How to generate a torus structure in MATLAB similar to Minecraft builds?

I am trying to use MATLAB to generate and visualize a torus shaped structure. Mathematically, I know a torus can be parameterized as:

x=(R+rcosv)cosu， y=(R+rcosv)sinu， z=rsinv

where RRR is the major radius and rrr is the minor radius.

However, my goal is to make it look more like a block-based Minecraft torus build, where the shape is represented by discrete voxels or grid points rather than a smooth surface.

For reference, I found this Minecraft Torus Generator, which shows how different torus radii translate into block-based rings, but I would like to recreate the same effect programmatically in MATLAB.

My questions are:

1. What is the best approach in MATLAB to discretize the torus equation into a voxel/block grid representation?
2. Should I use meshgrid and thresholding, or is there a more efficient way to represent and render such a structure?
3. Once I have the data points, is voxelPlot or isosurface a good visualization method to achieve a Minecraft-style look?

Any insights or example code would be greatly appreciated!

Answer 1

[Mathieu NOE]

hello Sarah

maybe this ?

to create the initail mesh I used this fex submission : Mesh/Voxel spheres, ellipsoids, toroids, and test objects - File Exchange - MATLAB Central but you can of course use your own code. This fex is quite interesting in case you want more complex shapes or combination of them

you will also need this one : inpolyhedron - are points inside a triangulated volume? - File Exchange - MATLAB Central

my result sor far

meshed taurus:

voxelized taurus :

demo code :

% Taurus parameters

R=[45];
r=[6]; 
stepSize=1;

centres=[0 0 0];
deform=[1 1 1];
rotation=[-45, 0, 45];

% defining only  major (R) and minor (r) radii builds a series of
% concentric toroid rings at [0 0 0]
FV=multiMeshToroidCreator(R, r, centres, deform, rotation, stepSize);
figure; axis equal; 
patch(FV, 'FaceColor', 'b', 'edgecolor', 'r'); 

  % Convert the mesh to a voxelvolume
  % Define a 3D grid
  a = ceil((R + r)*2.2) ; 
  d = 3; % define your "block" size 
[x, y, z] = ndgrid(-a:d:a, -a:d:a, -a:d:a); % Adjust grid size as needed
gridPoints = [x(:), y(:), z(:)];

% Check if points are inside the mesh
inMesh = inpolyhedron(FV.faces, FV.vertices, gridPoints);
% fex : https://fr.mathworks.com/matlabcentral/fileexchange/37856-inpolyhedron-are-points-inside-a-triangulated-volume

% Reshape to voxel grid
voxelGrid = reshape(inMesh, size(x));

  %  Show iso surface of result
  figure, axis equal; 
  patch(isosurface(voxelGrid,0.1), 'Facecolor', [1 0 0]);

[Mathieu NOE]

this may also inerest you :

Polygon2Voxel » Pick of the Week - MATLAB & Simulink