Pooling transient solutions of time-dependent heat equation, a domain decomposition problem is addressed. Using the connection between heat equation and random walk in a discrete lattice, an apparatus for feature guided non-linear measuring of the space is devised. Using this measure, a complex 3D volume is decomposed in order to aid additive manufacturing, which is one of the advanced processes to make a 3D object. In the case that the 3D object is composed of several attachments around a main body, the cut surface (or the gluing surface) separating (or gluing) the main body and an attachment is curved due to rounding effect of the heat equation. This behavior can be manipulated by allowing designer imposed constraints; nevertheless, this may be an advantage in terms of distributing stress. The central body can be honeycombed or hollowed to reduce the weight, if needed.