The medial axis transform of the region defined by Hermite curve tangent to unit circle

The design of curves, surface, and solid are important in computer aided geometric design (CAGD). Images, surround by boundary curves, are also investigated by many researchers. One way to describe an image is using the medial axis transform. Under this consideration, the properties of the boundary curves tangent to circles become important to design for 2D images. In this paper, we want find the medial axis transform (MAT) for a special class of region, which is bounded by unit circle and the curves whose end points is on a the circle, and endpoints tangent vectors are parallel to the tangent of circle at the end points. There are 4 cases, symmetric/non-symmetric region with singular point/local maximum curvature point, and proposed algorithm for these 4 cases.