Date of Award


Document Type

Open Access Thesis




College of Arts and Sciences

First Advisor

Peter Binev


The primary goal of our work is to establish a method to relate simple measures to a given set of moments. We calculate the moments of squares via linear polynomial weight measures and straight line cuts and use this to calculate the centre of mass of the square. The one-to-one correspondence that is found is needed to represent surfaces with gaps, which can estimate arbitrary measures on squares. From this, a subdivision scheme is developed, which successively quadrisects squares and uses the relation to estimate the new measures in order to provide a good representation of the original surface. One application of this work is for processing point clouds and their related surfaces.

Included in

Mathematics Commons