How do I make a scatter 3D plot move towards a line

would it be possible to make a moving plot for these scatter points to move towards a line in the middle of the 3d plot and stop when it reaches the line?

a rough example would be:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
countmax=5; % units are in micrometres 
view([-37.5 30])


X = zeros(1,countmax);
Y = zeros(1,countmax);
Z = zeros(1,countmax);
n=0;
m=0;
y=1;
d = 10;
%d = 15/1000; %distance between each molecule => 15/1000 is 15 micrometre
s = 6; % size of particle
for i = 2:countmax
    for j = 2:countmax
        for k = 2:countmax
             X(i) = X(i-1) + d; %%1 = distance between each molecules (add an equation for it)
             Y(j) = Y(j-1) + d;
            Z(k) = Z(k-1) + d;
        end
    end
end
q= 1;
for n = 1:countmax
     for m = 1:countmax
        b = repelem(X(n),countmax);
        c = repelem(Y(m),countmax);
        a = [b;c;Z]; %% Check Coordinates
        scatter3(a(1,:),a(2,:),a(3,:),s,'Filled','r') %% 4 value from left changes the size of each point
        
        %xlim([d (countmax-1)*d]) % Axis limitsg
        %ylim([d (countmax-1)*d])
        %zlim([d (countmax-1)*d])
        xlabel('My x label') % Axis Labels
        ylabel('My y label')
        zlabel('My z label')
hold on
rotate3d on
     end
end
grid off;
Image = getframe();
K = sum(sum(rgb2gray(Image.cdata)==255));                                 
percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
q = percentageofwhite(y);
%delete(findall(gcf,'type','text'))
txt=text(0.0,0.95,sprintf('Water Volume = %0.3f%%',q(1,1)),'Units','normalized');
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
countmax=5; % units are in micrometres 
view([-37.5 30])


X = zeros(1,countmax);
Y = zeros(1,countmax);
Z = zeros(1,countmax);
n=0;
m=0;
y=1;
d = 10;
%d = 15/1000; %distance between each molecule => 15/1000 is 15 micrometre
s = 6; % size of particle
for i = 2:countmax
    for j = 2:countmax
        for k = 2:countmax
             X(i) = X(i-1) + d; %%1 = distance between each molecules (add an equation for it)
             Y(j) = Y(j-1) + d;
            Z(k) = Z(k-1) + d;
        end
    end
end
q= 1;
for n = 1:countmax
     for m = 1:countmax
        b = repelem(X(n),countmax);
        c = repelem(Y(m),countmax);
        a = [b;c;Z]; %% Check Coordinates
        scatter3(a(1,:),a(2,:),a(3,:),s,'Filled','r') %% 4 value from left changes the size of each point
        
        %xlim([d (countmax-1)*d]) % Axis limitsg
        %ylim([d (countmax-1)*d])
        %zlim([d (countmax-1)*d])
        xlabel('My x label') % Axis Labels
        ylabel('My y label')
        zlabel('My z label')
hold on
rotate3d on
     end
end
grid off;
Image = getframe();
K = sum(sum(rgb2gray(Image.cdata)==255));                                 
percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
q = percentageofwhite(y);
%delete(findall(gcf,'type','text'))
txt=text(0.0,0.95,sprintf('Water Volume = %0.3f%%',q(1,1)),'Units','normalized');

Answer 1

[Thiago Henrique Gomes Lobato]

It mostly depends of what points should move (only neighbours or all of them), but after you decide it you can calculate the closest point in the line for each point and then move it lineary in that direction. Here is an example moving all points to a line defined by three points

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
countmax=5; % units are in micrometres 
view([-37.5 30])
X = zeros(1,countmax);
Y = zeros(1,countmax);
Z = zeros(1,countmax);
n=0;
m=0;
y=1;
d = 10;
%d = 15/1000; %distance between each molecule => 15/1000 is 15 micrometre
s = 6; % size of particle
for i = 2:countmax
    for j = 2:countmax
        for k = 2:countmax
             X(i) = X(i-1) + d; %%1 = distance between each molecules (add an equation for it)
             Y(j) = Y(j-1) + d;
            Z(k) = Z(k-1) + d;
        end
    end
end
q= 1;
for n = 1:countmax
     for m = 1:countmax
        b = repelem(X(n),countmax);
        c = repelem(Y(m),countmax);
        a = [b;c;Z]; %% Check Coordinates
        scatter3(a(1,:),a(2,:),a(3,:),s,'Filled','r') %% 4 value from left changes the size of each point
        
        %xlim([d (countmax-1)*d]) % Axis limitsg
        %ylim([d (countmax-1)*d])
        %zlim([d (countmax-1)*d])
        xlabel('My x label') % Axis Labels
        ylabel('My y label')
        zlabel('My z label')
hold on
rotate3d on
     end
end
grid off;
Image = getframe();
K = sum(sum(rgb2gray(Image.cdata)==255));                                 
percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
q = percentageofwhite(y);
%delete(findall(gcf,'type','text'))
txt=text(0.0,0.95,sprintf('Water Volume = %0.3f%%',q(1,1)),'Units','normalized');
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
countmax=5; % units are in micrometres 
view([-37.5 30])
X = zeros(1,countmax);
Y = zeros(1,countmax);
Z = zeros(1,countmax);
n=0;
m=0;
y=1;
d = 10;
%d = 15/1000; %distance between each molecule => 15/1000 is 15 micrometre
s = 6; % size of particle
for i = 2:countmax
    for j = 2:countmax
        for k = 2:countmax
             X(i) = X(i-1) + d; %%1 = distance between each molecules (add an equation for it)
             Y(j) = Y(j-1) + d;
            Z(k) = Z(k-1) + d;
        end
    end
end
q= 1;

