cg_lab_triangles


cg_lab_triangles, a MATLAB code which carries out computational investigations involving triangles, for a computational geometry class.

The text of the assignment itself is available in cg_lab_triangles.pdf.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

cg_lab_triangles is available in a MATLAB version.

Related Data and Programs:

geometry, a MATLAB code which evaluates various geometric quantities.

random_data, a MATLAB code which can uniformly sample points from a variety of regions.

stroud, a MATLAB code which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

triangle_dunavant_rule, a MATLAB code which defines Dunavant rules for quadrature on a triangle.

triangle_fekete_rule, a MATLAB code which defines Fekete rules for quadrature or interpolation on a triangle.

triangle_ncc_rule, a MATLAB code which defines Newton-Cotes closed quadrature rules on a triangle.

triangle_nco_rule, a MATLAB code which defines Newton-Cotes open quadrature rules on a triangle.

triangle_wandzura_rule, a MATLAB code which defines Wandzura rules for quadrature on a triangle.

Reference:

  1. Adrian Bowyer, John Woodwark,
    A Programmer's Geometry,
    Butterworths, 1983,
    ISBN: 0408012420.
  2. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
    Computational Geometry,
    Springer, 2000,
    ISBN: 3-540-65620-0.
  3. Joseph ORourke,
    Computational Geometry,
    Second Edition,
    Cambridge, 1998,
    ISBN: 0521649765,
    LC: QA448.D38.
  4. Allen VanGelder,
    Efficient Computation of Polygon Area and Polyhedron Volume,
    in Graphics Gems V,
    edited by Alan Paeth,
    AP Professional, 1995,
    ISBN: 0125434553,
    LC: T385.G6975.

Examples:

PROGRAM_01 demonstrates point and line orientation.

PROGRAM_02 demonstrates point and triangle orientation.

PROGRAM_03 demonstrates barycentric coordinates.

PROGRAM_04 demonstrates sampling a triangle.

PROGRAM_05 demonstrates sampling a triangle, and displays the points.

PROGRAM_06 demonstrates Monte Carlo integration on the unit triangle.

PROGRAM_07 demonstrates Monte Carlo integration on a general triangle.

PROGRAM_08 demonstrates quadrature rule integration on the unit triangle.

PROGRAM_09 demonstrates quadrature rule integration on a general triangle.


Last revised on 03 February 2007.