Conical Perspective Image of an Architectural Object Close to Human Perception

Abstract

The aim of the study is to develop a method of computer aided constructing conical perspective of an architectural object, which is close to human perception. The conical perspective considered in the paper is a central projection onto a projection surface being a conical rotary surface or a fragment of it. Whereas, the centre of projection is a stationary point or a point moving on a circular path. The graphical mapping results of the perspective representation is realized directly on an unrolled flat projection surface. The projective relation between a range of points on a line and the perspective image of the same range of points received on a cylindrical projection surface permitted to derive formulas for drawing perspective. Next, the analytical algorithms for drawing perspective image of a straight line passing through any two points were formulated. It enabled drawing a perspective wireframe image of a given 3D object. The use of the moving view point as well as the application of the changeable base elements of perspective as the variables in the algorithms enable drawing conical perspective from different viewing positions. Due to this fact, the perspective drawing method is universal. The algorithms are formulated and tested in Mathcad Professional software, but can be implemented in AutoCAD and majority of computer graphical packages, which makes drawing a perspective image more efficient and easier. The presented conical perspective representation, and the convenient method of its mapping directly on the flat unrolled surface can find application for numerous advertisement and art presentations.