next up previous contents index
Next: Point on Rational Circle Up: Basic Data Types for Previous: Transformation ( TRANSFORM )   Contents   Index


Point Generators ( point generators )

All generators are available for point, rat_point, real_point, d3_point, and d3_rat_point. We use POINT to stand for any of these classes. The corresponding header files are called random_point.h, random_rat_point.h, random_real_point.h, random_d3_point.h, and random_d3_rat_point.h, respectively. These header files are included in the corresponding kernel header files, e.g., random_rat_point.h is part of rat_kernel.h.

We use the following naming conventions: square, circle, segment, and disk refer to two-dimensional objects (even in 3d) and cube, ball, and sphere refer to full-dimensional objects, i.e, in 2d cube and square, ball and disk, and circle and sphere are synonymous.

void random_point_in_square(POINT& p, int maxc)
    returns a point whose x and y-coordinates are random integers in [- maxc..maxc]. The z-coordinate is zero.

void random_points_in_square(int n, int maxc, list<POINT>& L)
    returns a list L of n points ... .

void random_point_in_unit_square(POINT& p, int D = (1«30) - 1)
    returns a point whose coordinates are random rationals of the form i/D where i is a random integer in the range [0..D]. The default value of D is 230 - 1.

void random_points_in_unit_square(int n, int D, list<POINT>& L)
    returns a list L of n points ... .

void random_points_in_unit_square(int n, list<POINT>& L)
    returns a list L of n points ... . The default value of D is used.

void random_point_in_cube(POINT& p, int maxc)
    returns a point whose coordinates are random integers in [- maxc..maxc]. In 2d this function is equivalent to random_point_in_square.

void random_points_in_cube(int n, int maxc, list<POINT>& L)
    returns a list L of n points ... .

void random_point_in_unit_cube(POINT& p, int D = (1«30) - 1)
    returns a point whose coordinates are random rationals of the form i/D where i is a random integer in the range [0..D]. The default value of D is 230 - 1.

void random_points_in_unit_cube(int n, int D, list<POINT>& L)
    returns a list L of n points ... .

void random_points_in_unit_cube(int n, list<POINT>& L)
    as above, but the default value of D is used.

void random_point_in_disc(POINT& p, int R)
    returns a random point with integer x and y-coordinates in the disc with radius R centered at the origin. The z-coordinate is zero.
Precondition R < = 230.

void random_points_in_disc(int n, int R, list<POINT>& L)
    returns a list L of n points ... .

void random_point_in_unit_disc(POINT& p, int D = (1«30) - 1)
    returns a point in the unit disc whose coordinates are quotients with denominator D. The default value of D is 230 - 1.

void random_points_in_unit_disc(int n, int D, list<POINT>& L)
    returns a list L of n points ... .

void random_points_in_unit_disc(int n, list<POINT>& L)
    returns a list L of n points ... . The default value of D is used.

void random_point_in_ball(POINT& p, int R)
    returns a random point with integer coordinates in the ball with radius R centered at the origin. In 2d this function is equivalent to random_point_in_disc.
Precondition R < = 230.

void random_points_in_ball(int n, int R, list<POINT>& L)
    returns a list L of n points ... .

void random_point_in_unit_ball(POINT& p, int D = (1«30) - 1)
    returns a point in the unit ball whose coordinates are quotients with denominator D. The default value of D is 230 - 1.

void random_points_in_unit_ball(int n, int D, list<POINT>& L)
    returns a list L of n points ... .

void random_points_in_unit_ball(int n, list<POINT>& L)
    returns a list L of n points ... . The default value of D is used.

void random_point_near_circle(POINT& p, int R)
    returns a random point with integer coordinates that lies close to the circle with radius R centered at the origin.

void random_points_near_circle(int n, int R, list<POINT>& L)
    returns a list L of n points ... .

void random_point_near_unit_circle(POINT& p, int D = (1«30) - 1)
    returns a point close to the unit circle whose coordinates are quotients with denominator D. The default value of D is 230 - 1.

void random_points_near_unit_circle(int n, int D, list<POINT>& L)
    returns a list L of n points ... .

void random_points_near_unit_circle(int n, list<POINT>& L)
    returns a list L of n points ... . The default value of D is used.

void random_point_near_sphere(POINT& p, int R)
    returns a point with integer coordinates close to the sphere with radius R centered at the origin.

void random_points_near_sphere(int n, int R, list<POINT>& L)
    returns a list L of n points ... .

void random_point_near_unit_sphere(POINT& p, int D = (1«30) - 1)
    returns a point close to the unit sphere whose coordinates are quotients with denominator D. In 2d this function is equivalent to point_near_unit_circle.

void random_points_near_unit_sphere(int n, int D, list<POINT>& L)
    returns a list L of n points ... .

void random_points_near_unit_sphere(int n, list<POINT>& L)
    returns a list L of n points ... . The default value of D is used.

Wit the rational kernel the functions _on_circle are guaranteed to produce points that lie precisely on the specified circle. With the floating point kernel the functions are equivalent to the _near_circle functions.

void random_point_on_circle(POINT& p, int R, int C = 1000000)
    returns a random point with integer coordinates that lies on the circle with radius R centered at the origin. The point is chosen from a set of at least C candidates.

void random_points_on_circle(int n, int R, list<POINT>& L, int C = 1000000)
    returns a list L of n points ... .

void random_point_on_unit_circle(POINT& p, int C = 1000000)
    returns a point on the unit circle. The point is chosen from a set of at least C candidates.

void random_points_on_unit_circle(int n, list<POINT>& L, int C = 1000000)
    returns a list L of n points ... .

void random_point_on_sphere(POINT& p, int R)
    same as random_point_near_sphere.

void random_points_on_sphere(int n, int R, list<POINT>& L)
    returns a list L of n points ... .

void random_point_on_unit_sphere(POINT& p, int D = (1«30) - 1)
    same as random_point_near_unit_sphere.

void random_points_on_unit_sphere(int n, int D, list<POINT>& L)
    returns a list L of n points ... .

void random_points_on_unit_sphere(int n, list<POINT>& L)
    returns a list L of n points ... . The default value of D is used.

void random_point_on_segment(POINT& p, SEGMENT s)
    generates a random point on s.

void random_points_on_segment(SEGMENT s, int n, list<POINT>& L)
    generates a list L of n points ... .

void points_on_segment(SEGMENT s, int n, list<POINT>& L)
    generates a list L of n equally spaced points on s.

void random_point_on_paraboloid(POINT& p, int maxc)
    returns a point (x, y, z) with x and y random integers in the range [- maxc..maxc], and z = 0.004*(x*x + y*y) - 1.25*maxc. The function does not make sense in 2d.

void random_points_on_paraboloid(int n, int maxc, list<POINT>& L)
    returns a list L of n points ... .

void lattice_points(int n, int maxc, list<POINT>& L)
    returns a list L of approximately n points. The points have integer coordinates id /maxc for an appropriately chosen d and - maxc/d < = i < = maxc/d.

void random_points_on_diagonal(int n, int maxc, list<POINT>& L)
    generates n points on the diagonal whose coordinates are random integer in the range from - maxc to maxc.


next up previous contents index
Next: Point on Rational Circle Up: Basic Data Types for Previous: Transformation ( TRANSFORM )   Contents   Index
root 2008-01-09