Hi,
As per my understanding, you are trying to implement a "corner detection algorithm" for point clouds in MATLAB, to identify the corners of an object represented by a collection of planar surfaces and the above algorithm involves iterating through all combinations of three planes from the input set to find potential corner points i.e the intersection of the planes.
Please refer to the following as a possible workaround:
- To make the code more efficient and concise subtract the centre "C" from all the vertices "C" at once.
- Initialize "cross_products" to store the norms of the cross products of "n" with each "PV".
- The condition "if norm(d_vc) < norm(d_pc)" is used to check if the point "P" is closer to the plane's centre "C" than the vertices "V". If "P" is closer, we then check if it is within the threshold distance "d_th". In the provided code above the comparison "if (norm(d_vc) < norm(d_pc));" might not correctly reflect the pseudocode's intent due to the misplaced semicolon.
Please refer to the code below for better understanding:
function boolean = intersect(line, plane, d_th)
P = line.P; % intersection point of 3 planes and potential object corner point
n = line.n; % normal vector of the intersection line between two planes
C = plane.center; % center of the plane
V = plane.vertices; % 4 corner vertices of the plane
% Compute vectors from the plane center to each vertex
VC = bsxfun(@minus, V, C);
% Compute the vector from the plane center to the intersection point
PC = P - C;
% Compute the cross product of the normal with the PC vector
d_pc = cross(n, PC);
% Initialize a vector to store the cross product norms
cross_products = zeros(1, size(V, 2));
% Compute the cross product of the normal with each PV vector
for i = 1:size(V, 2)
PV = P - V(:, i);
cross_products(i) = norm(cross(n, PV));
end
% Find the minimum norm of the cross products
[d, min_element] = min(cross_products);
% Compute the cross product of the normal with the corresponding VC vector
d_vc = cross(n, VC(:, min_element));
% Initialize boolean flag as false
boolean = false;
% Check if the intersection point is within the threshold distance
if norm(d_vc) < norm(d_pc)
if d <= d_th
boolean = true;
end
else
boolean = true;
end
end
The code here assumes that "v" is a 3 by N matrix where each column represents the coordinates of a vertex, and "c" and "p" are column vectors representing the coordinates of centre and the intersection point.
Please refer to the following MATLAB Answer which gives a similar workaround on "Intersection between two planes in MATLAB" for further understanding:
Hope this helps!
