On the Construction of Planar Embedding for a Class of Orthogonal Polyhedra

2D-representations of 3D digital objects find versatile applications to computer vision, robotics, medical imaging, and in discrete geometry. This work presents an algorithm for constructing a planar embedding with only straight-line edges for a general non-intersecting orthogonal polyhedron that has genus 0. We discover certain characterizations of vertices and edges of a polyhedron that lead to efficient graph-drawing on the 2D plane. The original orthogonal polyhedron can be fully reconstructed from this graph provided the information regarding the coordinates of vertices, are preserved. The time complexity of the proposed embedding is linear in the number of edges of the orthogonal polyhedron.