Volume estimation of biomedical objects described by multiple sets of non-trimmed Bézier triangles

Abstract

Estimating the volume of a 3D model of an object is an actual task in many scientific and engineering fields (for example, CAD systems, biomedical engineering tasks etc.). Spline surfaces is one of the most powerful and flexible methods used to describe a 3D model. At the same time, it is rather difficult to estimate the volume of an object described by spline surfaces. A model of a Bézier triangle is a simple type of a spline surface, but it is practically advantageous. This paper describes a method of estimating the volume for 3D objects that are described by a set of Bézier triangles. The proposed method was tested on 3D models of objects of biomedical origin. A theorem is presented in this paper for volume estimation, based on different properties of researched models, acquired by a projection of a set vertices of a Bézier triangle onto a coordinate system axis. The proposed approach is based on using methods of differential geometry: surface integrals of scalar fields, Euler’s integral of the first kind and Beta functions. Experimental results prove the accuracy of presented theorems. The proposed method can be successfully used to calculate the volume of different 3D models, including objects of biomedical origin.