Digital Geometry Processing Basics DCEL (cont.)

Digital Geometry Processing
Basics
DCEL (Doubly-Connected Edge List)
Record for each face, edge and vertex:
Geometric information
Topological information
Attribute information
aka Half-Edge Structure
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DCEL (cont.)
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Vertex record:
Coordinates
next(e)
Pointer to one
half-edge that has
prev(e) IncFace(e) e
v as its origin
twin(e)
Face record:
Pointer to one halfedge
on its
boundary
origin(e)
Half-edge record:
Pointer to its origin, origin(e)
Pointer to its twin half-edge, twin(e)
Pointer to the face it bounds, IncidentFace(e) (face lies to left
of e when traversed from origin to destination)
Next and previous edge on boundary of IncidentFace(e)
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Copyright 2002-2006 A. Sheffer & C. Gotsman
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Digital Geometry Processing
Basics
DCEL (cont.)
Operations supported:
Walk around boundary of given face
Visit all edges incident to vertex v
Queries:
Most queries are O(1)
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DCEL - example
v 3
f
f 1 e
e 3,2
3,1
f 2
v
e
e 8,1
5,1 4
f 4
3
e 7,1
v 5
e 1,1
e 6,1
e 4,1
e 7,2
e 9,1
v 1
v 2
e 2,1
e 4,2
v 6
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Vertex
coordinate
V 1
(x 1
,y 1
,z 1
)
v 2
(x 2
,y 2
,z 2
)
v 3
v 4
(x 3
,y 3
,z 3
)
v 5
(x 4
,y 4
,z 4
)
(x 5
,y 5
,z 5
)
v 6
(x 6
,y 6
,z 6
)
IncidentEdge
e 2,1
e 5,1
e 1,1
e 7,1
e 9,1
e 7,2
face
edge
f 1
e 1,1
f 2
f 3
e 5,1
e 4,2
f 4
e 8,1
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Copyright 2002-2006 A. Sheffer & C. Gotsman
UBC/ Technion
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Digital Geometry Processing
Basics
DCEL – example (cont.)
v 3
f
f 1 e
e 3,2
3,1
f 2
v
e
e 8,1
5,1 4
f 4
3
e 7,1
v 5
e 1,1
e 6,1
e 4,1
e 7,2
e 9,1
v 6
v 1
v 2
Half-edge
origin
twin
IncidentFace
next
prev
e 3,1
v 2
e 3,2
e 4,1
v 3
v 4
e 4,2
v 3
e 2,1
e 4,2
e 6,1
e 3,2
e 3,1
e 4,2
e 4,1
f 1
f 2
f 2
f 3
e 1,1
e 5,1
e 3,2
e 7,1
e 2,1
e 4,1
e 5,1
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DCEL – pros and cons
Pros:
All queries in O(1) time
All operations are O(1) (usually)
Cons:
Represents only manifold meshes
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British Columbia
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Copyright 2002-2006 A. Sheffer & C. Gotsman
UBC/ Technion
Page 16