Basic 3D represention

Shape

3D models are made up of a series of triangles all of which are completely flat. That is if we were to look at each of the 3 corners of a triangle, all 3 would be on the same plane. multiple triangles that are adjacent to each other form meshes. While each individual triangle must be flat, the triangles within a mesh do not need to be co-planar. the edge between two triangle allows for the creation of curves.

The more triangles in the model, the smoother the shape of the model. As we can see from the meshes above, the first model (top left) only gives the general shape of a bunny while the bottom bunny shows a lot more curvature and much more details regarding the shape of the model.

Programmatically a mesh is stored as a series of vertices and edges that make up a number of faces. Each vertex is described as simply 3 values, x, y and z. These values represent the location of the vertex in 3D space. An edge, describes the connection between two vertices. A face is described by 3 or more vertices given in a particular order. Exactly how the data is stored and represented can be different between different 3D applications and thus, understanding that is key when you have to deal with the models programmatically.

In the end, what we need to understand is that the more triangles we have, the more data must be stored which can then have an affect rendering time.

Textures

The values of the vertices only define the shape of the object. In order to create details (like adding eyes to the bunny for example) we need to apply a texture to a mesh. A texture is simply a 2D image that is pinned to the mesh. Each face is laid out onto a 2D surface and the portion of the texture within that face is applied to the surface of the 3D mesh.

The location of each vertex of each face on this image is represented by 2 values, the u and v coordinates. If the u and v coordinates are different, the image will be laid out in a different manner on the object. In the picture below, two identical spheres have the same texture applied to it. However, they each have a different uv layout. Thus, the resulting spheres have a different pattern on it.