# MathSciDoc: An Archive for Mathematician ∫

#### Geometric Modeling and Processingmathscidoc:1608.16077

Computer Aided Design, 33, (14), 1059-1072, 2001
This paper presents a new approach for reconstructing solids with planar, quadric and toroidal surfaces from three-view engineering drawings. By applying geometric theory to 3-D reconstruction, our method is able to remove restrictions placed on the axes of curved surfaces by existing methods. The main feature of our algorithm is that it combines the geometric properties of conics with affine properties to recover a wider range of 3-D edges. First, the algorithm determines the type of each 3-D candidate conic edge based on its projections in three orthographic views, and then generates that candidate edge using the conjugate diameter method. This step produces a wire-frame model that contains all candidate vertices and candidate edges. Next, a maximum turning angle method is developed to find all the candidate faces in the wire-frame model. Finally, a general and efficient searching technique is proposed for finding valid solids from the candidate faces; the technique greatly reduces the searching space and the backtracking incidents. Several examples are given to demonstrate the efficiency and capability of the proposed algorithm.
Reconstruction, engineering drawings
```@inproceedings{shi-xia2001reconstruction,
title={Reconstruction of curved solids from engineering drawings},
author={Shi-Xia Liu, Shi-Min Hu, Yu-Jian Chen, and Jia-Guang Sun},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826222323291111460},
booktitle={Computer Aided Design},
volume={33},
number={14},
pages={1059-1072},
year={2001},
}
```
Shi-Xia Liu, Shi-Min Hu, Yu-Jian Chen, and Jia-Guang Sun. Reconstruction of curved solids from engineering drawings. 2001. Vol. 33. In Computer Aided Design. pp.1059-1072. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826222323291111460.