ken as 
ttribute 
ttribute 
ttribute 
f share 
ttribute 
> With 
further 
ttribute 
ary to 
imitive 
h, the 
aspect- 
-aspect 
we can 
imitive 
which 
ct and 
  
tructing 
CT- 
can not 
> a part 
| object 
pre we 
ce the 
n CAD 
relation 
e data 
realize 
ph. So 
ructure 
  
an object represented with this kind of data 
structure, the object can be divided into volume, 
face, ring, edge and vextice[10]. Obviously, the 
mode attribute hypergraph describing this 3-D 
object can directly be constructed in term of its 
= data structure. The primitive graph describing 
| Fem primitive can also directly be constructed 
t — according to its data structure. The attribute 
En F F backward . "yn 
DES ' — forward relational graph describing face can be 
" = constructed in the same way. 
So the order of constructing mode aspect- 
graph is attribute hypergraph, primitive attribute 
+ Pop graph and attribute graph, which correspond to 
object, volume and face respectively. The 
i LP backward constructing regulation is the same as one of 
Cylinder 
| F bottom 
forward Lo image aspect-graph above. For example, the Fig. 
CLP bottom 11a is an industrial object and its data structure 
. represented with combining CSG and B-rep in 
f Zee GEMS[10,11], Fig. 11b is its attribute 
between volumes. Fig. 11c is an attribute graph, 
which describes faces and their connected 
acrel relation. The graph El and E2 are volume graph 
describing cone and cylinder respectively. How 
to transfer data structure into model aspect- 
(er ) © graph was described in detail in 
(b) references[6,10,1 1]. 
5. MODEL MATCHING and DATA 
STRUCTURE 
In order to look for the relation between image 
graph and model graph, we quote several 
lemmas as follows [20]. 
lemma I The total number of nodes in a model 
graph is equal to the total number of faces in the 
3-D object. 
lemma 2 The total number of branches in a 
model graph is equal to the total number of 
edges in the 3-D object. An edge may be a 
straight or curved physical edge. 
lemma 3 The connecting total number of every 
node is equal to the total number of all physical 
edges which the node lies in surface. 
lemma 4 The projection from 3-D space does 
not change the topology of how the vertices are 
Fig. 11 CAD data construct and its aspect-graph connected, The projection only hides some of 
the straight and junction in 2-D. These are called 
hidden straight and hidden surface in computer 
graphics literature. 
lemma 5 The projection graphs constructed from 
the 2D projections of 3D object are subgraph 
isomorphism of the model graph constructed 
from the 3D object. Simply speaking, projection 
graph is subgraph isomorphism of model graph. 
P2 
| P1 | | hypergraph, which describes connected relation 
edged edge2 
  
An object is represented by Construct Solid 
Geology(CSG) and Boundary represent(B-rep) 
in applied CAD system[10,11], i.e. an object is 
composed of many primitives by Boolean 
operator(unit, intersection and difference), and 
the primitive is described in B-rep. The Wing- 
edge structure is used as describing the topology 
information of boundary model[10,11]. In such 
1023 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996