CG_2007
Computational Geometry Lab Exercises

CG_2007 is the home page for a set of laboratory exercises focusing on computational geometry, in particular triangles, tetrahedrons, meshes, the Monte Carlo method, basis functions, mapping, quadrature, and searching.

The labs were prepared for the Department of Scientific Computing at Florida State University, Fall Session 2007.

• cg_lab_barycentric_tetrahedrons.pdf, explains the use of barycentric coordinates in a tetrahedron;
• cg_lab_barycentric_triangles.pdf, explains the use of barycentric coordinates in a tetrahedron;
• cg_lab_fem.pdf, discusses the finite element method;
• cg_lab_fem_basis_tetrahedron.pdf, shows how to define finite element basis functions for a tetrahedron;
• cg_lab_fem_basis_triangle.pdf, shows how to define finite element basis functions for a triangle;
• cg_lab_fem_basis_triangulation.pdf, shows how a basis function is defined over a mesh of triangles;
• cg_lab_mapping_tetrahedrons.pdf, shows how to map one tetrahedron to another, which is a key to the method of reference elements;
• cg_lab_mapping_triangles.pdf, shows how to map one triangle to another, which is a key to the method of reference elements;
• cg_lab_mesh_function_triangulation.pdf, shows how to define, evaluate, differentiate, integrate and display a finite element function defined on a triangular finite element mesh;
• cg_lab_misc.pdf, covers some miscellaneous topics.
• cg_lab_monte_carlo_tetrahedrons.pdf, discusses the Monte Carlo method implemented on a mesh of tetrahedrons;
• cg_lab_monte_carlo_triangles.pdf, discusses the Monte Carlo method implemented on a triangle;
• cg_lab_monte_carlo_triangulation.pdf, discusses the Monte Carlo method implemented on a mesh of triangles;
• cg_lab_quadrature.pdf, discusses quadrature, the approximation of integrals of functions defined over a region that has been triangulated;
• cg_lab_search_tet_mesh.pdf, discusses searching for a point in a mesh of tetrahedrons;
• cg_lab_search_triangulation.pdf, discusses searching for a point in a mesh of triangles;
• cg_lab_tetrahedrons.pdf, discusses geometric properties of tetrahedrons;
• cg_lab_triangles.pdf, discusses geometric properties of triangles;
• cg_lab_triangulations.pdf, discusses the creation and use of meshes of triangles;