alphahull (version 2.2)

inter: Intersection of two circumferences

Description

This function calculates the intersection of two circumferences, given their centers and radius \(c1,r1\) and \(c2,r2\), respectively.

Usage

inter(c11, c12, r1, c21, c22, r2)

Arguments

c11

X-coordinate of the center \(c1\).

c12

Y-coordinate of the center \(c1\).

r1

Radius \(r1\).

c21

X-coordinate of the center \(c2\).

c22

Y-coordinate of the center \(c2\).

r2

Radius \(r2\).

Value

A list with the following components:

n.cut

Number of intersection points (0,1,2, or Inf).

v1

If there are two intersection points, v1 is the numeric vector whose components are the coordinates of the unitary vector that has its origin in \(c1\) and it's perpendicular to the chord that joins the intersection points of the two circumferences. Otherwise, v1=(0,0)

theta1

Angle that forms v1 with the radius that joins the center \(c1\) with an intersection point.

v2

If there are two intersection points, v2 is the numeric vector whose components are the coordinates of the unitary vector that has its origin in \(c2\) and it's perpendicular to the chord that joins the intersection points of the two circumferences. Otherwise, v2=(0,0)

theta2

Angle that forms v2 with the radius that joins the center \(c2\) with an intersection point.

Details

The function inter is internally called by the function ahull.