We study the feasibility of design for a layer-deposition manufacturing process called stereolithography which w orks by controlling a vertical laser beam which when targeted on a photocurable liquid causes the liquid to harden. In order to better understand the power as well as the limitations of this manufacturing process, we de ne 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 modelled as a polygon or a polyhedron, we give algorithms that decide in On time whether or not the object can be constructed by v ertical stereolithography. If the answer is in the a rmative, the algorithm reports a description of all the orientations in which the object can be made. We then de ne a more exible model that more accurately re ects the actual capabilities of stereolithography referred to as variable-angle stereolithography and again study the class of feasible objects for this model. We give a n On time algorithm for polygons and On logn a s w ell as On time algorithms for polyhedra. We show that objects formed with variable-angle stereolithography can also be constructed using another manufacturing process known as gravity casting. F urthermore, we show that the polyhedral objects formed by v ertical 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 variable-angle stereolithography resembles a terrain with overhangs, thus initiating the study of more realistic terrains than the standard ones considered in geographic information systems. Finally, w e relate our results to the area of grasping in robotics by showing that the polygonal and polyhedral objects that can be built by v ertical stereolithography can be clamped by parallel jaw grippers with any positive sized gripper.
We study the feasibility of design for a layer-deposition manufacturing process called stereolithography which w orks by controlling a vertical laser beam which when targeted on a photocurable liquid causes the liquid to harden. In order to better understand the power as well as the limitations of this manufacturing process, we de ne 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 modelled as a polygon or a polyhedron , we give algorithms that decide in O n time whether or not the object can be constructed by v ertical stereolithography. If the answer is in the a rmative, the algorithm reports a description of all the orientations in which the object can be made. We then de ne a more exible model that more accurately re ects the actual capabilities of stereolithography referred to as variable-angle stereolithography and again study the class of feasible objects for this model. We give a n O n time algorithm for polygons and O n logn a s w ell as O n time algorithms for polyhedra. We show that objects formed with variable-angle stereolithography can also be constructed using another manufacturing process known as gravity casting. F urthermore, we show that the polyhedral objects formed by v ertical 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 variable-angle stereolithography resembles a terrain with overhangs, thus initiating the study of more realistic terrains than the standard ones considered in geographic information systems. Finally, w e relate our results to the area of grasping in robotics by showing that the polygonal and polyhedral objects that can be built by v ertical stereolithography can be clamped by parallel jaw grippers with any positive sized gripper.
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