Jaal: Surface Quadrangulation

Contents:

  1. Introduction.
  2. Literature Survey on Quadrangulation.
  3. Suneeta's Tree Matching Algorithm.
  4. Mesh Quality Improvement
    1. Quality Measures
    2. Smoothing
    3. Topological Cleanup
    4. Shape Optimization
  5. Results
  6. Future Work
  7. Acknowledgement
  8. Software user guide and download information

Introduction:

Literature Survey on Quadrangulation:

Tree matching Algorithm








square
 bfs
 dfs
Triangulated Mesh
 BFS Tree
 DFS Tree


Results:

lake
Figure:  Lake Superior triangulated mesh generated using "Triangle"

DataSet Size
#Triangles
 BFS Tree Matching
#Quads
 DFS Tree Matching
#Quads
 Edmond's Graph Matching
#Quads
3084
 1475
 1413
 1542
23791
 11620
 10907
 11895
236274
 115350
 108760
 118136
2406597
 1176314
 1108598




Table : Matching Triangulated Mesh


DataSet
 BFS
(in sec)
 DFS
(in sec)
 Edmond
(in sec)
















Table: Performance of tree v/s graph matching algorithms

Future Work:


Acknowledgment


Software user guide and download information


Module

Description
Mesh.h Mesh.cc
 Mesh data structures, Mesh IO, Entity Relation Managment
DualGraph.h
DualGraph.cc
 Construct Dual Graph of a given triangulated mesh.
binarytree.h
binarytree.cc
 Constructs BFS or DFS binary tree of a given dual graph.
percolateup.cc
 Implements Tree matching using Suneeta's  Algorithm
qpercolateupdown.cc
 Implements Tree matching where unmatched nodes are the leaves
tquadrangualte.cc
 Modified qpercolateupdown to insert steiner points to create quadmesh.
laplacesmooth.cc
 Apply laplacian smoothing: using Meshquite Software
meshcleanup.cc
 Topological improvement code. (Face open, Face Close, Swapping, Dicing)
shapeoptimization.cc
 Improves the shape quality of the quads ( using Meshquite Software)
meshquality.cc
 Evaluates quality of the final mesh ( topological and geometric quality )