Descriptive and Computer Aided Drawing Perspective on an Unfolded Polyhedral Projection Surface

Abstract

The aim of the herby study is to develop a method of direct and practical mapping of perspective on an unfolded prism polyhedral projection surface. The considered perspective representation is a rectilinear central projection onto a surface composed of several flat elements. In the paper two descriptive methods of drawing perspective are presented: direct and indirect. The graphical mapping of the effects of the representation is realized directly on the unfolded flat projection surface. That is due to the projective and graphical connection between points displayed on the polyhedral background and their counterparts received on the unfolded flat surface. For a significant improvement of the construction of line, analytical algorithms are formulated. They draw a perspective image of a segment of line passing through two different points determined by their coordinates in a spatial coordinate system of axis x, y, z. Compared to other perspective construction methods that use information about points, for computer vision and the computer aided design, our algorithms utilize data about lines, which are applied very often in architectural forms. Possibility of drawing lines in the considered perspective enables drawing an edge perspective image of an architectural object. The application of the changeable base elements of perspective as a horizon height and a station point location enable drawing perspective image from different viewing positions. The analytical algorithms for drawing perspective images are formulated in Mathcad software, however, they can be implemented in the majority of computer graphical packages, which can make drawing perspective more efficient and easier. The representation presented in the paper and the way of its direct mapping on the flat unfolded projection surface can find application in presentation of architectural space in advertisement and art.