The article is devoted to the two-dimensional and three-dimensional orthogonal polyhedrons outlines obtaining algorithms. An orthogonal polyhedron is a geometric figure representing the union of non-overlapping orthogonal objects (rectangles or parallelepipeds in the two-dimensional or three-dimensional case, respectively) with a fixed position relative to each other, considered as a single whole object. The need to use the orthogonal polyhedrons as individual objects arises, in particular, during solving certain resource allocation problems. The popular application program interfaces for rendering graphic images such as OpenGL and DirectX do not provide the ability to visualize only the outline of the union instead of all the edges of its objects. The developed algorithms are based on the idea of searching and cutting off segments located on edges belonging to several orthogonal objects belonging to the considered orthogonal polyhedron. The described algorithms provide the possibility of visualization of arbitrary orthogonal polyhedrons, including those containing any holes. These algorithms are implemented in the developed applied software intended to optimize the solution of resource allocation problems of any dimension, including the orthogonal packing and rectangular cutting problems.