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# Real Circles ( real_circle )

Definition

An instance C of the data type real_circle is an oriented circle in the plane passing through three points p1, p2, p3. The orientation of C is equal to the orientation of the three defining points, i.e. orientation(p1, p2, p3). If |   {p1, p2, p3}   |= 1 C is the empty circle with center p1. If p1, p2, p3 are collinear C is a straight line passing through p1, p2 and p3 in this order and the center of C is undefined.

#include < LEDA/geo/real_circle.h >

Types

 real_circle::coord_type the coordinate type (real). real_circle::point_type the point type (real_point).

Creation

 real_circle C(const real_point& a, const real_point& b, const real_point& c) introduces a variable C of type real_circle. C is initialized to the oriented circle through points a, b, and c. real_circle C(const real_point& a, const real_point& b) introduces a variable C of type real_circle. C is initialized to the counter-clockwise oriented circle with center a passing through b. real_circle C(const real_point& a) introduces a variable C of type real_circle. C is initialized to the trivial circle with center a. real_circle C introduces a variable C of type real_circle. C is initialized to the trivial circle with center (0, 0). real_circle C(const real_point& c, real r) introduces a variable C of type real_circle. C is initialized to the circle with center c and radius r with positive (i.e. counter-clockwise) orientation. real_circle C(real x, real y, real r) introduces a variable C of type real_circle. C is initialized to the circle with center (x, y) and radius r with positive (i.e. counter-clockwise) orientation. real_circle C(const circle& c, int prec = 0) introduces a variable C of type real_circle initialized to the circle c. (The second argument is for compatibility with rat_circle.) real_circle C(const rat_circle& c) introduces a variable C of type real_circle initialized to the circle c.

Operations

 real_point C.center() returns the center of C. Precondition The orientation of C is not 0. real C.radius() returns the radius of C. Precondition The orientation of C is not 0. real C.sqr_radius() returns the squared radius of C. Precondition The orientation of C is not 0. real_point C.point1() returns p1. real_point C.point2() returns p2. real_point C.point3() returns p3. bool C.is_degenerate() returns true if the defining points are collinear. bool C.is_trivial() returns true if C has radius zero. bool C.is_line() returns true if C is a line. real_line C.to_line() returns line(point1(), point3()). int C.orientation() returns the orientation of C. int C.side_of(const real_point& p) returns -1, +1, or 0 if p lies right of, left of, or on C respectively. bool C.inside(const real_point& p) returns true iff p lies inside of C. bool C.outside(const real_point& p) returns true iff p lies outside of C. bool C.contains(const real_point& p) returns true iff p lies on C. real_circle C.translate(real dx, real dy) returns C translated by vector (dx, dy). real_circle C.translate(const real_vector& v) returns C translated by vector v. real_circle C + const real_vector& v returns C translated by vector v. real_circle C - const real_vector& v returns C translated by vector - v. real_circle C.rotate90(const real_point& q, int i=1) returns C rotated about q by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise. real_circle C.reflect(const real_point& p, const real_point& q) returns C reflected across the straight line passing through p and q. real_circle C.reflect(const real_point& p) returns C reflected across point p. real_circle C.reverse() returns C reversed. list C.intersection(const real_circle& D) returns C D as a list of points. list C.intersection(const real_line& l) returns C l as a list of (zero, one, or two) points sorted along l. list C.intersection(const real_segment& s) returns C s as a list of (zero, one, or two) points sorted along s. real_segment C.left_tangent(const real_point& p) returns the line segment starting in p tangent to C and left of segment [p,C.center()]. real_segment C.right_tangent(const real_point& p) returns the line segment starting in p tangent to C and right of segment [p,C.center()]. real C.distance(const real_point& p) returns the distance between C and p. real C.sqr_dist(const real_point& p) returns the squared distance between C and p. real C.distance(const real_line& l) returns the distance between C and l. real C.distance(const real_circle& D) returns the distance between C and D. bool radical_axis(const real_circle& C1, const real_circle& C2, real_line& rad_axis) if the radical axis for C1 and C2 exists, it is assigned to rad_axis and true is returned; otherwise the result is false.

Next: Real Triangles ( real_triangle Up: Basic Data Types for Previous: Straight Real Lines (   Contents   Index