Extrusion without self intersection - graphics

I have a mesh constituted by triangles or quadrilaterals, and I need to extrude it.
Unfortunately, I have discovered that the mesh has inner cells, and then I produce self-intersecting solids. Here is a cat that contains inner triangles for what I can only suppose is the mouth and tongue. A closer image may shed some light on the mesh.
Is there a library that can help me produce extruded solids that are not self-intersecting? VTK and CGAL both say that can produce self-intersection.
As an alternative, is there a know algorithm that can help me?

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Computer graphics: polygon mesh

So a polygon mesh is defined as the following:
class Triangle{
int vertices[3]; //vertex indices
float nx, ny, nz; //face-plane normal
};
Is this a convenient way to represent a mesh used with flat shading? Explain
Suggest an object for which this is a good mesh format when used with Gouraud shading. Explain
Suggest an object for which this is a bad mesh format when used with Gouraud shading. Explain
So for 1, I said yes because the face plane normal can be easily converted to a point in the middle of the face. I read somewhere that normals don't have positions?
For 2 I said a ball; more gentle angles
And 3 a box; steeper angles.
I don't know, I don't think I really understand what the normal vector is.
mostly yes
from geometry computations is this OK however from rendering aspect having triangles in indices form only can be sometimes problematic (depends on the rendering engine, HW, etc). Usually is faster to have the triangle points directly in vector form instead of just indexes sometimes triangle contains both... However that is wasting space.
depends on how you classify what is OK and what not.
smooth objects like sphere will look like this
while flat side meshes like cube will be rendered without visible distortions in shape (but with flat shaded like colors only so lighting will be corrupted)
So answer to this is depend on what you want to achieve less lighting error, or better shape recognition or what. Basically using 1 normal for face will turn Gourard into flat shading.
Lighting can be improved by dividing big flat surfaces into more triangles
is unanswerable exactly for the same reasons as #2
So if you want to answer #2,#3 you need to clarify what it means good and bad ...

Create a polygon from a texture

Let's say I've got a rgba texture, and a polygon class , which constructor takes vector array of verticies coordinates.
Is there some way to create a polygon of this texture, for example, using alpha channel of the texture ...?
in 2d
Absolutely, yes it can be done. Is it easy? No. I haven't seen any game/geometry engines that would help you out too much either. Doing it yourself, the biggest problem you're going to have is generating a simplified mesh. One quad per pixel is going to generate a lot of geometry very quickly. Holes in the geometry may be an issue if you're tracing the edges and triangulating afterwards. Then there's the issue of determining what's in and what's out. Alpha is the obvious candidate, but unless you're looking at either full-on or full-off, you may be thinking about nice smooth edges. That's going to be hard to get right and would probably involve some kind of marching squares over the interpolated alpha. So while it's not impossible, its a lot of work.
Edit: As pointed out below, Unity does provide a method of generating a polygon from the alpha of a sprite - a PolygonCollider2D. In the script reference for it, it mentions the pathCount variable which describes the number of polygons it contains, which in describes which indexes are valid for the GetPath method. So this method could be used to generate polygons from alpha. It does rely on using Unity however. But with the combination of the sprite alpha for controlling what is drawn, and the collider controlling intersections with other objects, it covers a lot of use cases. This doesn't mean it's appropriate for your application.

Point cloud: Surface Reconstruction help needed (meshlab)

I am new to meshlab and am trying to reconstruct an stl file which has a number of issues such as over 700 self-intersecting faces, non-manifold edges and flipped triangles. The part I am trying to fix is a sunglass frame just to give you some perspective. I was able to remove the flipped triangles using Netfabb, which reduced the number of self-intersecting faces. I attempted to fix the rest of the problems by using features within the "Cleaning and Repairing" tab in Meshlab such as remove non-manifold edges and intersecting faces; however, I was unable to fix all problems with the features in the "Cleaning and Repairing" tab alone. Thus I decided to convert the mesh into a point cloud, calculate normals from the "Sampling" tab and try surface reconstruction: poisson. This method gave me a mesh that looked like a big blob instead of the detailed part that I was trying to achieve.
Can anyone please give me a step by step outline of how I can convert the point cloud back into a mesh with surface reconstruction while maintaining the part's dimensional integrity and avoiding self-intersecting faces? Or if you have any other suggestions, I'd be more than happy to listen.
Thank you!

Generating coordinates for abstract triangulation

I have a piece of abstract triangulation, made entirely out of equilateral triangles, that describes a curved 2d space. As such, some vertices have for example 7 equilateral triangles attached to them. Now I want to draw this as a terrain.
This has to be done in 3d, so I expect a lot of saddle nodes and some cone-like structures. I am currently trying to find a nice algorithm that does this for me, but as of yet I have come out empty handed. In principle you could 'just' solve a large set of quadratic equations that fixes all the distances, but this is unfeasible. I would be content with an algorithm that gives a best approximation.
Any advice?

How to draw a cylinder geometry using webgl?

I need to draw a cylinder geometry using webgl, but don't know how to realize it. The parameters may be radius,subdivisions and two central point of bottom faces.Any ideas will be appreciated,thanks~
Fundamentally, you will build it with triangles. It would be easiest to think of it more as an "n-sided" prism. The top and bottom faces will need to be made of triangle "fans", where each triangle shares one point in the center.
You will need to use simple math (including trigonometry) to calculate the locations of the points for each triangle.
If you don't know how to draw triangles with WebGL, check out NeHe's excellent WebGL guide at learningwebgl.com.

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