APPLICATION OF DANDELIN’S THEOREM TO DRAWING CIRCLES IN PARALLEL PERSPECTIVE
Keywords:visual cone, asymptote, conics, point of sight, picture plane, perspective projection system
The paper analyses a problem of great theoretical importance in practice of perspective: the nature of the perspective of a circle from the horizontal plane according to the relative position between the spectator plane (parallel to the picture plane) and the given circle. Depending on the position of the neutral line to the circle, the nature of the perspective of a point describing the circle can be determined, because the corresponding visual radius generates a conical surface, and the perspective of the mobile point becomes the conical section made in the conical surface by the picture plane. The paper intends to highlight the validity of Dandelin's theorem when putting a circle into perspective. A discussion of examples characteristic for this problem is offered. Several conclusions distinguish the main points and results of the paper.
D’Amelio, J., (2004). Perspective drawing handbook, Dover Publications, INC., Mineola, New York.
Dobre, D., (2017). Perspectiva si axonometrie, Editura Bren, Bucuresti.
Dumitrescu, Z., (2002). Ars Perspectivae, Editura Nemira, Bucuresti.
Norling, E.R., (1999). Perspective made easy, Dover Publications, INC., Mineola, New York.
Paré, E.G., Loving, R.O., Hill, I.L., Paré, R.C., (1997). Descriptive geometry, 9th ed., Prentice-Hall, Inc., Upper Saddle River, New Jersey.
Storey, G.A., (2006). The theory and practice of perspective, Oxford, Clarendon Press.
Tanasescu, A., (1975). Geometrie descriptiva, Perspectiva, Axonometrie, Editura Didactica si Pedagogica, Bucuresti.
Copyright (c) 2020 Journal of Industrial Design and Engineering Graphics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.