[XX,YY,ZZ] = meshgrid(X,Y,Z);
AllDimensions = [XX(:),YY(:),ZZ(:)];

LinePoints = [30,10,20;
              30,20,20;
              30,30,20;
              30,40,20];
% Find which points should be directed to where
LinePointMap = zeros(length(AllDimensions),1);
for idx=1:length(AllDimensions)
    [~,idxMin] = min( sum(abs(AllDimensions(idx,:)-LinePoints).^2,2) );
    LinePointMap(idx) = idxMin;
end
Differences = LinePoints(LinePointMap,:)-AllDimensions;

MaxStep = 50;
for idxAnimation = 1:MaxStep
scatter3(AllDimensions(:,1)+idxAnimation/MaxStep*Differences(:,1),...
         AllDimensions(:,2)+idxAnimation/MaxStep*Differences(:,2),...
         AllDimensions(:,3)+idxAnimation/MaxStep*Differences(:,3),...
         s,'Filled','r') %% 4 value from left changes the size of each point
        
xlim([d (countmax-1)*d]) % Axis limitsg
ylim([d (countmax-1)*d])
zlim([d (countmax-1)*d])
xlabel('My x label') % Axis Labels
ylabel('My y label')
zlabel('My z label')
hold off
rotate3d on

grid off;
pause(0.1)
end

Image = getframe();
K = sum(sum(rgb2gray(Image.cdata)==255));                                 
percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
q = percentageofwhite(y);
%delete(findall(gcf,'type','text'))
txt=text(0.0,0.95,sprintf('Water Volume = %0.3f%%',q(1,1)),'Units','normalized');

[sui zhi lau]

Hi Thiago, thank you for commenting. i would like ALL points to be pointing towards that line. I tried your code but it shows that the matrix dimensions are not equal for the LinePoints.

Error using  - 
Matrix dimensions must agree.

    [~,idxMin] = min( sum(abs(AllDimensions(idx,:)-LinePoints).^2,2) );

[Thiago Henrique Gomes Lobato]

What version of matlab do you have? Some old versions don't perform the implicity expansion. Change to this line and it should work

    [~,idxMin] = min( sum(abs( repmat(AllDimensions(idx,:),size(LinePoints,1),1)-LinePoints).^2,2) );

Also, in my example I use three points, because your line in the example was just a segment in the middle. If you want a parametric line the distance that you should minimize is not the distance to point but the distance to a parametric line, for reference you can check here.

[sui zhi lau]

Hi Thiago,

I have the 2015 version of MATLAB. and yes it does meet what i want! I would just need to change the lines point to meet what i want.(I just need it to be in the centre of the plot).

I tried putting a meshgrid for the LinePoints but it is showing me initial error from previous.

I am sorry if i am kinda asking a fundamental question. MATLAB is still a relatively new software for me and I am still trying to understand this.

I added this to the code to get a constant line in the centre.

[a,b,c]=meshgrid(max(X)/2,max(Y)/2,Z);
LinePoints = [a,b,c]

[Thiago Henrique Gomes Lobato]

Meshgrid will not allow you to create a line like that. Imagine a line in +X, the values of Y and Z remains constant and only X change. The same if the line is in Y and Z. If you have no inclination on your line you will only need to change one coordinates (it will be more depending of how you want to tillt it). So, suppose you want to make a line in Z, the result will be something like this:

halfLength = 10;
Zpositions = max(Z)/2-halfLength:max(Z)/2+halfLength;
Xposition  = max(X)/2; Yposition = max(Y)/2;
LinePoints = zeros(length(Zpositions),3);
LinePoints(:,3) = Zpositions;
LinePoints(:,1) = Xposition; % if it doesn't work, = repmat(Xposition,length(Zpositions),1)
LinePoints(:,2) = Yposition;

[sui zhi lau]

Ah so if I want to tilit it in the y direction, it would be seomthing like this?

because i tried it but i could not get it to run. Like they said it was undefined for the Zposition, I do not know what am I doing wrong.

halfLength = 10;
Ypositions = max(Y)/2-halfLength:max(Y)/2+halfLength;
Xposition  = max(X)/2; 
Zposition = max(Z)/2;
LinePoints = zeros(length(Zpositions),3);
LinePoints(:,3) = Zpositions;
LinePoints(:,1) = Xposition; % if it doesn't work, = repmat(Xposition,length(Zpositions),1)
LinePoints(:,2) = Yposition;

[Thiago Henrique Gomes Lobato]

Your variable names are wrong, i.e, you used different variable names in each step

halfLength = 10;
Ypositions = max(Y)/2-halfLength:max(Y)/2+halfLength;
Xposition  = max(X)/2; 
Zposition = max(Z)/2;
LinePoints = zeros(length(Ypositions),3);
LinePoints(:,3) = Zposition;
LinePoints(:,1) = Xposition; % if it doesn't work, = repmat(Xposition,length(Zpositions),1)
LinePoints(:,2) = Ypositions;