Sine function along inclined z axis

Im wanting to create a 'trench' like topography running down an inclined z plane. currently all my sine functions are along the y/x axis and are just creating bumps in the z plane.

The aim is to create a 's' shape with adjustable depth and thickness down the inclined z plane.

Is there a function to rotate a sine wave to do this? or am i approaching the problerm incorrectly? My code i have so far is below.

row = 94;
col = 195;
h = 10 ;
grid_row = linspace(0,h,row);
grid_col = linspace(0,h,col);

%% Setting the rows and columns into a meshed matrix to generate x and y coordinates
[x y] = meshgrid(grid_col,grid_row);

%% Setting up the initial flat plane which travels
z_vector = ones(row,col).* sort(linspace(h,0,length(x)));
z_matrix_flat = zeros(height(y),length(x))+ z_vector;

%% Z function which defines the trench

Z = z_matrix_flat + 0.5*sin(3*x);
Z_rotated = rot90(Z);
%Z = repelem(Z_rotated,2,4);
Z_scaled = imresize(Z,[94,195]);

%% Testing for loop to replace the orginal z plane in a predescribed area with the z values of the trench
%initialising the trench matrix to be the right size
trench = zeros(row, col);
for i= floor((0.1*height(x))):floor(0.9*height(x))
    for j = floor(0.02*length(y)):floor(0.95*length(y))
        
        trench(i,j) = trench(i,j) + Z_scaled(i,j);
        
    end
    
end
ind = find(trench == 0); %finds where the trench matrix is 0 and changes the value to be the corresponding one on the plane.
trench(ind) = z_matrix_flat(ind) ;

surf(x,y,trench)
xlabel 'X', ylabel 'Y'

[Matt J]

Your code doesn't run:

Index in position 2 is invalid. Array indices must be positive integers or logical
values.

Error in test (line 25)
        trench(i,j) = trench(i,j) + Z_scaled(i,j);

[Johnny Dessoulavy]

oops, I have updated the code.

Answer 1

[DGM]

Actually, I think I misinterpreted what you meant by "trough". Let's start over.

% surface parameters
s = [500 500]; % [columns rows]
xyrange = [0 10]; % range of x,y axes
zrange = [0 10]; % range of z axis (and inclined plane)

% sine wave parameters
wamp = 1;
wfreq = 1;
woffset = mean(xyrange);
wdepth = 0.25;
wwidth = 1.5;

x = linspace(xyrange(1),xyrange(2),s(2));
y = linspace(xyrange(1),xyrange(2),s(1)).';

% i'm going to cheat and use image processing tools to create wave
% use a dummy image display to generate a binary image of the profile
% normally this doesn't show up, but it does in web-view
yw = wamp*sin(wfreq*x) + woffset;
h = image(x,y,ones(s(1),s(2)));
L = images.roi.Polyline(gca);
L.Position = [x; yw].';

% get mask and dilate to desired width
% this really relies on s being square, otherwise strel needs to be elliptical
% that can be done, but not with strel().  lemme know if that's needed.
ypxperunit = s(1)/range(xyrange);
mask = imdilate(createMask(L),strel('disk',round(wwidth/2*ypxperunit)));

% scale and incline mask to final form
zramp = linspace(zrange(1),zrange(2),s(2)); % oriented along x-axis
mask = zramp - wdepth*double(mask);

h = surf(x,y,mask);
shading flat
light('position',[-5 -10 10])
view(-68,6)
colormap(jet)

That said, there are definitely shortcomings to this approach. I'll let you see if any of them are an obstacle for your usage.

[Johnny Dessoulavy]

Thank you! thats exactly what I am after. When i tried to run the code i got an error though.

"Unable to resolve the name images.roi.Polyline.

Error in trench_test (line 19)

L = images.roi.Polyline(gca);"

Unfortunately I will need a non square matrix of rows columns; could this be recitified by using "imresize" on the mask matrix?

[DGM]

The ROI tools are part of the Image Processing Toolbox, which I guess you don't have.

As to whether the non-square issue could be resolved by resizing, I imagine it could with some foresight. There are also ways to create elliptical strel without strel():

https://www.mathworks.com/matlabcentral/answers/1466966-is-an-ellipse-shaped-structuring-element-possible

but all of that is moot if you don't have IPT. Matt's answer may be of more use to you.

[Johnny Dessoulavy]

There is nothing stopping me from using that tool box so I'll download that and give it a go!

[Johnny Dessoulavy]

Got it to work with the resize! Thank you for all your help.

Answer 2

[DGM]

Consider the 1-D example:

rotangle = 45;

x = linspace(0,6*pi,500);
y = 2*sin(x);
trl = tand(rotangle)*x;

% simple method using a linear offset
xs = x;
ys = y + trl;

% actual rotation
x2 = linspace(0,6*pi/cosd(rotangle),500); % needs to be longer due to angle
r = sqrt(x2.^2 + y.^2);
t = atan2(y,x2)+deg2rad(rotangle);
xr = r.*cos(t);
yr = r.*sin(t);

h(1) = plot(x,trl,':'); hold on
h(2) = plot(xs,ys);
h(3) = plot(xr,yr);
axis equal

legend(h,{'trend line','skewed','rotated'},'location','northwest')

[Johnny Dessoulavy]

This is what i am after, but in a 3D sense. Would you know how to shift this represenation ( the rotated plot) to be in 3D?

