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Unformatted text preview: Introduction Common intersection computation Linear programming in 2D Casting a polyhedron Computational Geometry Lecture 5: Casting a polyhedron Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D CAD/CAM systems CAD/CAM systems allow you to design objects and test how they can be constructed Many objects are constructed used a mold Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D Casting Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D Casting A general question: Given an object, can it be made with a particular design process? For casting, can the object be removed from its mold without breaking the cast? Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D Casting Objects to be made are 3D polyhedra Its boundary is like a planar graph, but the coordinates of vertices are 3D Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D Casting in 2D First the 2D version: can we remove a 2D polygon from a mold? Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D Casting in 2D Certain removal directions may be good while others are not Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D Casting in 2D What top facet should we use? When can we even begin to move the object out? What kind of movements do we allow? An edge of the polygon should not directly run into the touching mold edge Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D Casting in 2D Assume the top facet fixed; we can try all An edge of the polygon should not directly run into the touching mold edge Let us consider translations only Computational Geometry Lecture 5: Casting a polyhedron Introduction Common intersection computation Linear programming in 2D Automated manufacturing Casting in 2D Casting in 2D Observe: For a given top facet, if the object can be translated over some (small) distance, then it can be translated all the way out Consider a point p that at first translates away from its mold side, but later runs into the mold ......
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This note was uploaded on 05/27/2011 for the course CIS 4930 taught by Professor Staff during the Fall '08 term at University of Florida.
 Fall '08
 Staff

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