How to generate a dynamic plane of points?

I need to generate a dynamic plane of points perpendicular to a given input vector.

For example, if given input vector of [0 0 1], I want to generate a set of points that are uniformly distributed and perpendicular to the input vector, similar to this:

As an output, I get a list of coordinates for each point in the array -- see the attached .mat file for an example.

For an input vector such as the above example, this is a very straightforward process and I had this working very quickly. The issue is when the vector is complex and not parallel to an axis. How can I automatically generate these points when given a more complicated vector such as [1 2 0] or [-5 3 2]?

Answer 1

[VINAYAK LUHA]

Hi Estel,

It is my understanding that you wish to find grid points on a plane perpendicular to a given input vector.

Here's a workaround -

% Input vector
inputVector = [1 1 1];

% Normalize the input vector
inputVector = inputVector / norm(inputVector);

% Find two orthogonal vectors perpendicular to the input vector using dot
% and cross products
if inputVector(1) ~= 0 || inputVector(2) ~= 0
    orthogonalVector1 = [inputVector(2) -inputVector(1) 0];
else
    orthogonalVector1 = [0 1 0];
end
orthogonalVector2 = cross(inputVector, orthogonalVector1);

% Define grid parameters
gridSize = 10; 
gridSpacing = 1; 

% Generate grid points in a rectangular pattern
[X, Y] = meshgrid(-gridSize/2 : gridSize/2, -gridSize/2 : gridSize/2);
gridPoints = [X(:), Y(:)];

% Transform grid points to be perpendicular to the input vector
gridPointsPerpendicular = gridPoints(:, 1) * orthogonalVector1 + gridPoints(:, 2) * orthogonalVector2;

% Calculate the center of the grid
center = [mean(gridPointsPerpendicular(:, 1)), mean(gridPointsPerpendicular(:, 2)), mean(gridPointsPerpendicular(:, 3))];

% Display the grid points and the input vector arrow
figure;
hold on;
scatter3(gridPointsPerpendicular(:, 1), gridPointsPerpendicular(:, 2), gridPointsPerpendicular(:, 3), 'filled');
quiver3(center(1), center(2), center(3), inputVector(1), inputVector(2), inputVector(3), 'r', 'LineWidth', 2);
hold off;

xlabel("x")
ylabel("y")
zlabel("z")
axis equal;

Hope this helps.

[Estel]

Thank you very much!

As a quick follow-up: what is the purpose of the "gridSpacing" variable? I don't see it used anywhere after you initially set a value.

[VINAYAK LUHA]

Hi Estel,

I initially thought to include a functionality to specify the degree of sparseness of the grid, however later I felt it may go out of the scope of the question and left that on you to explore and implement if needed.

Thanks