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

摘要： 针对线框模型中二次曲面的重建，在面片边界回路确定的基础上提出了通过曲面片边界上9个点约束构建曲面方程的方法。先从回路中提取二次曲面片边界上顺次连接的3条曲线，并在这3条曲线上各取3点，形成9个对二次曲面方程系数的线性约束，再添加一个附加系数比例约束，确定二次曲面方程的全部10个系数。对退化二次曲面点约束缩减的情况，通过增加退化约束来补偿以求得精确解，同时也给出了一个求近似解的简化方案。最后对二次曲面的分类进行了讨论。实验结果表明该方法准确且高效。

关键词: 线性约束, 二次曲面, 重建, 系数