Abstract: The segmented object is represented in terms of a numerical volume by calculating the gradients of the physical quantities loaded into the volume elements of this numerical volume. The gradients are shown to be perpendicular to the true surface of the object to be segmented and that they determine a surface more precisely than a treatment carried out on the surface of the segmented object. To eliminate the artefacts of a contour line which are visible in particular in the regions of low relief, the gradients assigned to volume elements of the surface of the object are weighted with respect to gradients assigned to volume elements adjacent to these volume elements by apparent facets of this segmented object.

Abstract: The problems of selection of objects having complex shapes and usually apprehended by a plurality of facets are solved by making use of curved surfaces, the equation of which is of the second degree. In a test calculation for checking whether a node of an octree decomposition does or does not belong to the surface thus defined, the terms of the second degree are replaced by a constant. It is shown that this approximation permits rapid determination of the complex shapes without having to perform the calculations corresponding to the second degree. The method also permits easy determination of the normal to the object for calculation of shadowing when it is employed for display.

Abstract: The 3D display device of the invention is based on an octree structure of data pertaining to an object to be displayed. This structure is memorized in a memory associated with a cache memory sending blocks of data on a bus to which a geometrical processor and an image-generating circuit are connected. The geometrical processor generates the visible part of another octree corresponding to a target universe which may be positioned in any way in relation to the object universe (a cube enclosing all the data to be represented).