Polygon mesh data structure

My first tests with OpenGL use a triangle soup which is basically a collection of triangles with no relationship whatsoever. In order to implement a more complex shader I need to work on a more complex and powerful data structure: the polygon mesh

A polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D computer graphics and solid modeling. The faces usually consist of triangles, quadrilaterals or other simple convex polygons, since this simplifies rendering, but may also be composed of more general concave polygons, or polygons with holes.

[Wiki Polygon Mesh]

There's a variety of ways to represent a polygon mesh and they basically differ in how the vertex and topology information are stored. One of the most used representation in the filed computer graphics and geometry processing is the halfedge data structure.

Polygonal meshes consist of geometry (vertices) and topology (edges, faces). Data structure for polygonal meshes mainly differ in the way they store the topology information. While face-based structures lack the explicit representation of edges, and edge-based structures loose efficiency because of their missing orientation of edges, halfedge-based structures overcome this disadvantages. The halfedges (that result in splitting the edges in two oriented parts) store the main connectivity information:

Intuitively, this provides a natural and simple way to represent vertices, edges and faces, as well as arbitrary polygons. 

[OpenMesh]

Many operations and queries are very natural on the halfedge data structure, in particular the circulation on the neighbors of vertices and faces.

Traversal of one-ring neighbors of a center vertex. From left to right: 

1. Start from center vertex. 
2. Select outgoing halfedge (and access its target vertex). 
3. Move to previous halfedge. 
4. Move to opposite halfedge (access its target vertex)

[SB11]

As far as i know the high-quality publicly C++ libraries available are:

1. CGAL
2. OpenMesh
3. SurfaceMesh



CGAL Logo

4. Mesquite

I have never used Mesquite. This is mainly focused on the mesh optimization [BFKLM03]. Although the CGAL is a very powerful library for the compuational geometry, its polygonal mesh implementation has a major drawback: all the custom properties associated with a mesh entity must be declared at compile time.

Aachen University
Computer GraphicsLogo

OpenMesh and SurfaceMesh are more flexible and much easier to use than CGAL. OpenMesh was originally developed at the Aachen University [BSBK02] and the version 3.0 was recently released. On the other hand SurfaceMesh is more recent [SB11] and it was developed at the Bielefeld university.

They have very much in common, starting with one of their developers, Mario Botsch who is also the head of the Computer Graphics & Geometry Processing Group at Bielefeld.

Based on our experience in academic research and teaching as well as in industrial cooperations, our primary design goal [of the SurfaceMesh] is ease of use. An easy-to-use data structure is learned faster, allows to focus on the main problem (instead of on the details of the data structure), and fosters code exchange between academic or industrial research partners. The data structure should therefore be just as flexible and generic as needed, but should otherwise be free of unnecessary switches and parameters. At the same time, however, we have to make sure not to compromise computational performance and memory consumption. Otherwise the data structure would be easy to use, but not useful, and hence would probably not be used at all.
[SB11]

The SurfaceMesh primary design goal is the ease of use, therefore it satisfy the requirements for the OpenGL-Sandbox very well, therefore I will adopt it as a polygonal mesh data structure in my program.

In the end I'll show you an example of the SurfaceMesh which computes the mean valence of the mesh vertices

References

[SB11] Design, Implementation, and Evaluation of the Surface_mesh Data Structure
[BFKLM03] The Mesquite mesh quality improvement toolkit

[BSBK02] OpenMesh – a generic and efficient polygon mesh data structure
[OpenMesh]
[Wiki Polygon Mesh]
[CGAL]
[Mesquite]

OpenGL Sandbox - My first shader

Here it is the rendering of the Utah Teapot and the Stanford Dragon rendered with my first shader. 

It's a very simple shader and it does not create any light source in the scene. The depth perception is given by the coloration of the triangles. As you can see in the teapot image, each triangle is colored using a blend of the axes color given by the triangle's normal vector.

The shader's code is straightforward:


Here below the code which passes the vertex attributes to the shader is presented. Qt helper classes are a good choice in order to write quickly a more readable code. For this reason I will use this approach whenever it's possible

OpenGL Sandbox - New data and camera handling

I am working quite hard on the OpenGL Sandbox: you can find the repository on GitHub.

I've included some data of the Standord Scannin Repository's into the list of the available 3D models,
the "Stanford bunny" is rather important in the field of computer graphics and deserves a special mention: If you are intrested in it's history, here you can read something about it.

Furthermore, I have also included a very flexible logging system which grants me the possibility to know exactly what happening inside my program.

The other important thing that I've done is to create my own camera handling framework. The original idea was to implement an FPS like camera, although this set up turned out to be rather unconfortable.Therefore, I redesigned to work in the following way.

The camera points at a fixed point $\bar{C_l}$ in the space, and it can rotate on a sphere centered in $\bar{C_l}$ with a radius $C_r$.
You can move the camera on that sphere with a left-click and drag of your mouse. The radius $C_r$ can be modified with the mouse wheel.

You can also move the point $\bar{C_l}$ around and you might use your keyboard to do that. With W/S keys you can shift $\bar{C_l}$ on the Z-axis, A/S keys you can shift on the X-axis and with R/F on the Y-axis. I'm sorry to disappoint you but the R key does not involve any reload operation ;)

At the moment I'm striving to start to work on the shading, I need to add just a few modification in the application and then I can start working on it.

My first OpenGL application

After a 2-years work in the field of 3D reconstruction, computational geometry and 3D modeling I've realized that I need to learn also a little bit of rendering as well. During my free time I have watched several online video lectures and started the online course "Interactive 3D Graphics" on Udacity.

I've decided to use OpenGL as rendering API, because it is multiplatform and easily extendable to the Web application thanks to WebGL and Three.js

The first thing to do is to buy the Red Book of OpenGl.Another useful way to start is the video lecture, available in the SIGGRAPH University program, called "An Introduction to OpenGL Programming".

After some reading and watching I've created my first application. Although I just started from the "hellogl" test I alredy reorganized the code in order to make it easier to add new tests and so on.

The next step is to create the "Hello world" test that could only be the rendering of the Utah Teapot!


PS: for the lazy people here's the video lecture that I mentioned before