I tried but it only returned a ramp.

Answer 3

[Matt J]

So, the problem is just adjusting the direction of the waves? If so, then perhaps as follows?

row = 94;
col = 195;
h=10;
theta=50;

%% Setting the rows and columns into a meshed matrix to generate x and y coordinates
grid_row = linspace(0,h,row);
grid_col = linspace(0,h,col);
[X,Y] = meshgrid(grid_col,grid_row);
T=cosd(theta)*X+sind(theta)*Y;


slope=h/max(T(:));
fun=@(t) slope*t+0.5*sin(3*t);  %desired profile

Z=fun(T);

surf(X,Y,Z);
xlabel X, ylabel Y

[Johnny Dessoulavy]

Yes. I need to adjust the sin wave to travelling down the z-plane. The way I require it would be as if you we looking down on a typical x-y-z grid and the sine wave is being projected from the x-y plane onto the z-plane. Thus, creating an almost 's' shape which snakes down the inclined z-plane.

essentially it is the 3d version of DGM's (another commentor) rotated plot imposed on my inclined z-plane.

[Matt J]

row = 94;
col = 195;
h=10;
theta=50;

%% Setting the rows and columns into a meshed matrix to generate x and y coordinates
grid_row = linspace(0,h,row);
grid_col = linspace(0,h*sqrt(2),col);
[X,Y] = meshgrid(grid_col,grid_row);


Z=0.5*sin(3*X);

h=surf(X,Y,Z,'EdgeColor','none'); xlabel X, ylabel Y,axis equal

Mx=makehgtform('xrotate',pi/2);
My=makehgtform('yrotate',-pi/4);
Mz=makehgtform('zrotate',theta*pi/180);
hg=hgtransform('Parent',gca,'Matrix', Mz*My*Mx);
h.Parent=hg;
view(-36,43)
ylim([-5,5]);

[Johnny Dessoulavy]

I have drawn (crudely, and i apologise for that in advance) what i mean by my above explanation. I want the sine wave to be projected onto the z plane (the red 's' shape) which will have a depth of P (arbitrary) and a thickness T (again, arbitrary). The effect i am looking for is effectively to have a regular 1D sine wave rotated 90 degrees, transformed into a 3D system and then depressed into the z-plane (what the red 's' has been drawn on)

[Matt J]

Your drawing is a line plot with the xy plane rotated. Therefore, I cannot tell if we are still talking about a surface plot. If it's a surface plot that you want, my solution already gives you that, just set the rotation angles to put the wave where you want. If it's a line plot you want, below is a a very simple modification of the above.

Basically, you should just plot whatever you want to plot at an easy orientation and then rotate it as desired with hgtransform().

h=fplot(@(x) sin(3*x),[0,10]);

My=makehgtform('yrotate',-pi/4);
Mz=makehgtform('zrotate',20*pi/180);
hg=hgtransform('Parent',gca,'Matrix', Mz*My);
h.Parent=hg;
view(-20,10)

[Matt J]

If DGM's latest answer correctly interprets your question, then here is code to produce the same thing with my approach.

row = 94*2;
col = 195*2;
h=10;
P=1.5;%depth
T=2;  %thickness

%% Setting the rows and columns into a meshed matrix to generate x and y coordinates
grid_row = linspace(-h,h,row);
grid_col = linspace(-h,h,col);
[X,Y] = meshgrid(grid_col,grid_row);


%% Generate unrotated surface
Z=0*X+P;
S=sin(X/2.5);
Z(S-T/2<=Y  & Y<=S+T/2)=0;
h=surf(X,Y,Z,'EdgeColor','none','FaceColor','interp'); xlabel X, ylabel Y,axis square

%% Tilt the surface by 45 degrees
My=makehgtform('yrotate',-pi/4);
hg=hgtransform('Parent',gca,'Matrix', My);
h.Parent=hg;
view(-40,20)
ylim([-5,5]);

[DGM]

I suppose we still need to clarify whether the "groove" gets inclined by addition (skewing) or by actual rotation. My first answer shows both in 1D, my second answer shows skewing. Matt J's latest example uses rotation. It all depends what your needs are.

A: rotated

B: skewed

[Matt J]

Earlier @Johnny Dessoulavy seemed to confer that it was A

"essentially it is the 3d version of DGM's (another commentor) rotated plot imposed on my inclined z-plane."

[Johnny Dessoulavy]

Yes! thats exactly what im after. Thank you so much! I think it has something to do with the "makehgtform", but is there a way to not have it rotate around the origin? I ask because if i can help it i would not like to have negative axis.

@DGM The rotated solution fits to what I have in my head the best!

[Matt J]

but is there a way to not have it rotate around the origin?

With makehgtform, you can do any combination of rotations and translations that you wish. You can also compute the transform matrix of a rotation about an arbitrary 3D line using,

https://www.mathworks.com/matlabcentral/fileexchange/30864-3d-rotation-about-shifted-axis

[Johnny Dessoulavy]

Yep I got it to work! thank you so much. It was great seeing these two different methods and learning two new things :D