COMPUTER REPRESENTATION OF PLANE FIGURES AND 3D SOLIDS USING ADDITIVE ALGORITHMS

The paper presents a definition of figures and curves in the plane and solids and surfaces in the 3D space based on the notion of (generalized) pixels and voxels. The corner points of the pixels/voxels form a point grid in the plane or in the space and a grid value is attached to each grid point by means of additive algorithms. A plane figure or a 3D solid consists of those pixels/voxels for which the grid values ib all four/eight corner points are negative. Some basic transformations of the algorithms generating the grid values (and thus the plane figures and 3D solids) are ivestigated useful in constructing axonometric and perspective projections. The paper is a first one of a series of publications intending to present a new philosophy for solving a wide range of problems in computational eometry, such as representation and manipulation of different types of curves, surfaces, plane figures and solids; finding points/curves of intersection and contour lines; finding different 2D projections of 3D objects, etc