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Masking 3D Surfaces and Carving Pumpkins - A Halloween Special!

Vasilis Bellos on 4 Nov 2024 at 20:11 (Edited on 4 Nov 2024 at 21:00)
Latest activity Edit by Vasilis Bellos on 4 Nov 2024 at 21:00

Pumpkins have been a popular, recurring, and ever-evolving theme in MATLAB during the past few years, and particularly during this time of year. Much of this is driven by the epic work of @Eric Ludlam and expanded upon by many others. The list of material is too extensive to go through everything individually, but I'm listing some of my favourite resources below and I highly recommend these to everyone as they're a lot of fun to play with:
Pumpkins are also particularly prominent during the yearly Mini Hack Contests. This year, I have jumped onto the bandwagon myself with my Floating Pumpkins entry:
In this post, I would like to introduce the concept of masking 3D surfaces in a festive and fun way, by showcasing how to apply it for carving faces on pumpkins step by step.
Let's start by drawing the pumpkin's body. The following was adapted from Eric's code:
n = 600; % Number of faces
% Shape pumpkin's rind (skin)
[X,Y,Z] = sphere(n);
% Shape pumpkin's ribs (ridges)
R = (1-(1-mod(0:20/n:20,2)).^2/12);
X = X.*R; Y = Y.*R; Z = Z.*R;
Z = (.8+(0-linspace(1,-1,n+1)'.^4)*.3).*Z;
function plotPumpkin(X,Y,Z)
figure
surf(X,Y,Z,'FaceColor',[1 .4 .1],'EdgeColor','none');
hold on
box on
axis([-1 1 -1 1 -1 1],'square')
xlabel('x'); xticks(-1:0.5:1)
ylabel('y'); yticks(-1:0.5:1)
zlabel('z'); zticks(-1:0.5:1)
material([.45,.7,.25])
camlight('headlight')
camlight('headlight')
lighting gouraud
end
plotPumpkin(X,Y,Z)
The next step is drawing the face for the mask. This can be done in 2D and can consist of any number of lines that form polygonal closed shapes and are appropriately scaled relative to the coordinates of the pumpkin. A quick example:
% Mouth
xm = [-.5:.1:.5 flip(-.5:.1:.5)];
ym = [.15 -.3 -.25 -.5 -.4 -.6 flip([.15 -.3 -.25 -.5 -.4]) .15 -.05 0 -.25 -.15 -.3 flip([.15 -.05 0 -.25 -.15])];
% Right eye
xr = [-.35 -.05 -.35];
yr = [.1 0 .5];
% Left eye
xl = abs(xr);
yl = yr;
figure('Color','w')
set(gcf,'Position',get(gcf,'Position')/2)
axes('Visible','off','NextPlot','Add')
axis tight square
fill(xm,ym,'k')
fill(xr,yr,'k')
fill(xl,yl,'k')
We then need to apply the 2D mask to the 3D surface. To do that, we project it onto the intersections of the surface with the XY plane. However, as we need the face to appear on the side of the pumpkin, we first need to rotate the pumpkin so that the front side is facing upwards. Essentially, we need to rotate the pumpkin around the x-axis by -Ï€/2 rad.
Let's do this from first principles to better understand the process:
theta = [-pi/2,0,0];
[X,Y,Z] = xyzRotate(X,Y,Z,theta);
function [X,Y,Z] = xyzRotate(X,Y,Z,theta)
% Rotation matrices
Rx = [1 0 0;0 cos(theta(1)) -sin(theta(1));0 sin(theta(1)) cos(theta(1))];
Ry = [cos(theta(2)) 0 sin(theta(2));0 1 0;-sin(theta(2)) 0 cos(theta(2))];
Rz = [cos(theta(3)) -sin(theta(3)) 0;sin(theta(3)) cos(theta(3)) 0;0 0 1];
for i=1:size(X,1)
for j=1:size(X,2)
r=Rx*Ry*Rz*[X(i,j);Y(i,j);Z(i,j)];
X(i,j)=r(1);
Y(i,j)=r(2);
Z(i,j)=r(3);
end
end
end
More information about these transformations can be found here:
rotx - Rotation matrix for rotations around x-axis
