ASA_2011_GEOMETRY.TEX
Computational Geometry Algorithms

ASA_2011_GEOMETRY.TEX is the LaTeX source for a classroom presentation on computational geometry algorithms, presented to the class on Algorithms for Science Applications, Department of Scientific Computing, Florida State University, Spring Semester 2011.

A PDF version is available as ../../classes/asa_2011/asa_2011_geometry.pdf.

• asa_2011_geometry.tex, the LaTeX file
• big_elements.png, the elements of a triangulation.
• big_nodes.png, the nodes of a triangulation.
• car_model.png, a finite element model of a car.
• casablanca_three.png, the Casablanca image using 3 shades chosen by KMEANS
• climbing_alone.png, a lone climber.
• climbing_team.png, a climbing team.
• conforming_grid.png, a closeup of a grid on the Earth's surface.
• convex_hull_edge0.png, a PNG image of step 0 of a convex hull calculation.
• convex_hull_edge1.png, a PNG image of step 1 of a convex hull calculation.
• convex_hull_edge2.png, a PNG image of step 2 of a convex hull calculation.
• convex_hull_edge3.png, a PNG image of step 3 of a convex hull calculation.
• convex_hull_edge4.png, a PNG image of step 4 of a convex hull calculation.
• convex_hull.png, a PNG image of the resultant convex hull.
• data_hull.png a PNG image of data for a convex hull calculation.
• double_c.png, a "double C" data set.
• example_delaunay_triangulation.png a PNG image of Delaunay triangulation of the 16 nodes.
• example_nodes.png a PNG image of 16 nodes.
• example_nondelaunay_triangulation.png a PNG image of a non-Delaunay triangulation of the 16 nodes.
• fifty_points.png a PNG image of 50 2D points, sampled uniformly at random from [0,4] to [3,1].
• general_triangle_quadrule.png, a quadrature rule for a general triangle.
• fsu_logo.pdf, a PDF file of a logo.
• hand.png, an image of a hand.
• hand_outline.png a PNG image of the outline of a hand.
• hand_triangulated.png, an image of the hand polygon after triangulation.
• i18.png, a PNG image of an 18-node polygon to be triangulated.
• i18_triangulated.png, a PNG image of a triangulated 18-node polygon.
• kn57_hull.png, a PNG image of the convex hull of 57 points in 2D.
• kn57_nodes.png, a PNG image of 57 points in 2D.
• knapsack.png, an illustration of the knapsack problem.
• line_dist.png, a PNG image that illustrates the t coordinate for a point that is not on the line.
• line_perp.png, a PNG image that illustrates the s coordinate for a point that is not on the line.
• line_points.png, a PNG image that illustrates how points on a line are generated from a formula.
• linear_programming.png, an illustration of the linear programming problem.
• p08_mesh.png, a triangulated region.
• point_triangle_orientation.png, a PNG image of the problem of determining the orientation (in/on/out) of a point with respect to a triangle.
• quad_1d_errors.png, a PNG image of errors in approximating an integral over an interval using the Monte Carlo method.
• quad_1d_values.png, a PNG image of Monte Carlo approximations to an integral over an interval.
• random_walkers.png, an image of a random walk experiment.
• roulette_wheel.png, a roulette wheel.
• seamount.png, a PNG image of the surface of an underwater seamount.
• snake_polygon.png, a PNG image of a polygon to be triangulated.
• snake_polygon_triangulated.png, a PNG image of a triangulated polygon.
• teapot.png, the triangulated surface of a teapot.
• triangle_area_formula.png, a PNG image that illustrates the formula for the area of a triangle.
• triangle_centroid.png, a PNG image that illustrates the formula for the centroid of a triangle.
• triangle_distance.png, a PNG image that illustrates the problem of determining the distance from a point to a triangle.
• triangle_example1.png, a PNG image of a triangle, with vertex coordinates indicated.
• triangle_orientation.png, a PNG image that illustrates how the plus or minus sign of three line orientation values can tell you where you are in a triangle
• triangle_orientation2.png, a PNG image that illustrates how the plus, zero or minus sign of three line orientation values can tell you where you are in a triangle
• triangle_pythagoras.png, a PNG image that illustrates the use of the Pythagorean theorem to measure the length of a line segment.
• unit_triangle.png, a PNG image of a unit triangle.
• unit_triangle_quadrule.png, a quadrature rule defined in the unit triangle.
• usa_knuth.png, a graph that suggests the adjacency of the individual states of the US.

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