A mathematical description of layered manufacturing fabrication

This study is attempted to use a mathematical definition to describe the principles of Layer Manufacturing Processing. The concept of model decomposition (layered subtraction for 3D model slicing) and material accumulation (layered addition for prototyping fabrication) and the associated sequence function and sequence potential to explain and define the layered manufacturing processing is presented. In the mathematical description, a 3D CAD model is graphically represented by a set of points collected within the bounded surfaces. In addition to its geometric feature, a processing sequence indicator is also assigned to each point as an attribute to associate with its slicing and fabricating sequence. Model decomposition slices the collected points into a series of point sets according to their sequence indicator, and material accumulation processes the layered fabrication by stacking the point sets to form the designed object. A scalar field function is used to express the variation of the sequence indicators for the selected point sets and to define iso-sequence planes. The iso-sequence planes are the processing layers consisting of all points with the same sequence indicator. Material accumulation is conducted in the gradient direction of each iso-sequence plane. Example of using proposed scalar field function and the iso-sequence plane for flat and no-flat layered prototyping processing is also presented.