The Tangent Medial Circles Inside the Region Defined by Hermite Curve Tangent to Unit Circle

The design of curves, surfaces, and solids 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 to 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. During the process, we want find the medial circle tangent to other medial circle, until we reach the medial circle whose center is the center of the osculating circle for the point with local maximum curvature. There are 4 cases, symmetric/non-symmetric region with singular point/local maximum curvature point, and proposed algorithm for these 4 cases. We introduced algorithm for this 4 cases in this paper.