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Area overlapped between ​​a circle and a rectangle, when the center of the circle is included

작성자 Uploader : simplelife 작성일 Upload Date: 2019-03-07변경일 Update Date: 2019-03-11조회수 View : 500

Calculation of the area overlapped between ​​a circle of radius r and a rectangle, as shown in the figure.

The area S to be obtained consists of a rectangle, two right-angled triangles and a sector.

1. Area of the ​​rectangle
  Sr = dx*dy

2. Area of ​​right triangles
  Sty = (1/2)*dx*(r^2-dx^2)^(1/2)
  Stx = (1/2)*dy*(r^2-dy^2)^(1/2)

3. Area of the sector
  Center angle of the sector : A = 360-90-arccos(dy/r)-arccos(dx/r)
  Ss = π*r^2*(A/360)

Therefore, the total area is as follows.

S = dx*dy+(1/2)*dx*(r^2-dx^2)^(1/2)+(1/2)*dy*(r^2-dy^2)^(1/2)+π*r^2*((270-arccos(dy/r)-arccos(dx/r))/360)  

*** 참고문헌[References] ***
S = dx*dy+(1/2)*(dx*(r^2-dx^2)^(1/2)+dy*(r^2-dy^2)^(1/2))+π*r^2*((270-arccos(dy/r)-arccos(dx/r))/360)
변수명 Variable 변수값 Value 변 수 설 명 Description of the variable


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