Mid-surfaces of profile-based freeforms for mold design

Mid-surfaces of complex thin objects are commonly used in CAD applications for the analysis of casting and injection molding. However, geometrical rep resentation in CAD typically takes the form of a solid representation rathe r than a mid-surface; therefore, a process for extracting the mid-surface i s essential. Contemporary methods for extracting mid-surfaces are based on numerical computations using offsetting techniques or Voronoi diagram proce sses where the data is discrete and piecewise linear These algorithms usual ly have high computational complexity, and their accuracy is not guaranteed . Furthermore, the geometry and topology of the object are not always prese rved. To overcome these problems, this paper proposes a new approach for ex tracting a mid-surface from a freeform thin object. The proposed method mat ching technique in which a nonlinear optimization function is defined and s olved reduces the mid-surface problem into a parametrization problem that i s based on a according to mid-surface criteria. Then, the resulting mid-sur face is dictated by a reparametrization process. The algorithm is implement ed for free form ruled, swept, and rotational surfaces, that are commonly u sed in engineering products. Reducing the problem to the profile curves of these surfaces alleviates the computational complexity of the 3D case and r estricts it to a 2D case. Error is controlled globally through an iterative refinement process that utilizes continuous symbolic computations on the p arametric representation The feasibility of the proposed method is demonstr ated through several examples.