毕业设计（论文）曲线曲面构造中的加密问题探讨.docVIP

摘 要 曲线和曲面的研究是当前计算机图形学的重要研究内容之一，它不仅被应用于形体的表示上，而且在其他领域也有着重要的应用，例如实验数据、统计数据的图形表示(可视化）等等。其中Bézier曲线曲面和B样条曲线曲面也是当前最常用的曲线曲面。目前，大多数的曲线和曲面是以参数多项式来构造的。因此，在几何造型领域中的曲线曲面加密主要是通过改变他们的，从而实现对原曲线曲面的加密。 本文给出了一种将两个基函数的系数矩阵加以混合的算法，文章首先介绍了多项式曲线曲面的矩阵表示，然后定义了基函数系数矩阵混合的加密算法。通过算法，将三次Bézier曲线基函数的系数矩阵与三次B样条曲线基函数的系数矩阵进行混合得到新的混合矩阵，再以混合后的新矩阵作为系数矩阵构造出新的样条函数，实现了对三次B样条曲线曲面和三次三角B样条曲线曲面的加密。实验，，同时可以得到恢复，从而保证了曲线曲面信息的安全传播。 关键词：系数矩阵; ; Bézier; B样条; 加密 Abstract The study of the curves and surfaces is one of the important studies in computer graphics. It is not only applied to the representation of the body and also has important application in other fields, such as the experimental data, a graphical representation of the statistical data (visualization) and so on. The Bézier and the B-spline curve and surface are also most commonly used. At present, most of the curves and surfaces are constructed with parametric polynomials. Therefore, the field of the curve and surface encryption is constructed mainly by changing their basis function in geometric modeling, in order to achieve the original curve and surface encryption. In this paper, we give an algorithm to blend the coefficient matrices of two basis functions. This paper introduces the matrix representation of the polynomial curve surface, and then defines the encryption algorithm of the blending matrix. By this algorithm, the coefficient matrix of the cubic Bézier curve basis functions is mixed with the matrix of the coefficients matrix of the cubic B-spline basis functions. And then a new spline function is constructed by using the new matrix after blending as the coefficient matrix, The encryption of the cubic B - spline curve and trigonometric B - spline curve is realized. The experimental results show that the new curve and surface generated by the encryption algorithm, has some similarity with the original the curve and surface, and can be restored at the same time, thus ensuring the safe propagation of curve and surface information. Key words: