Normals are an important piece of geometry for rendering
smooth surfaces. Generation of proper normals is very straightforward
for continuous surfaces. To calculate a smooth normal for a vertex,
average the facet normals of all the polygons that the vertex is in.
However, this does not work when there are edges that are to be
preserved in the model. This method will smooth out all edges.
Therefore, it is desirable to selectively average normals according to
a threshold for edge preservation.
A good example is a model of a cube. It is desirable for
the cube to have flat faces. However, if all the facet normals around
a vertex are averaged, and the resulting average normal is used, the
cube takes on a spherical look (see figure 1),
which is probably not the desired effect.
Another gotcha when creating smooth normals is duplicate
vertices. These can be eliminated by 'welding' vertices that are
closer than a tolerance to each other. Then the normals are recalculated. See figure 2 for an example of this.
Different models require different edge tolerance angles.
Sometimes the angle across some edges is the same as the angle between
some geometry that should be smooth. This is a problem with my
current algorithm. It could be dealt with by localizing the averaging
according to user defined areas. See figure 3 for
an example of problems of this kind (the base of the pawn is faceted,
when it shouldn't be, but the tolerance must be 76° for the edge in
the middle to appear).
/* glmVertexNormals: Generates smooth vertex normals for a model.
* First builds a list of all the triangles each vertex is in. Then
* loops through each vertex in the the list averaging all the facet
* normals of the triangles each vertex is in. Finally, sets the
* normal index in the triangle for the vertex to the generated smooth
* normal. If the dot product of a facet normal and the facet normal
* associated with the first triangle in the list of triangles the
* current vertex is in is greater than the cosine of the angle
* parameter to the function, that facet normal is not added into the
* average normal calculation and the corresponding vertex is given
* the facet normal. This tends to preserve hard edges. The angle to
* use depends on the model, but 90 degrees is usually a good start.
* model - initialized GLMmodel structure
* angle - maximum angle (in degrees) to smooth across