Interface

#include <codecogs/geometry/area/circle.h>

using namespace Geometry::Area;

	double	circle (double r, double h)[inline] Computes the area of the circular segment within a circle tangent to a reference line.
	Real	cc_circle (Real r, Real h) This function is available as a Microsoft Excel add-in.

---

Function Documentation

This module computes the area of the circular segment formed between a circle tangent to a reference line and a line found at a given distance from this reference line.

The various cases are described by the images given in the following documentation, where the area which we want to compute is that of the filled shape.

Solution

Consider an orthogonal coordinate system and a circle so that there exists with on the x-axis. Also let be parallel to the x-axis so that the distance from it to the x-axis is and .

Let be the area which we must determine. Based on the relation between and we get the following cases:

1)

Further information available when you purchase a licence.

2)

Because , we find the solution:

(7)

3)

Further information available when you purchase a licence.

4)

Because , the solution is:

(14)

Output:

r = 2.5
 
h = 0.0   Area = 0.000
h = 0.5   Area = 1.022
h = 1.0   Area = 2.796
h = 1.5   Area = 4.954
h = 2.0   Area = 7.334
h = 2.5   Area = 9.817
h = 3.0   Area = 12.301
h = 3.5   Area = 14.681
h = 4.0   Area = 16.839
h = 4.5   Area = 18.613
h = 5.0   Area = 19.635
h = 5.5   Area = 19.635

Example:

#include <codecogs/geometry/area/circle.h>
#include <stdio.h>
 
int main()
{
  // the length of the radius
  double r = 2.5;
 
  // display the lenghts of the radius
  printf("r = %.1lf\n\n", r);
 
  // display the area for different values of h
  for (double h = 0; h < 5.6; h += 0.5)
  printf("h = %.1lf   Area = %.3lf\n", h, 
  Geometry::Area::circle(r, h));
 
  return 0;
}

Parameters:

r	the radius of the circle
h	the distance between line and the reference line

Returns:

The value of the desired area.

Authors:

Eduard Bentea (September 2006)

Source Code:

- To get code register with CodeCogs. Already a Member, then Login.