1. From Point Clouds To Trimmed NURBS

2. MOTIVATION Digitizing Geometry CAD Modeling Field of Entertainment

3. Reverse Engineering Point clouds Surfaces Manipulate existing objects
Create new objects from existing objects
Model objects otherwise difficult to model

4. Common Surface Representations
NURBS
Industry Standard
Compact Representation
Intuitive Shape Control
Triangle Meshes

5. Point Cloud Data Characteristics Large data sets Holes in the Geometry
Problems
Noisy
Missing data

6. Our Approach Smoothing for noise removal
Hole filling and triangulation
Parameterization
Fitting by blending local fits

7. Smoothing Find the local neighborhood of each point
Project each point onto the surface obtained using MLS approximation about that point

8. Hole Filling Local Method Introduce points in the parameterization
Introduce points radially inwards along the boundary of the hole.
Project each point onto its MLS surface
Triangulate

9. Hole Filling – Curve Example

10. Hole Filling

11. Triangulate Hole
Step 1: Eliminate extremely small angles along the border by introducing a new triangle
Triangulating Hole
Step 2: Introduce new point for each point in the border and simultaneously add it to the closest triangle.
Repeat Step 1 and Step 2 until you have a boundary with just 3 vertices.

12. Triangulation Step 2 Unfilled Hole Step 1 Unfilled Hole
Filled and Triangulated

13. Hole Filling

14. Parameterization
Harmonic maps

15. Data Fitting Moving Least Squares
Least Squares Fit
Moving Least Squares fit at point (xj , yj)

16. Fitting
Hierarchial Subdivision of Domain

17. Blending Local Fits

18. Blending Local Fits

19. The Tank Model
Engine
Wheel

20. Parts of the Tank Model

21. Blending Fits- Surface

22. Engine from the Tank Model

23. Extending Boundaries (Completing Rectangular Domain)

24. Completing the Parametric Domain