Algorithmic Solutions > LEDA > LEDA Guide > Geometry > Generators for Geometric Objects

## Generators for Geometric Objects

There is a frequent need to generate geometric objects, random or otherwise.

### 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

There are three generators for 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

Data Types for 2D Geometry

Data Types for 3-D Geometry

Writing Kernel Independent Code

Geometry

Advanced Data types for 2-D geometry

Geometry Algorithms

GeoWin

Manual Entries:

Manual Page Point Generators

Manual Page Polygon