Ray-shooting and isotopy classes of lines in 3-dimensional space
Preprocess n triangles so as to efficiently answer the query: “Given a ray, which is the first triangle hit?” (Ray-shooting problem). We discuss the ray-shooting problem for both disjoint and non-disjoint triangles and several space/time trade offs.
Efficiently detect the first face hit by any ray in a set of axis-oriented polyhedra.
Preprocess n lines (segments) so as to efficiently answer the query “Given 2 lines, is it possible to move one into the other without crossing any of the initial lines (segments)?” (Isotopy problem). If the movement is possible produce an explicit representation of it.
Construct the arrangement generated by n intersecting triangles in 3-space in an output-sensitive way, with a subquadratic overhead term.
Count the number of pairs of intersecting lines in a set of n lines in space.
KeywordsComputational Geometry Query Point Query Time Hyperplane Arrangement Isotopy Class
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