Efficient Fitting and Rendering of Large Scattered Data SetsUsing Subdivision Surfaces

Vincent Scheib1, Jörg Haber2,

Ming C. Lin1, Hans-Peter Seidel2

1-UNC Chapel Hill 2-MPI für Informatik

Presentation Overview

Introduction we are here

Fitting method

Rendering technique

Results

Goal

Interactively display a smooth surface defined by many scattered data points. arbitrary 2d functional data: height-fields

Method

Fit a smooth surface to data points

Display smooth surface interactively

Challenges

Large number of data points (1,000,000) Fitting is difficult

Large continuous surface with much detail Rendering is slow

Challenges – Solutions

Large number of data points (1,000,000) Fitting is difficult Local area support

Large continuous surface with much detail Rendering is slow Adaptive level of detail

Contribution Overview

Adaptive subdivision of scattered data points via binary triangle tree (BTT)

Local least squares fitting based on BTT

Modified Butterfly subdivision surface fit to BTT

Adaptive BTT terrain rendering algorithm used to simplify butterfly control mesh.

Previous Work – Fitting

Primary: Haber et al. 01Fitting: Franke 82, Lancaster et al. 86, Lodha et al. 99, Schumaker 76Tensor product splines & Nurbs: Dierckx 93, Forsey et al. 95, Greiner et al. 96, Qin et al 96Other spline methods: Lee et al. 97, Schmitt 86, Zhang et al. 98Radial basis methods: Buhmann 00, Carr et al. 01, Franke et al. 90, Powell 87

Previous Work – Terrain

Adaptive LOD: Duchaineau et al. 97, Ferguson et al. 90, Lindstrom et al. 96, Lindstrom et al. 01LOD: Stewart 97, Wiley et al. 97Visibility: Cohen et al. 93, Cohen et al. 95, Coquillart et al. 84, Lee et al. 97TIN: Cignoni et al. 97, Klein et al. 98Subdivison Surface: Rose et al. 01

Presentation Overview

Introduction

Fitting method we are here

Rendering technique

Results

Fitting – Challenges

Large number of data points (millions)

Unknown 2D domain

Unknown ordering

Holes possible

Varied Density

773756.18 219787.37 743056.96101338.63 458053.70 756748.44237783.93 487348.18 457761.01882215.91 453792.33 905793.92013454.35 346526.21 445262.09130348.26 361542.99 924993.53572820.22 878734.42 262069.23993199.99 428390.50 434400.99463460.63 858168.16 280848.09420387.06 832663.36 798203.96372409.45 644566.37 497683.69962804.19 911252.39 621007.75128392.59 154947.23 948117.55673782.18 426081.35 756265.86498310.05 114353.99 281902.11771987.34 898968.70 982882.92104486.49 373192.70 336830.10

Fitting – Divide and Conquer

Binary Triangle Tree (BTT)

Fitting – SVD

Obtain Z value for each vertexLocal AreasSingular Value DecompositionLeast Squares fit Bivariate Polynomial

Presentation Overview

Introduction

Fitting method

Rendering technique we are here

Results

Rendering – Overview

High detail Large area

Rendering – Tessellation

Rendering – Tessellation

Binary triangle tree without and with butterfly subdivision

Rendering – Adaptive LOD

a. butterfly b. stitching c. control mesh (BTT)d. decimated control mesh

View point on left

Rendering – Video

Video illustrating tessellation

Presentation Overview

Introduction

Fitting method

Rendering technique

Results we are here

Results – Platforms

Several PC graphics workstations Pentium2 .4GHz GeForce 2GTS Pentium3 .9GHz nVidia GeForce 2GTS Xeon 1.5GHz nVidia GeForce 3

Videos recorded form this machine Pentium3 1.7GHz nVidia GeForce 3

Results – Data Sets

Scientific Visualization 10,000 data points

Survey Terrain Data 45,000 & 736,000 data points

Fractal Terrain Data 1,000,000 & 4,000,000 data points

Results – Error

1 million point 12x12 km real world data

15m max error; 0.8m RMS error

13 seconds fitting computation

Results – Performance

Animation comparing new method with previous Bezier patch method.

Conclusions

CPU bound conservative triangle rendering

Adaptive tessellation error metrics for terrain simplification subdivision surface

Tolerable error accepted for speed

Combination of fast fitting and interactive rendering

Future Work

Exploit coherency

Balance CPU/GPU workload Static display lists, Tile based?

Acknowledgments

Funding Intel Corporation National Science Foundation Office of Naval Research

Acknowledgments

Sample BTT and Butterfly Subdivision Code Gamasutra.com & Andrew Zaferakis

Data sets Landesamt für Kataster-, Vermessungs- und

Kartenwesen des Saarlandes Leandra Vicci

Advice Dinesh Manocha