
 References
  
References 6. Face Tracing
 
6. Face Tracing
1. Find the vertex list of all the polygon faces
2. Adjust Vertex list order of the face to be
counter-clockwise
3. Reduce all polygons to triangles
 
1.  Face Tracing Algorithm
 
 
| For Each Egde 
 Repeat if desired (until each edge is marked exactly twice) | 
For rendering purposes, we would like to have
the normals of all faces facing outward.  We use the right-hand rule
(counter-clockwise) to determine the direction of the normal.  Using
the vertices of one of the mapped model, we can calculate the normal of
a polygon face and the vector from the center of the model to the face. 
Calculate the dot product of the two, we can determine if the polygon is
facing outward or inward.  If the polygon is facing inward, we simply
reverse the order of the vertex list of the polygon face.
 
3.  Triangles-only club
We need to make sure all polygon faces are triangles
since a triangle is always flat.  This is done for rendering purpose
also.  We used a very simple method of reducing polygon to triangles. 
Take any vertex of a face and draw a line to the rest of the vertices. 
We can use this method since we are guaranteed to have convex polygon faces.
 
 
 7. Polygon Interpolation
  
7. Polygon Interpolation
This is the simplest scheme. The coordinates X, Y and Z are linearly interpolated from PM1 to PM2 with the same rate. The result is similar to putting the air to one object and it inflates to become the other.
2. Non-Linear Symmetric Interpolation
The variant of this scheme is that the coordinates
X, Y and Z are non-linearly (exponentially) interpolated from PM1 to PM2,
but still with the same rate.  The result is similar to putting the
air to one object and it inflates to become the other.  The different
is that the object morph slowly at the beginning and fast at the end. 
 
3.  Non-Linear Non-Symmetric Interpolation
The variant of this scheme is that the coordinates
X, Y and Z are not interpolated with the same rate.  The result is
non-symmetric transformation.
 
 


 8. Applications
  
8. Applications



 9. Source Code Distribution
  
9. Source Code Distribution
 10. Summary
  
10. Summary
 References
  
References[2]    J, R. Kent, W. E. 
Carlson and R. E. Parent, Shape Transformation for Polyhedral Objects. 
In Computer Graphics (SIGGRAPH'92 proceedings), volume 26, pages
47-54, July 1992.
 
[3]    Kent, J, Parent, R. and
Carlson, W.  Establishing Correspondences by Topological Merging: 
A new Approarch to 3-D Shape Transformation.  Proceedings of Graphics
Interface '91 (Calgary, Alberta, June, 1991) 271-278.
  
[4]    Foley, J., A. van Dam,
S. Feiner and J. Hughes, Computer Graphics - Principles and Practice, Addison-Wesley
Publishing Company, Inc., Reading, Massachusetts, 1990.
  
[5]    Neider, J., Davis, T. and
Woo, M.  Polygon Construction and Rendering Scheme.  In OpenGL
Programming Guide, The Official Guide to Learning OpenGL, Version 1.1,
Addison Wesley Public Company, January 1997.