Smooth Geometry Images - PowerPoint PPT Presentation

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Smooth Geometry Images

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Smooth Geometry Images. Frank Losasso, Hugues Hoppe, Scott ... Special type of cut curve. Make a X-cut centered at x. Unfold domain into a square image ... – PowerPoint PPT presentation

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Title: Smooth Geometry Images


1
Smooth Geometry Images
  • Frank Losasso, Hugues Hoppe, Scott Schaefer, Joe
    Warren

2
Overview
  • Provide a simple representation using a single
    uniform bi-cubic B-spline

Multiple Patches
Single Patch
3
Geometry Images
Gu et al 2002
  • Sample arbitrary surface using a regular 2D grid
  • Connectivity is implicit

4
Gu et al 2002
cut
parametrize
5
Gu et al 2002
cut
sample
6
Gu et al 2002
cut
store
render
r,g,b x,y,z
7
General cut
Gu et al 2002
  • Supports surfaces of arbitrary genus
  • But, boundary has complicated topology requires
    sideband

a
a
a
a
8
Our Approach X-Cut
  • Special type of cut curve
  • Make a X-cut centered at x
  • Unfold domain into a square image
  • Creates simple boundary symmetries

9
The X-Cut
10
Spherical Remeshing
image I
domain D
sphere S
mesh M
demo
Praun and Hoppe 2003
11
How To Obtain Control Points
  • B-spline is approximating ? should not directly
    sample surface
  • Instead, use least-squares fitting

?
12
How To Obtain Smoothness
  • Application of boundary rules
  • Pad image to recreate 1-ring around all vertices

13
How To Obtain Smoothness
  • All vertices regular, except boundary midpoints

generally not C1
14
Bi-cubic Subdivision on GPU
  • 4 operators, stored as fragment programs

limit
bilinearsubdivision
meshaveraging
tangent
repeat
15
Bi-cubic Subdivision on GPU
  • 4 operators, stored as fragment programs

limit
bilinearsubdivision
meshaveraging
tangent
repeat
16
Rendering
  • Interpret as vertex array (OpenGL extension)
  • Render using triangles

17
Discrete Subdivision Levels
  • Both sub-sampling and subdivision are easily
    implemented

(2k1) x (2k1)
Original Image
18
Continuous Subdivision Levels
  • Prevent popping when changing subdivision levels

gk
gk1
19
Continuous Subdivision Levels
  • Prevent popping when changing subdivision levels

linearsubdivision
1-?

?
gk?
meshaveraging
bilinearsubdivision
gk
gk1
20
Real-Time Demo
21
Displacement Mapping
simulation
GPU
CPU
33x33
GPU
scalardisplacementmap
257x257
22
Performance Results
23
Drawbacks and Limitations
  • Genus cannot be gt0
  • Surface rippling

24
Summary
  • Closed smooth surface using single patch
  • Stored as geometry image
  • Simple and efficient GPU evaluation
  • Continuous level-of-detail
  • Displacement mapping

5x5
9x9
25
Eye candy
65x65
33x33
65x65
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