Reconstruction of Smooth Surface Suitable for LOD Model Construction

1
Reconstruction of Smooth Surface Suitable for LOD
Model Construction
Jaroslav Semancík
KSVI MFF UK
MIS 2003
Josefuv Dul, 21-22. 1. 2003
2
Motivation to use smooth surface

• Accuracy and efficiency
• Advancements in theory of geometric modeling
• Hardware acceleration
• Low-level ? high-levelanalogy with programming

3
The goal
?

• Flexible and efficient representation
• ? Net of triangular parametric patches
• Interpolation

4
Smooth surface reconstruction

• Two steps
• Construct boundary curves over the mesh edges
• Fill the interiors by triangular patches(Coons
  patch)
• Smoothness on patch boundaries

? 2.
? 1.
5
1. Boundary curves construction
?

• Cubic Hermit curves
• Determined by endpoints andtangent vectors
• Tangent vector calculation

6
2. Triangular Coons patch
?

• Interpolates arbitrary boundary curves
• Construction by blending of 3 auxiliary patches

7
2. Triangular Coons patch cont.

• Convex combination of 3 patches each of them
  interpolating a pair of curves

P X uP1X vP2X wP3X
P1X
P2X
P3X
.
.
.


u
v
w
8
Smoothness on patch boundaries

• The same tangent plane ? G1-smoothness
• Construct tangent plane fields along
  boundaries(tangent plane ? normal)
• Modified patch construction to respect the
  boundary normals

?
9
Conclusion and results
?

• Smooth surface interpolating input mesh vertices
• Problems
• LOD model construction

10
Results