the actual cutter axis of the milling machine (s. 
fig. 3.1-1). The filtered raw data are rearranged 
and interpolated so that on every plane, loop 
contours are generated. These contours are 
described either by straight lines, by arcs or by 
splines. As these geometries are analytical 
formulated, they can be resolved in almost any 
required resolution. A typical example of loop 
contours built up by spline curves is shown in 
fig. 3.1-1. The workpiece was mapped by 4D-LM. The 
description of a surface by contours form the 
input for all further processing functions (e.g. 
positive, negative and pocket milling)and for the 
NC-program generation according to DIN 66025 or to 
a manufacturer specification format (e.g. FIDIA, 
Siemens, Bosch, Fanuc). In this processing level 
e.g. cutter orientation, cutter offset and 
material thickness are arbitrarily chosen by the 
operator. Within the NC-program generation all 
known geometric operations, e.g. rotation, 
scaling, mirror imaging and translation, are 
possible. In addition the user has the possibility 
of a visual control of the NC-program by 
simulating graphically the milling process on a 
display. The simulation result can be stored 
either in postscript file or an HPGL file for 
later printing. 
Fig. 3.1-2 shows the measurement results of a 
typical workpiece in a wiregrid and the cor- 
responding projected contours. In fig. 3.1-3 the 
contours are perspectively plotted. The contours 
are calculated from the three dimensional measure- 
ment data and are described by spline curves 
internal the computer model generator. 
  
  
   
    
  
  
   
  
  
  
   
    
    
    
   
   
     
    
   
   
    
   
   
     
      
     
  
    
   
  
    
     
  
  
     
    
  
  
  
  
   
  
  
  
   
3.2 Surface Modelling and Data Generation for 
CAD/CAM-Systems 
In current CAD/CAM- and CAP-systems which are 
applied in tooling and molding industry the 
molding workpieces are mainly modelled mathe- 
matically. In most practical applications the 
analytical description of such objects is not 
sufficient. In these cases an approximation and 
interpolation is necessary which rises the space 
and time complexity. If a freeform surface is 
digitized one has to handle a very hight amount of 
data (Mega Bytes) which demand too much calcu- 
lation performance from existing CAD/CAM-systems. 
To solve this problem a data reduction is required 
to carry out an efficient data processing. E.g. by 
computing spline curves and spline surfaces em- 
ploying different algorithms, a data reduction of 
better than 80% can be achieved in dependence of 
the complexity of the workpiece. 
The following algorithms were studied and 
implemented: 
- bicubic Bezier, 
= polynomial representation (Coons), 
= B-Spline, 
- Non Uniform Rational B-Splines (NURBS) 
representation (s. fig. 3.2-1). 
These computed internal representation of the 
digitized object is obtained by the Advanced 
Surface Modelling Software Package (ASMOS) de- 
veloped by the Institute for Control Technology 
for Machine Tools and Manufacturing Systems (ISW) 
of the University of Stuttgart and can be proces- 
sed by all 2D / 3D oriented CAD/CAM-Systems. For 
the Datatransfer within CAD's- and CAP's-Sytems 
following Interfaces are available: 
- IGES 4.0 and 
- VDAFS 2.0. 
  
Fig. 
3.2-1: NURBS Representation