Shape Modification of Parametric Curves

A technique of shape modification and deformation for parametric curves through cosine extension function (CEF) is presented. First, a special extension function is defined, based on which a shape operator matrix is constructed. Then combining such matrix with the center of extension and principal directions, two kinds of deformation matrices are defined. Finally, curve deformation is achieved through multiplying its position vector in a local coordinate system by deformation matrix or adding the multiplication of a vector field and quasi-deformation matrix to its position vector in the original coordinate system. Since CEF contains several variable parameters, each of which generates a different effect of shape modification such as controlling the degree of continuity of the modified part of curve with the unchanged part, ideal deformation effects can be got fairly and easily. Examples of theoretical analysis show that the method is potentially useful for geometric modeling, computer graphics and so on.