We propose an adaptive geometry compression method based on 4-point interpolatory subdivision schemes. It can work on digital curves of arbitrary dimensions. With the geometry compression method, a digital curve is adaptively compressed into several segments with different compression levels. Each segment is a 4-point subdivision curve with a subdivision step. In the meantime, we provide high-s...

This paper presents a new curve subdivision algorithm called interproximate subdivision for generating curves that interpolate some given vertices and approximate the other vertices. By the interproximate subdivision, only the vertices specified to be interpolated are fixed and the other vertices are updated at each refinement step. The refinement rules are derived to ensure that the eigenvalue...

Subdivision provides an efficient method to generate smooth curves and surfaces. Recently matrixvalued subdivision schemes were introduced to provide more flexibility and smaller subdivision templates for curve and surface design. For matrix-valued subdivision, the input is a set of vectors with the first components being the vertices of the control polygon (or the control net for surface subdi...

The objective of this paper is to study and construct matrix-valued templates for interpolatory curve subdivision. Since our investigation of this problem was motivated by the need of such subdivision stencils as boundary templates for interpolatory surface subdivision, we provide both spline and non-spline templates that are necessarily symmetric, due to the lack of direction-orientation in ca...

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and produce sequences of vertices fj and bj respectively. We proposed to analyze a subdivision scheme Js that blends the rules of these two refinement methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a...

In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data points. A maximum error has been determined to preserve the absolute fitting error less than a criterion and it administers the process of curv...

We propose an adaptive geometry compression method with labels based on 4-point interpolatory subdivision schemes. It can work on digital curves of arbitrary dimensions. With the geometry compression method, a digital curve is adaptively compressed into several segments with different compression levels. Each segment is a 4-point subdivision curve with a subdivision step. Labels are recorded in...