A matrix-based approach to reconstruction of 3D objects from three orthographic views

Abstract

Presents a matrix-based technique for reconstructing solids with quadric surfaces from three orthographic views. First, the relationship between a conic and its orthographic projections is developed using matrix theory. We then address the problem of finding the theoretical minimum number of views that are necessary for reconstructing an object with quadric surfaces. Next, we reconstruct the conic edges by finding their matrix representations in 3D space. This effectively constructs a model corresponding to the three views. Finally, volume information is searched within the wireframe model to form the final solids. The novelty of our algorithm is in the use of the matrix representation of conics to assist in the 3D reconstruction, which increases both the efficiency and the reliability of the proposed approach.