How to unwrap a 3D mesh such that the dimensions are preserved - graphics

Imagine you have a papercrafted circle in real life and put in on your forearm. This curved object now represents a 3D object. I need to map this 3D object back to its original 2D shape by unwrapping the 3D object.
I have looked into LSCM and angle-based flattening but they are in need of the geometrical faces of the object, which i dont have.
Is there anything out which could solve my problem?

Related

VTK - create 3D model

I'm trying to create a 3D mask model from the 3D coordinate points that are stored in the txt file. I use the Marching cubes algorithm. It looks like it´s not able to link individual points, and therefore holes are created in the model.
Steps: (by https://lorensen.github.io/VTKExamples/site/Cxx/Modelling/MarchingCubes/)
First, load 3D points from file as vtkPolyData.
Then, use vtkVoxelModeller
Put voxelModeller output to MC algorithm and finally visualize
visualization
Any ideas?
Thanks
The example takes a spherical mesh (a.k.a. a set of triangles forming a sealed 3D shape), converts it to a voxel representation (a 3D image where the voxels outside the mesh are black and those inside are not) then converts it back to a mesh using Marching Cubes algorithm. In practice the input and output of the example are very similar meshes.
In your case, you load the points and try to create a voxel representation of them. The problem is that your set of points is not sufficient to define a volume, they are not a sealed mesh, just a list of points.
In order to replicate the example you should do the following:
1) building a 3D mesh from your points (you gave no information of what the points are/represent so I can't help you much with this task). In other words you need to tell how these points are connected between then to form a 3D shape (vtkPolyData). VTK can't guess how your points are connected, you have to tell it.
2) once you have a mesh, if you need a voxel representation (vtkImageData) of it you can use vtkVoxelModeller or vtkImplicitModeller. At this point you can use vtk filters that need a vtkImageData as input.
3) finally in order to convert voxels back to a mesh (vtkPolyData) you can use vtkMarchingCubes (or better vtkFlyingEdges3D that is a very similar algorithm but much faster).
Edit:
It is not clear what the shape you want should be, but you can try to use vtkImageOpenClose3D so the steps are:
First, load 3D points from file as vtkPolyData.
Then, use vtkVoxelModeller
Put voxelModeller output to vtkImageOpenClose3D algorithm, then vtkImageOpenClose3D algorithm output to MC (change to vtkFlyingEdges3D) algorithm and finally visualize
Example for vtkImageOpenClose3D:
https://www.vtk.org/Wiki/VTK/Examples/Cxx/Images/ImageOpenClose3D

Best way to project an arbitrary 2D polygon onto a 3D triangle mesh?

What is the best way to project an arbitrary 2D polygon onto a 3D triangle mesh?
To make thing clearer, here is a visualization of the problem:
The triangle mesh is representing terrain and thus can be considered 2.5D. I want to be able to treat the projected polygon as a separate object.
This particular implementation is done in WebGL and three.js but any solution that fits an interactive 3D application is of interest.
If your question is not how to texture map the surface, then you really have to generate new 3D polygons.
You will be using some projection mechanism (such as a parallel one) that turns your 3D problem to 2D.
First backproject the surface onto the polygon plane. The polygon will be overlaid on a corresponding 2D mesh. Now for every facet, find the intersection (in the Boolean sense) of the facet and the polygon.
You will need a polygon intersection machinery for that purpose, such as the Weiler-Atherton or Sutherland-Hodgman clipping algorithms (the latter is much simpler, but works on convex windows only). (Also check http://www.angusj.com/delphi/clipper.php)
After clipping, you project to the original facet plane.

What's the purpose of a unit normal vector when creating a 3D shape?

I understand that to create a shape (let's say a 3D sphere for an example) that I have to first find the vertex locations of the shape and second, use the parametric equation in order to create the x, y, z points of the triangle meshes. I am currently looking at a sample code to create shapes and it appears that after using the parametric equation in order to find the vectors of the triangle meshes, unit normals to the sphere at the vertices are found.
I understand why regular vectors in the first step are used to create the 3D shape and that a normal vector is perpendicular to the shape object, but I don't understand why the unit normal vectors at the vertices are used to create the shapes? What's the purpose of finding the normal of the vectors?
I am not sure I totally understand your question, but one very important use for normals in computer graphics is calculating reflections. For instance, if you're writing a simple raytracer, Lambertian reflectance is quite easy to compute if you know the normal vector where your camera ray intersects a surface. Normals are similarly required for (off the top of my head) the majority of calculations involved in more complex rendering techniques.

Rendering 3D shapes on a voxel

I have a 3D shape (primitive shapes like cuboid, sphere, pyramid etc.). The shape is described by a set of necessary geometric parameters. For example, for a cube, I have information about the vertices, dimensions and orientation of the cube. Now, I have a voxel (kind of 3D grid of pixels). How can I determine which cells of the voxel needs to be filled and which will remain empty for "rendering" the cube in 3D?
Are there existing libraries for the same? Or, can someone point out the approach/algorithm that would help in this task? Also, what is this process exactly called, so that I can search on the Internet in the right direction?
It is called "Mesh to Voxel conversion" or "Mesh voxelization" or to be a bit more general "Volume Visualization".
If you are interested in math here is some good articles about it:
cs.swansea.ac.uk/~csmark/PDFS/cgfvoxel.pdf
Complete Polygonal Scene Voxelization
Ray Cast Methods

how can 3d shape data project onto your 2d screen in computer graphics?

So correct me if i'm wrong, but I think all elements in 3d graphics are meshes.
So the question is really, how do you take mesh data and create a 2d projection based on the mesh data, the camera location, rotations of camera & mesh, etc.
I realize this is fairly complicated and I would be satisfied by just knowing what the technical term for this is called so I may search and research it.
You can read about 3D projection on Wikipedia.

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