# ellipse

Computes the area of the ellipse segment determined by the intersection of an ellipse and a line parallel to the reference line.

Controller: **CodeCogs**

**Contents**

## Dependents

## Interface

C++

## Ellipse

doubleellipse( | double | a | |

double | b | ||

double | h | )[inline] |

## Solution

Let us consider an ellipse with semiaxis*a*parallel to the reference line and semiaxis

*b*perpendicular to this reference line, with the equation: The center of the ellipse is at . We also consider a line parallel to the reference line at a distance from it. The filled shape in the next image represents the area we must find.

##### MISSING IMAGE!

**1/ellipse01-378.jpg** cannot be found in /users/1/ellipse01-378.jpg. Please contact the submission author.

##### MISSING IMAGE!

**1/ellipse02-378.jpg** cannot be found in /users/1/ellipse02-378.jpg. Please contact the submission author.

Purchase a Licence for more information.

### Example 1

#include <codecogs/maths/geometry/area/ellipse.h> #include <stdio.h> int main() { // the value of the height double h = 0.973; // the length of the semiaxes for the first ellipse (a>b) double a1 = 1.925, b1 = 1.309; // display the lenghts of the semiaxes for the first ellipse and the value of the height printf("a1 = %.3lf\nb1 = %.3lf\nh = %.3lf\n\n", a1, b1, h); // display the area for the first ellipse printf("Area is %.5lf\n\n",Geometry::Area::ellipse(a1, b1, h)); // the length of the semiaxes for the second ellipse (a<b) double a2 = 1.125, b2 = 2.345; // display the lenghts of the semiaxes for the second ellipse and the value of the height printf("a2 = %.3lf\nb2 = %.3lf\nh = %.3lf\n\n", a2, b2, h); // display the area for the first ellipse printf("Area is %.5lf\n",Geometry::Area::ellipse(a2, b2, h)); return 0; }

**Output:**a1 = 1.925 b1 = 1.309 h = 0.973 Area is 2.67888 a2 = 1.125 b2 = 2.345 h = 0.973 Area is 1.24346

### Parameters

a semiaxis of the ellipse parallel to the reference line b semiaxis of the ellipse perpendicular to the reference line h the distance between line *d*and the reference line

### Returns

- The area of the desired shape.

### Authors

*Lucian Bentea, Eduard Bentea (September 2006)*

##### Source Code

Source code is available when you buy a Commercial licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.