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 decoll1Position (layered subtraction for 3D model slicing) and material accumulation (layered addition for <prot()typjng fabrication) and the associated sequence function and seql.lence· 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.