Calculate normals from nodes which generate a 3D curve

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Hi! I have two matrices:
  • the matrix 'coord' containing the coordinates of nodes (see black nodes in the figure)
  • a matrix 'normals' having in each row the normal N=[a,b,c] (a: first column, b: second column, c: third column) for the first 10 nodes in 'coord'.
How can I determine the normals of the other nodes in 'coord' by following the trend of the nodes (red line in figure)?
load("test_pp.mat")
figure
plot3(coord(:,1),coord(:,2),coord(:,3),'k.','Markersize',20);
hold on
plot3(coord(:,1),coord(:,2),coord(:,3),'-r','LineWidth',2);
hold off
axis equal
EDIT: re-formulated question
  5 Comments
Umar
Umar on 9 Aug 2024
Hi @ Alberto Acri,
Please see “missing code snippet” updated in my recent post.

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Answers (1)

Gayathri
Gayathri on 14 Aug 2024
To calculate the “normals” of remaining entries in matrix “coord” we can do interpolation in 3-D space. This can be done using the function “scatteredInterpolant”. This function performs interpolation on scattered data that resides in 2-D or 3-D space. For more information, please refer the below mentioned link.
Then the new “normal” values can be found using the interpolant obtained in the above-mentioned method.
Please find the code below for your reference.
load("test_pp.mat")
known_coords=coord(1:10,:);
F_x = scatteredInterpolant(known_coords(:,1), known_coords(:,2), known_coords(:,3), normals(:,1), 'natural', 'linear');
F_y = scatteredInterpolant(known_coords(:,1), known_coords(:,2), known_coords(:,3), normals(:,2), 'natural', 'linear');
F_z = scatteredInterpolant(known_coords(:,1), known_coords(:,2), known_coords(:,3), normals(:,3), 'natural', 'linear');
% Interpolate normals for the remaining points
remaining_coords = coord(11:end, :);
interp_normals = zeros(size(remaining_coords));
for i = 1:size(remaining_coords, 1)
interp_normals(i, 1) = F_x(remaining_coords(i, 1), remaining_coords(i, 2), remaining_coords(i, 3));
interp_normals(i, 2) = F_y(remaining_coords(i, 1), remaining_coords(i, 2), remaining_coords(i, 3));
interp_normals(i, 3) = F_z(remaining_coords(i, 1), remaining_coords(i, 2), remaining_coords(i, 3));
end
% Combine known and interpolated normals
all_normals = [normals; interp_normals];
% Display results
disp(all_normals)
Hope you find this information helpful.

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