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 GNU LGPL 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_01.m the source code.
• program_01.txt the output from a run of the program.
• point_line_orientation.png a PNG image which suggests how points can be oriented with respect to a line.

PROGRAM_02 demonstrates point and triangle orientation.

• program_02.m the source code.
• program_02.txt the output from a run of the program.
• point_triangle_orientation.png a PNG image which suggests how points can be oriented with respect to a triangle.

PROGRAM_03 demonstrates barycentric coordinates.

• program_03.m the source code.
• program_03.txt the output from a run of the program.

PROGRAM_04 demonstrates sampling a triangle.

• program_04.m the source code.
• program_04.txt the output from a run of the program.

PROGRAM_05 demonstrates sampling a triangle, and displays the points.

• program_05.m the source code.
• program_05.txt the output from a run of the program.
• program_05_bad.png a PNG image of 1000 sample points generated by the "bad" scheme.
• program_05_good.png a PNG image of 1000 sample points generated by the "good" scheme.

PROGRAM_06 demonstrates Monte Carlo integration on the unit triangle.

• program_06.m the source code.
• program_06.txt the output from a run of the program.

PROGRAM_07 demonstrates Monte Carlo integration on a general triangle.

• program_07.m the source code.
• program_07.txt the output from a run of the program.

PROGRAM_08 demonstrates quadrature rule integration on the unit triangle.

• program_08.m the source code.
• program_08.txt the output from a run of the program.

PROGRAM_09 demonstrates quadrature rule integration on a general triangle.

• program_09.m the source code.
• program_09.txt the output from a run of the program.