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matlabareasurface

MATLAB: How to find area of an arbitrary surface in a 2d closed shape

I have a closed 2d surface as below:

r=1+0.1*sin(5*theta)+a*sin(6*theta);
x=r.*cos(theta);
y=r.*sin(theta);
plot(x,y);

I was wondering what would be the most efficient way to find its area?

Solution

  • From MATLAB documentation: http://www.mathworks.com/help/matlab/ref/polyarea.html

    You can use polyarea

    Sintax

    A = polyarea(X,Y)
A = polyarea(X,Y,dim)

    Description

    A = polyarea(X,Y) returns the area of the polygon specified by the vertices in the vectors X and Y.

    If X and Y are matrices of the same size, then polyarea returns the area of polygons defined by the columns X and Y.

    If X and Y are multidimensional arrays, polyarea returns the area of the polygons in the first nonsingleton dimension of X and Y.

    A = polyarea(X,Y,dim) operates along the dimension specified by scalar dim.

    Example

    L = linspace(0,2.*pi,9);
xv = 1.2*cos(L)';
yv = 1.2*sin(L)';

xv = [xv ; xv(1)];
yv = [yv ; yv(1)];

A = polyarea(xv,yv)

// Result A = 4.0729

    plot(xv,yv);
title(['Area = ' num2str(A)])
axis image

    enter image description here