Estimating Area Enclosed by Multiple Arcs and Discrete Points in 3D

Hello MATLAB Community,

I am working on a problem where I need to estimate the area enclosed by multiple arcs and a set of discrete points in a 3D space using MATLAB. Each arc is defined by its center, radius, orientation vectors, and rotation angle. The goal is to compute the cumulative minimum distance between each discrete point and these arcs, and use this information to estimate the enclosed area formed by the points and arcs.

Is it valid to compute the cumulative sum of minimum distances between each point and the arcs? Would this approach provide an estimation of the area enclosed by the points and arcs? Any insights or alternative approaches would be greatly appreciated.

Thank you!

Answer 1

[Umar]

Hi Jianing,

To estimate the area enclosed by the points and arcs, computing the cumulative sum of minimum distances between each point and the arcs is a valid approach. This method can provide an estimation of the enclosed area formed by the points and arcs. By summing the minimum distances, you can approximate the total area enclosed by the arcs and points. An alternative approach could involve using numerical integration techniques to calculate the enclosed area more accurately. However, the cumulative sum of minimum distances is a practical and feasible method to estimate the enclosed area in this scenario.

Here is a simple example in MATLAB to demonstrate this concept:

% Sample data for arcs and points

arcs = struct('center', [0, 0, 0], 'radius', 1, 'orientation', [1, 0, 0], 'angle', pi/2);

points = rand(10, 3); % Generating 10 random points

% Calculating minimum distances

min_distances = zeros(size(points, 1), 1);

for i = 1:size(points, 1) distances = zeros(size(arcs, 2), 1); for j = 1:size(arcs, 2)

        % Calculate distance between point and arc j
        distances(j) = % Add distance calculation here based on point and arc properties
    end
    min_distances(i) = min(distances);
end

% Compute cumulative sum of minimum distances

enclosed_area_estimate = sum(min_distances);

disp(['Estimated enclosed area: ', num2str(enclosed_area_estimate)]);

The above code snippet showcases a basic implementation. You can customize the distance calculation based on your specific arc and point properties for a more accurate estimation. Feel free to explore alternative approaches based on your requirements.

Hope this answers your question.