Mathematical Problems in Engineering
Volume 8 (2002), Issue 3, Pages 207-219

Reconstruction of quadratic curves in 3-D from two or more perspective views

R. Balasubramanian,1 Sukhendu Das,2 and K. Swaminathan1

1Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, India
2Department of Computer Science and Engineering, Indian Institute of Technology, Madras, Chennai 600 036, India

Received 26 June 2001; Revised 28 August 2001

Copyright © 2002 R. Balasubramanian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The issues involved in the reconstruction of a quadratic curve in 3-D space from arbitrary perspective projections are described in this paper. Correspondence between the projections of the curve on the image planes is assumed to be established. Equations for reconstruction of the 3-D curve, which give the parameters of the 3-D quadratic curve are determined. Uniqueness of the solution in the process of reconstruction is addressed and solved using additional constraints. As practical examples, reconstruction of circles, parabolas and pair of straight lines in 3-D space are demonstrated.