Algorithmic background, data structures, computational models in geometric elements. Geometric search, point-location problems, range-search problems. Convex trunk, plane problem reporting and lower boundaries, convex trunk algorithms, graham scan, Jarvis gait, QUICKHULL techniques, dynamic convex trunk, 3D convex trunk. Proximity problem, accumulation of problems, a computation prototype: element uniqueness, lower bound, close pair problem: divide and manage approach, Voronoi diagram, proximity problems solved by Voronoi diagram triangulations, planar triangulations, Delaunay triangulation, intersections, application areas, planar applications: convex polygons, intersection of line segments. 3D applications: 3D convex polyhedral intersection, intersection in half areas.