关键词: 线性约束, 二次曲面, 重建, 系数

Abstract: An algorithm is presented for reconstruction of the quadric by nine point constraints.Firstly，three conics which are on the quadric and connected sequentially are found，and three points are got from each conic.Nine points are nine linear constraints for equation coefficient，and an extra constraint is added.So the ten coefficients are determined by ten constraints.Then，as for the degenerate quadric，the point constraints are reduced to eight.A degeneracy constraint compensates for the reduction and so the exact solutions can be obtained，meanwhile，within the limits of experimental error，a simplified scheme for calculating the coefficient of the degenerate quadric is proposed.Lastly，the classification of quadric is analyzed.The experimental results indicate the effectiveness of the proposed method.

Key words: linear constraint, quadric, reconstruction, coefficient