Matrix Rotations and Transformations
When plotting we get:
plotPumpkin(X,Y,Z)
Note that as we have only rotated this around the x-axis, Ry and Rz are equal to eye(3).
We can now apply the mask as discussed. We do this by using one of my favourite functions inpolygon. This gives us the corresponding indices of all the data points located inside our polygonal regions. At this stage, it's important to keep the following in mind:
  1. The number of faces (n) controls the discretization of the pumpkin. The larger it is, the smoother the mask will be, but at the same time the computational cost will also increase. If you are using this for the contest which has a timeout limit of 235 seconds, you might need to adjust it accordingly.
  2. You will also need to restrict the Z-coordinates appropriately (Z>=0) so that the mask is only applied on the front side of the pumpkin.
  3. If you are animating the face mask (more information about this below), and you need the eyes and mouth to fully close at any point, avoid using the second argument of the inpolygon function that gives you the points located on the edge of the regions.
The masking function is given below:
function [X,Y,Z] = Mask(X,Y,Z,xm,ym,xr,yr,xl,yl)
mask = ones(size(Z));
mask((inpolygon(X,Y,xm,ym)|inpolygon(X,Y,xr,yr)|inpolygon(X,Y,xl,yl))&Z>=0) = NaN;
Z = Z.*mask;
end
Applying the mask gives us:
[X,Y,Z]=Mask(X,Y,Z,xm,ym,xr,yr,xl,yl);
plotPumpkin(X,Y,Z)
arrayfun(@(x)light('style','local','position',[0 0 0],'color','y'),1:2)
We can see that MATLAB was thoughtful enough to automatically remove the pulp from inside the pumpkin, proving its convenience time and time again.
We can then rotate the pumpkin back and add the stem to get the final result:
theta = [pi/2,0,0];
[X,Y,Z] = xyzRotate(X,Y,Z,theta);
% Stem
s = [1.5 1 repelem(.7, 6)] .* [repmat([.1 .06],1,round(n/20)) .1]';
[t,p] = meshgrid(0:pi/15:pi/2,linspace(0,pi,round(n/10)+1));
Xs = repmat(-(.4-cos(p).*s).*cos(t)+.4,2,1);
Ys = [-sin(p).*s;sin(p).*s];
Zs = repmat((.5-cos(p).*s).*sin(t)+.55,2,1);
plotPumpkin(X,Y,Z)
arrayfun(@(x)light('style','local','position',[0 0 0],'color','y'),1:2)
surf(Xs,Ys,Zs,'FaceColor','#008000','EdgeColor','none');
And that's it. You can now add some change to the mask's coordinates between frames and play around with the lighting to get results such as these (more information on how to do this on my Teaser entry):
I hope you have found this tutorial useful, and I'm looking forward to seeing many more creative entries during the final week of the contest.

3 Comments

Adam Danz
Adam Danz on 4 Nov 2024 at 20:37
This jack-o'-lantern animation at the end is wicked!
> We can see that MATLAB was thoughtful enough to automatically remove the pulp from inside the pumpkin,
🎃🎃🎃🎃🎃🎃
Chen Lin
Chen Lin on 4 Nov 2024 at 20:29
Pumpkin has been a popular theme in our Mini Hacks thanks to @Eric Ludlam. I'm thrilled to see many creative pumpkin entires evolved. Another great artcile to introduce 3D surfaces masking in a festive and fun way! Thanks, Vasilis.
Vasilis Bellos
Vasilis Bellos on 4 Nov 2024 at 20:23
Meant to post this on Halloween but ran into some technical troubles. Massive thanks to @Anusha Sridharan, @Vinay Ramesh, @Chen Lin and Ops for helping resolve them.

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