# geometry

geometry, a C++ code which performs certain geometric calculations in 2, 3 and N space.

These calculations include angles, areas, containment, distances, intersections, lengths, and volumes.

Some geometric objects can be described in a variety of ways. For instance, a line has implicit, explicit and parametric representations. The names of routines often will specify the representation used, and there are routines to convert from one representation to another.

Another useful task is the delineation of a standard geometric object. For instance, there is a routine that will return the location of the vertices of an octahedron, and others to produce a series of "equally spaced" points on a circle, ellipse, sphere, or within the interior of a triangle.

### Languages:

geometry is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Programs:

ellipse, a C++ code which performs various geometric calculations for ellipses and ellipsoids.

hypersphere, a C++ code which carries out various operations for an M-dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.

polygon, a C++ code which computes properties of an arbitrary polygon in the plane, defined by a sequence of vertices, including interior angles, area, centroid, containment of a point, convexity, diameter, distance to a point, inradius, lattice area, nearest point in set, outradius, uniform sampling.

tetrahedron, a C++ code which computes properties including the centroid, circumsphere, dihedral angles, edge lengths, face angles, face areas, insphere, quality, solid angles, and volume of a tetrahedron in 3D.

triangle, a C++ code which computes properties, including angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality, of a triangle in 2D.

### Reference:

1. Gerard Bashein, Paul Detmer,
Centroid of a Polygon,
in Graphics Gems IV,
edited by Paul Heckbert,
AP Professional, 1994,
ISBN: 0123361559,
LC: T385.G6974.
2. SF Bockman,
Generalizing the Formula for Areas of Polygons to Moments,
American Mathematical Society Monthly,
Volume 96, Number 2, February 1989, pages 131-132.
A Programmer's Geometry,
Butterworths, 1983,
ISBN: 0408012420.
4. Paulo Cezar Pinto Carvalho, Paulo Roma Cavalcanti,
Point in Polyhedron Testing Using Spherical Polygons,
in Graphics Gems V,
edited by Alan Paeth,
ISBN: 0125434553,
LC: T385.G6975.
5. Daniel Cohen,
Voxel Traversal along a 3D Line,
in Graphics Gems IV,
edited by Paul Heckbert,
AP Professional, 1994,
ISBN: 0123361559,
LC: T385.G6974.
6. Thomas Cormen, Charles Leiserson, Ronald Rivest,
Introduction to Algorithms,
MIT Press, 2001,
ISBN: 0262032937,
LC: QA76.C662.
7. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
Computational Geometry,
Springer, 2000,
ISBN: 3-540-65620-0,
LC: QA448.D38.C65.
8. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979,
ISBN13: 978-0-898711-72-1,
LC: QA214.L56.
9. James Foley, Andries vanDam, Steven Feiner, John Hughes,
Computer Graphics, Principles and Practice,
Second Edition,
ISBN: 0201848406,
LC: T385.C5735.
10. Martin Gardner,
The Mathematical Carnival,
Knopf, 1975,
ISBN: 0394494067,
LC: QA95.G286.
Signed Distance From Point To Plane,
in Graphics Gems III,
edited by David Kirk,
ISBN: 0124096735,
LC: T385.G6973.
12. Branko Gruenbaum, Geoffrey Shephard,
Pick's Theorem,
The American Mathematical Monthly,
Volume 100, Number 2, February 1993, pages 150-161.
13. John Harris, Horst Stocker,
Handbook of Mathematics and Computational Science,
Springer, 1998,
ISBN: 0-387-94746-9,
LC: QA40.S76.
14. Barry Joe,
GEOMPACK - a software package for the generation of meshes using geometric algorithms,
Volume 13, 1991, pages 325-331.
15. Anwei Liu, Barry Joe,
Quality Local Refinement of Tetrahedral Meshes Based on 8-Subtetrahedron Subdivision,
Mathematics of Computation,
Volume 65, Number 215, July 1996, pages 1183-1200.
16. Jack Kuipers,
Quaternions and Rotation Sequences,
Princeton, 1998,
ISBN: 0691102988,
LC: QA196.K85.
17. Robert Miller,
Computing the Area of a Spherical Polygon,
in Graphics Gems IV,
edited by Paul Heckbert,
ISBN: 0123361559,
LC: T385.G6974.
18. Albert Nijenhuis, Herbert Wilf,
Combinatorial Algorithms for Computers and Calculators,
Second Edition,
ISBN: 0-12-519260-6,
LC: QA164.N54.
19. Atsuyuki Okabe, Barry Boots, Kokichi Sugihara, Sung Nok Chiu,
Spatial Tesselations: Concepts and Applications of Voronoi Diagrams,
Second Edition,
Wiley, 2000,
, ISBN: 0-471-98635-6,
LC: QA278.2.O36.
20. Joseph ORourke,
Computational Geometry,
Second Edition,
Cambridge, 1998,
ISBN: 0521649765,
LC: QA448.D38.
21. Edward Saff, Arno Kuijlaars,
Distributing Many Points on a Sphere,
The Mathematical Intelligencer,
Volume 19, Number 1, 1997, pages 5-11.
22. Philip Schneider, David Eberly,
Geometric Tools for Computer Graphics,
Elsevier, 2002,
ISBN: 1558605940,
LC: T385.S334.
23. Peter Schorn, Frederick Fisher,
Testing the Convexity of a Polygon,
in Graphics Gems IV,
edited by Paul Heckbert,
AP Professional, 1994,
ISBN: 0123361559,
LC: T385.G6974.
24. Moshe Shimrat,
Algorithm 112: Position of Point Relative to Polygon,
Communications of the ACM,
Volume 5, Number 8, August 1962, page 434.
25. Kenneth Stephenson,
Introduction to Circle Packing, The Theory of Discrete Analytic Functions,
Cambridge, 2005,
ISBN: 0521823560,
LC: QA640.7S74.
26. 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.
27. Daniel Zwillinger, Steven Kokoska,
Standard Probability and Statistical Tables,
CRC Press, 2000,
ISBN: 1-58488-059-7,
LC: QA273.3.Z95.

### Source Code:

Last revised on 10 March 2020.