Mathematical modeling and 3D visualization of binary trees with a minimum of self-intersections

Abstract

In the paper a new algorithm for constructing a 3d space-filling binary tree composed from tubes of circular cross sections is developed for the case when the lengths, diameters, branching angles and the number of generations are initially set. A practical implementation of the algorithm for 3d models of plain bifurcations with total minimum number of intersections is presented. The algorithm is adapted for simulations of vascular systems, computations of hemodynamic parameters and their visualization on the model.