Part II

  1. Shading techniques.
  
  1.1 Classical illumination model of a polygon mesh
  
   In the classical case (not the radiosity), the intensity (color or
   gray-scale) at each pixel, corresponding at a polygon, is calculated
   in attributing one color per facet (constant shading), by scalar
   interpolation (Gouraud) or vectorial interpolation (Phong).
   
   [LINK]-[IMAGE]
   
   For the following example:
   
   [LINK]-[IMAGE]
   
  1.2 Shading :
  
  1.2.1 Constant shading.
  
   Each facet of the object is illuminated by an average value for the
   entire polygon. This approach is fast and very simple, but it gives
   quite poor realistic results and non smooth surfaces. This is enhanced
   by the Mach effect: the intensity at the vicinities of the edges is
   overestimated for light values and underestimated for dark values.
   
   [LINK]-[IMAGE] On the left a Connolly surface of the ferrocene in
   Gouraud shading, and on the right the same surface with flat shading.
   
  1.2.2 Gouraud shading.
  
   The Gouraud shading eliminates intensity discontinuities by
   interpolating the intensity for each polygon. It uses the normal
   vector at each vertex and edges of the polygon mesh (obtained by
   averaging each normal of the facets sharing the same edge).
   
   [LINK]-[IMAGE]
   
   the model determines the intensity at each vertex and then
   interpolates linearely between each normal along the edge and then the
   same way between the edges for every scan-line. This scan-line
   algorythm is very often hardware implemented. The Mach effect is
   allmost completly eliminated (except for very high curvated surfaces).
   
   [LINK]-[IMAGE]
   
  1.2.3 Phong shading.
  
   The Phong shading is like the Gouraud shading based on an
   interpolation algorythm but this time, the interpolation is made by
   vectors. It uses the normals at each facet, the average normals at
   each vertex, and interpolates vectorially along the edges between to
   vertex, and then interpolates the same way between the edges along the
   scan-line (very heavy calculation, as it has a normalisation
   calculation at every step).
   
   [LINK]-[IMAGE]
   
   This model gives a nice render to specular lights. A new approach
   recently developped allows to simulate Phong shading for lesser
   computation costs, (see the 2D textures )
   
  1.2.4 Problems with interpolated shadings.
  
   The most common problems encountered with interpolated shading are
   overcomed by utilizing triangles as polygon or by enhancing the
   numbers of polygon (which is expensive).
   
   For example, a highly curved surface (typically a sphere) will clearly
   have a polygonal silhouette. This situation can be improved by
   breaking the surface into a greater number of smaller polygons, but
   with increase in expense.
   
   Anomalies are introduced also by the interpolation because the
   interpolation is performed after perspective transformation in th 3D
   screen coordinates, rather than in the World coordinates system.
   
   An orientation dependence exists due to the scan-line algorythm and
   can induce discontinuities when rotating the object, this can be
   overcome by using triangles as polygons.
   
   Not directly involved in the interpolation procedure but rather when
   calculating normals at each vertex, errors can araise when averaging
   over non-representative normals. As in the example of a sharp-toothed
   edge surface were all the normals at each vertex are parallel, the
   surface will be rendered flat. This can be overcome by assigning an
   eigen normal at each vertex.
   
   [LINK]-[IMAGE]
   
   [LINK]-[IMAGE] Chapter 2 and 3.
   
   [LINK]-[IMAGE]Table of contents.
   
     _________________________________________________________________
                                      
   
    Responsible : François Savary, savary@sc2a.unige.ch
    Group of Professor J. Weber, Department of Physical Chemistry,
    University of Geneva
    30, quai Ernest Ansermet CH-1211 Geneva 4
    tél.: +4122 702 65 32
    fax : +4122 702 65 18
.