Two ways of displaying an object represented in linear octtree form are presented. The object can have inherited attributes (such as gray-level, color or texture), each of which is represented by a field in the corresponding linear octtree node. The first method evaluates the surface of the object and, optionally, also all the attribute-to-attribute interfaces; a special field (BLOCKBIT) identifying the presence or absence of a node of the same size and/or attribute in each principal direction, enables us to solve, in most cases, the visibility problem so that only those octant-faces which are finally visible are indeed painted on the screen. The second method displays the object directly node by node, so that three faces are always displayed in a back-to-front order. The first method enables one to display the external surface as well as all attribute-to-attribute interfaces by applying the border algorithm only once; the second method enables one to display an object from external as well as internal view points, thus simulating a clipping capability.