How to calculate an irregular shape area?

Dear all,

I have a shape model in 3D space. I project it onto a 2D plane. Now I have to calculate the area of its projection area. Since the area is irregular, how can I calculate it? Is there any method in matlab can help me to make it?

Many thanks for your help.

Best wishes Wenlong

[Walter Roberson]

polyarea() ?

[Izaro]

I have the same problem. How do you solve it?

Thanks

[Mathieu NOE]

hello

as suggested by @Walter Roberson polyarea does the job even for irregular or concave shapes

Polyarea function concave or convex - MATLAB Answers - MATLAB Central

Answer 1

[Karan Singh]

Hi Wenlong and Izaro,

The answer is already covered in the comments above; however, I can assume that you might be working with different types of projections. A few come to mind:

• If your projection is a scattered set of plots, you can use "alphaShape" to create a boundary and then compute the area. alphaShape
• If it is a single polygon, you can use "boundary" and then "polyarea." polyarea
• If it contains holes, use "polyshape" and "rmholes" to remove holes and get the area. Maybe useful depends on cases.

[x, y, z] = sphere(50);
vertices_3d = [x(:), y(:), z(:)];

vertices_2d = vertices_3d(:, 1:2); % projection

shp = alphaShape(vertices_2d, 1); %alphaShape

Warning: Duplicate data points have been detected and removed.

area_alpha = area(shp);

k = boundary(vertices_2d(:,1), vertices_2d(:,2), 0.8);  % polyarea
boundary_vertices = vertices_2d(k, :);
area_poly = polyarea(boundary_vertices(:,1), boundary_vertices(:,2));

fprintf('Area via alphaShape: %.4f\n', area_alpha);

Area via alphaShape: 3.1333

fprintf('Area via boundary: %.4f\n', area_poly);

Area via boundary: 3.1333