Zu dieser Karteikarte gibt es einen kompletten Satz an Karteikarten. Kostenlos!
37
Explain Surface-Based Hole Filling! What are some problems of this approach?
Input: Boundary loop consisting of vertices
.
Goal: Triangulation
of the loop interior which minimizes some triangulation cost
which is a combination of e.g.
which produces a hole filling with low area and low normal deviation.
We denote by
the cost of the best triangulation for only the vertices
.
Obviously:
![](/pool/data/tex/d998382498e90fd507433bac2286a7c6.gif)
![](/pool/data/tex/24195f503a05d331f2e95b7acd858f8a.gif)
![](/pool/data/tex/f00a663e969035e0a5ffb82a5aa89051.gif)
Solve using dynamic programming.
Complexity:
(Compute table for
and
. For every entry, consider
possible middle triangles)
Optional post-processing steps
Refine the triangulation of the hole.
Apply smoothing to the hole region.
Problems
Does not work for islands.
Does not consider self-intersections.
![](/pool/data/tex/717346857ee3a79c12b311469935ea0f.gif)
Goal: Triangulation
![](/pool/data/tex/b9ece18c950afbfa6b0fdbfa4ff731d3.gif)
![](/pool/data/tex/f1290186a5d0b1ceab27f4e77c0c5d68.gif)
- the area of the triangles
- the maximum dihedral angle
which produces a hole filling with low area and low normal deviation.
We denote by
![](/pool/data/tex/4ec12d05c32929d0ea204c61439556f3.gif)
![](/pool/data/tex/32549cfe08ca82f71b3d5ecd0b46cc22.gif)
Obviously:
![](/pool/data/tex/d998382498e90fd507433bac2286a7c6.gif)
![](/pool/data/tex/24195f503a05d331f2e95b7acd858f8a.gif)
![](/pool/data/tex/f00a663e969035e0a5ffb82a5aa89051.gif)
Solve using dynamic programming.
Complexity:
![](/pool/data/tex/cef9dab61517fb65be93b8bd8c3386cb.gif)
![](/pool/data/tex/865c0c0b4ab0e063e5caa3387c1a8741.gif)
![](/pool/data/tex/363b122c528f54df4a0446b6bab05515.gif)
![](/pool/data/tex/1365bcfde2fa9abee53d248bc4bae2ae.gif)
Optional post-processing steps
Refine the triangulation of the hole.
Apply smoothing to the hole region.
Problems
Does not work for islands.
Does not consider self-intersections.
![](/pool/img/avatar_40_40.gif)
Karteninfo:
Autor: janisborn
Oberthema: Informatik
Thema: Computergrafik
Schule / Uni: RWTH Aachen
Ort: Aachen
Veröffentlicht: 18.05.2022