Yankovskaya L. Computer graphic form shaping of spherical objects in design based on the perspective contour line.

Dissertational research addresses a development of new methods for the computer graphic shape forming of spherical objects in design and architecture based on the perspective contour line. It is shown that contour and silhouette are essential characteristics of an object providing information about it in visual perception, fine art, geometry and design. It is noted that aforementioned characteristics should be considered in designing software for 3D modeling. Literature is reviewed for the possible implementation of perspective images in the shape forming procedure. Method for the object modeling based on its contour line on perspective images is formulated. Here the contour line is defined as a line on the projection plane which occludes a perspective image of some object. Including perspective contour line in the determinant of the shape being formed allows a user to model objects and the spatial scene itself in such a way that yields a desired appearance of the objects from the specified location of the viewer. This proposition is a basis for the described method. Shape forming methods for a sphere applied in various software packages are evaluated. Their analysis reveals that none of them allows a modeling of spherical objects derived from their perspective contour lines. It is further shown that spherical objects and their segments are often utilized as a shape-forming basis in the architecture and design. Numerous international exhibitions of design in recent years prove this notion. New methods for the graphic shape forming of spherical objects derived from their contour lines on perspective images are proposed. Formalism for specifying initial conditions of the project is developed. These initial conditions affect a spatial orientation of the perspective contour line of a sphere. Major approaches for the shape forming of the sphere utilizing elements of its perspective contour line are developed. Such elements may include points, incidental contour lines and their tangential lines as well as their combination. There proposed new method for the computer modeling of the sphere by graphic definition of the ellipse determinant elements as sphere's perspective contour line. Geometric models based on the proposed techniques are formulated. Methods for the selection of segments by plane through the graphic definition of its determinant elements on the perspective image of the spherical surface are developed. It is found that through the positioning of the prescribed set of points on the perspective image а user can define an intersecting line of sphere in space. Recognition of a segment of the arbitrary shaped sphere via 3-d tracing of its contour on the perspective image is considered. A new method for the spherical surface modeling based on two or more viewpoints is developed. Procedures are considered for the computer modeling of a set of spherical surface segments on the perspective image from contour lines. Several routines and algorithms are implemented for possible examples in design where the proposed technique can be used in the modeling of spherical objects. Keywords: 3D computer design, spherical surface, perspective, contour, contour line, visual perseption, geometric modeling.