminating the need for pattern recognition or the like. Not a geometrical object but a cloud-like three-dimensional distribution image is obtained as a display image and special anisotropically scattered part are displayed in the image. Therefore, the image is natural as a visual-feeling characteristic, and thus an observer can efficiently recognize it with less fatigue.