Generators for Geometric Objects

Generators for Random Points

There are generators for random points in squares, in discs, near circles, and on circles. For each generator there is a version that generates a single point and a version that generates a list of points. See the Manual Page Point Generators for details.

All generators are available for point, rat_point, d3_point, and d3_rat_point.

Example of Generators for Random Points

Generating Polygons

	POLYGON reg_n_gon(int n,CIRCLE C, double epsilon);
	POLYGON n_gon(int n, CIRCLE C, double epsilon);
	POLYGON hilbert(int n, RAT_TYPE x1, RAT_TYPE y1, RAT_TYPE x2, RAT_TYPE y2);

The first generates a regular n-gon. With the rational kernel the vertices of the n-gon are guaranteed to lie on the circle, with the floating point kernel they are only guaranteed to lie near C.
The second generator generates a (nearly) regular n-gon whose vertices lie near the circle C. For the floating point kernel both generators are equivalent. For the rational kernel the second function generates an n-gon with floating point arithmetic and then converts the resulting polygon to a rat_polygon.
The last generator generates the Hilbert polygon of order n within the rectangle with boundary (x1, y1) and (x2, y2).

We use the notation POLYGON (CIRCLE) to indicate that the algorithms work both for polygon (circle) and rat_polygon (rat_circle). RAT_TYPE is double for the floating point kernel and Rational for the rational kernel. (More information on Writing Kernel Independent Code.)

Example of Generators for Polygons

See also:

Data Types for 2D Geometry

Data Types for 3-D Geometry

Linear Lists

Writing Kernel Independent Code

Geometry

Advanced Data types for 2-D geometry

Geometry Algorithms

GeoWin

Manual Entries:

Manual Page Point Generators

Manual Page Polygon