1997
Feasibility of design in stereolithography
Publication
Publication
Algorithmica , Volume 19  Issue 1 p. 61 83
We study the feasibility of design for a layerdeposition manufacturing process called stereolithography which works by controlling a vertical laser beam which when targeted on a photocurable liquid causes the liquid to harden. In order to understand the power as well as the limitations of this manufacturing process better, we define a mathematical model of stereolithography (referred to as vertical stereolithography) and analyze the class of objects that can be constructed under the assumptions of the model. Given an object (modeled as a polygon or a polyhedron), we give algorithms that decide in O(n) time (where n is the number of vertices in the polygon or polyhedron) whether or not the object can be constructed by vertical stereolithography. If the answer is in the affirmative, the algorithm reports a description of all the orientations in which the object can be made. We also show that the objects built with vertical stereolithography are precisely those that can be made with a 3axis NC machine. We then define a more flexible model that more accurately reflects the actual capabilities of stereolithography (referred to as variableangle stereolithography) and again study the class of feasible objects for this model. We give an O(n)time algorithm for polygons and O(n log n) as well as O(n)time algorithms for polyhedra. We show that objects formed with variableangle stereolithography can also be constructed using another manufacturing process known as gravity casting. Furthermore, we show that the polyhedral objects formed by vertical stereolithography are closely related to polyhedral terrains which are important structures in geographic information systems (GIS) and computational geometry. In fact, an object built with variableangle stereolithography resembles a terrain with overhangs, thus initiating the study of more realistic terrains than the standard ones considered in geographic information systems. Finally, we relate our results to the area of grasping in robotics by showing that the polygonal and polyhedral objects that can be built by vertical stereolithography can be clamped by parallel jaw grippers with any positivesized gripper.
Additional Metadata  

3Axis NCmachine, Algorithms, Computational geometry, Computeraided design, Computeraided manufacturing, Geographic information systems, Grasping, Gravity casting, Manufacturing, Polygon, Polyhedra, Polyhedral terrains, Robotics, Stereolithography  
doi.org/10.1007/PL00014421  
Algorithmica  
Organisation  School of Computer Science 
Asberg, B. (B.), Blanco, G. (G.), Bose, P, GarciaLopez, J. (J.), Overmars, M. (M.), Toussaint, G. (G.), … Zhu, B. (B.). (1997). Feasibility of design in stereolithography. Algorithmica, 19(1), 61–83. doi:10.1007/PL00014421
