1. PPT10: Global and local approximation
CAP 6736
Geometric Modeling
PPT10: Global and local approximation
PPT and video are due no later than March 29
Submit to:
This template file is just an outline of the presentation
that you need to complete. Additional pages may
be necessary to fully explore the topic above.
Each page should contain adequate text as well
as illustrations. You are free to use all publicly
available information (text as well as graphics) as long as
the sources are properly acknowledged.

2. Team members’ contributions
Member [name]:

3. Part I: Technical details
For this part you will need an equation editor. You may use:
MS equation editor,
MathType,
LaTeX, or
Handwritten equations if all else fails

4. Global Approximation Suggested content: Way-up approach:
start with minimum number of control points
get approximating curve/surface
check the error
if deviation is less than the tolerance, done
else, increase number of control points and
approximate again
Way-down approach:
start with maximum number of control points
if deviation is less than the tolerance, reduce number of control points
else, return to previous curve/surface

5. Least-squares Curve Approximation
Suggested content:
least-square curve approximation
choose parameters and knots
compute control points

6. Least-squares Curve Approximation
Suggested content:
least-square curve approximation
solve matric equation

7. Least-squares Curve Approximation with end Conditions
Suggested content:
least-square curve approximation
choose parameters and knots
compute control points
Suggested content:
least-square curve approximation with end derivatives
choose parameters and knots
compute control points

8. Least-squares Curve Approximation with end Conditions
Suggested content:
least-square curve approximation
set up and solve matrix equation

9. Least-squares Curve Approximation with end Conditions
Suggested content:
least-square curve approximation
pseudocode algorithm

10. Least-squares Curve Approximation with end Conditions
Suggested content:
least-square curve approximation
examples with different number of control points

11. Weighted and Constrained Least Squares Curve Fitting
Suggested content:
least-square weighted and constraint curve approximation
constraint and unconstraint data
weights for unconstraint items
interpolate constraint data
approximate unconstraint data

12. Weighted and Constrained Least Squares Curve Fitting
Suggested content:
least-square weighted and constraint curve approximation
constraint and unconstraint data
setup the matrixes and solve

13. Weighted and Constrained Least Squares Curve Fitting
Suggested content:
least-square weighted and constraint curve approximation
examples

14. Least Squares Surface Fitting
Suggested content:
least-square surface approximation
fit curves to rows of data
fit curves to rows of control points

15. Least Squares Surface Fitting
Suggested content:
least-square surface approximation
surface approximation
error surface

16. Least Squares Surface Fitting
Suggested content:
least-square surface approximation
surface approximation
error surface

17. Least Squares Surface Fitting
Suggested content:
least-square surface approximation
data points
surface interpolation compared to approximation

18. Approximation to within a Tolerance
Suggested content:
curve approximation with error control
general strategy
error measures

19. Approximation to within a Tolerance
Suggested content:
curve approximation with error control
examples

20. Approximation to within a Tolerance
Suggested content:
surface approximation with error control
examples: tolerance = 0.0

21. Approximation to within a Tolerance
Suggested content:
surface approximation with error control
Examples with different tolerances

22. Approximation to within a Tolerance
Suggested content:
curve approximation with data smoothing
examples with one and two levels of smoothing

23. Local Curve Fitting Techniques
Suggested content:
local curve approximation
general quadratic and cubic fitting
strategy to find optimal number of arcs

24. Local Conic Curve Fitting Techniques
Suggested content:
local conic approximation
end tangents and weights

25. Local Conic Curve Fitting Techniques
Suggested content:
local conic approximation
examples

26. Local Conic Curve Fitting Techniques
Suggested content:
local conic approximation
examples

27. Local Cubic Curve Fitting Techniques
Suggested content:
local cubic approximation
choice of derivatives
constructing of control points
non-planar case

28. Local Cubic Curve Fitting Techniques
Suggested content:
local cubic approximation
choice of derivatives
constructing of control points
planar case

29. Local Cubic Curve Fitting Techniques
Suggested content:
local cubic approximation
error check

30. Local Cubic Curve Fitting Techniques
Suggested content:
local cubic approximation
examples

31. Local Cubic Curve Fitting Techniques
Suggested content:
local cubic approximation
2D and 3D examples

32. Local Cubic Curve Fitting Techniques
Suggested content:
local cubic approximation
3D examples

33. Part II: Design examples

34. Design Examples Suggested content:
Add design examples: images and/or videos
Give credit to the designers

35. Part III: GM lab
For this part of the assignment you may use an existing system,
such as Blender, or write the code and visualize the result
using graphics tools like Processing.

36. Geometric Modeling Lab
Suggested project:
Design shapes using approximation
Design common surfaces from point clouds