1. PPT9: Global and local interpolation
CAP 6736
Geometric Modeling
PPT9: Global and local interpolation
PPT and video are due no later than March 22
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. Curve and Surface Fitting
Suggested content:
interpolation vs. approximation
constraints at various locations
degree, smoothness data reduction
non-uniqueness, selection
global versus local methods
application domains

5. Global Curve Interpolation
Suggested content:
Global curve interpolation
Choose knots and parameters
Solve for control points

6. Global Curve Interpolation
Suggested content:
Parametrization types
uniform
chord length
centripetal

7. Global Curve Interpolation
Suggested content:
Knot types
uniform
averaging

8. Global Curve Interpolation: Example
Suggested content:
Global curve interpolation detailed example
data points
parameters
knots
system of equations

9. Global Curve Interpolation
Suggested content:
Global curve interpolation examples
general data set
data with collinear path

10. Global Curve Interpolation with end Derivatives
Suggested content:
Global curve interpolation with end derivatives
general data set
solve with derivative data

11. Global Curve Interpolation with end Derivatives
Suggested content:
Global curve interpolation with end derivatives
The use of end derivatives as a design tool

12. Cubic Spline Curve Interpolation
Suggested content:
Cubic spline interpolations
Knots and parameters
System of equations

13. Curve Fitting with First Derivatives
Suggested content:
Global curve interpolation with first derivatives
general data set
solve with derivative data at each point

14. Curve Fitting with First Derivatives
Suggested content:
Global curve interpolation with first derivatives
effect of derivative magnitudes
examples

15. Global Surface Interpolation
Suggested content:
Global surface interpolation
parameters in each direction
the choice of knots

16. Global Surface Interpolation
Suggested content:
Global surface interpolation
interpolate in one direction

17. Global Surface Interpolation
Suggested content:
Global surface interpolation
interpolate in another direction

18. Global Surface Interpolation
Suggested content:
Global surface interpolation examples

19. Global Surface Interpolation
Suggested content:
Global surface interpolation examples
co-planar data points

20. Local Parabolic Curve Fitting
Suggested content:
Local parabolic curve interpolation
Choice of tangents at each point
Bessel method
Akima method

21. Local Parabolic Curve Fitting
Suggested content:
Local parabolic curve interpolation
Geometric and parametric continuity

22. Local Parabolic Curve Fitting
Suggested content:
Local parabolic curve interpolation
Parametrization differences

23. Local Parabolic Curve Fitting
Suggested content:
Local parabolic curve interpolation
The choice of end tangents

24. Local Parabolic Curve Fitting
Suggested content:
Local parabolic curve interpolation
Results with Bessel and Akima tangents

25. Local Parabolic Curve Fitting
Suggested content:
Local parabolic curve interpolation
Interpolating corners and simple shapes

26. Rational Quadratic Curve Fitting
Suggested content:
Local rational quadratic curve interpolation
The choice of middle weight

27. Rational Quadratic Curve Fitting
Suggested content:
Local rational quadratic curve interpolation
Interpolation with lines and circles

28. Local Cubic Curve Fitting
Suggested content:
Local cubic curve interpolation
The choice of end derivatives

29. Local Cubic Curve Fitting
Suggested content:
Local cubic curve interpolation
Knots and control points

30. Local Cubic Curve Fitting
Suggested content:
Local cubic curve interpolation
Examples

31. Local Bicubic Surface Fitting
Suggested content:
Local bicubic surface interpolation
The choice of knots
Computation of boundary control points
Computation of the four inner control points

32. Local Bicubic Surface Fitting
Suggested content:
Local bicubic surface interpolation
From data points to Bezier control net

33. Local Bicubic Surface Fitting
Suggested content:
Local bicubic surface interpolation
From Bezier control net to B-spline

34. Local Bicubic Surface Fitting
Suggested content:
Local bicubic surface interpolation
Example

35. Local Bicubic Surface Fitting
Suggested content:
Local bicubic surface interpolation
Example

36. Local Bicubic Surface Fitting
Suggested content:
Local bicubic surface interpolation
Handling of local features

37. Local Bicubic Surface Fitting
Suggested content:
Local bicubic surface interpolation
The inability to handle irregular data points

38. Part II: Design examples

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

40. 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.

41. Geometric Modeling Lab
Suggested project:
Design shapes using interpolation
Design common surfaces from points