在工业生产、医学研究等领域通常对曲面的复原是利用点云数据，但是对于某些特殊情况，例如凹槽、截面不均匀或者条件不允许采集到云数据的情况，点云数据难以获得，此时对于少量散乱点的曲面造型值得学者们广为研究。所以，本文主要研究具有法矢约束的空间少量散乱点的曲面造型。 本文首先研究了Hermite插值算法，主要通过三切矢方程和法矢条件来推导出每个型值点处的方向切矢与混合切矢，从而给出三切矢Hermite曲面造型的定义。利用三切矢Hermite曲面本文首先在圆柱、球、圆锥面上进行反复试验，分析误差，然后将这一算法运用到空间上少量的散乱点上。其次本文研究了有理Bezier插值曲面，给出了通过调整曲面权值使得型值点处满足给定的法矢要求。实验发现求解权值过程计算量很大，通过对求解权值过程进行简化，提高了该算法的时间性能，从而较有效地拟合出满足法矢约束的有理Bezier曲面。最后采用了三次隐式函数拟合具有法矢约束的空间散乱点，将空间中每一个三角网格都拟合出三次隐式曲面片，并且可以使得曲面片间能够达到G1连续。利用这一算法，本文对球面上取出若干散乱点进行试验，分析误差得到算法可行，然后利用这一算法对空间散乱点拟合出能够达到G1连续的三次隐式曲面。 本文给出两种能够拟合具有法矢约束的少量空间散乱点的算法的推导过程，实现了基于法矢约束的隐式曲面的拟合。利用规则曲面上采集的少量散乱点进行试验，并且分析拟合曲面与实际曲面之间的误差，得出三种算法都是可行的，均能拟合出满足G1连续的曲面，并且在所给定的型值点处都能满足法矢要求。

In the field of industrial production, medical research, usually on surface reconstruction is based on point cloud data, but for some special cases, such as groove, cross section is not uniform or conditions do not permit the acquisition to the cloud data, point cloud data are difficult to obtain, at this time for surface modeling a few scattered points worthy of scholars to study. So, this paper mainly studies the method of surface modeling with vector constraints of space a few scattered points. This paper studied the Hermite interpolation algorithm, mainly through the three tangent vector equation and normal conditions are derived for each model points the direction tangent vectors and hybrid tangent vector, which gives the definition of three tangent vector of Hermite surface modeling. The three tangent Hermite surface in the first column, ball, cone surface of trial and error, error analysis ,and then applying this algorithm to the space on a small number of scattered points. Secondly, this paper studies the rational Bezier interpolation surface ,gives the model points to meet the normal requirements by adjusting the weights of a given surface. The experiment found that solving the right value process a very large amount of computation, simplifies the process of solving the weight ,improves the time performance of the algorithm, thus effectively fit rational Bezier surface normal constraint. By the end of the three implicit function fitting with the normal constraints of space scattered points, each triangle grid space are fitted with three implicit surfaces, and can make the surfaces can achieve G1 continuity. Using this algorithm, the spherical removed several scattered point test, error analysis is feasible, then using the algorithm of scattered points fitting can reach three times continuous implicit surface G1. This paper presents two kinds of small amounts of space to derivation of fitting with normal constraint points algorithm, to achieve a fitting implicit surface normal vector based on constraints. The tests were conducted using the acquisition rules on the surface of the small amount of scattered points, and analyze the error between the fitting surface and the surface, the three algorithms are feasible, can fit G1 continuous surface, and points can meet the normal requirements in the given type.