1. PPT8: Common Surfaces as NURBS
CAP 6736
Geometric Modeling
PPT8: Common Surfaces as NURBS
PPT and video are due no later than March 8
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. Bilinear Surfaces Suggested content:
Bilinear surfaces: control points and knots
Planar as well as non-planar surfaces
Example: saddle design

5. General Cylinder Suggested content: General cylinder as a sweep
Profile curve + sweeping

6. General Cylinder Suggested content: General cylinder examples
closed cylinder
open cylinder
general sweep

7. Ruled Surfaces Suggested content: Ruled surfaces rail curves ruling
surface form
control points and knots

8. Ruled Surfaces Suggested content: Ruled surface examples
rail curve compatibility
knot merging
surface form
several examples

9. Ruled Surfaces Suggested content: Ruled surface examples
rail curve after compatibility
ruled surface

10. Ruled Surfaces Suggested content: Ruled surface examples
open and closed cones
conoids
artistic applications

11. Ruled Surfaces Suggested content: Ruled surface examples
the art of ruling
sculptured surfaces as ruled surfaces

12. Ruled Surface via Symbolic Operators
Suggested content:
Ruled surface with symbolic operators
Rational curves ruled in homogeneous space
Creases in parametrization

13. Ruled Surface via Symbolic Operators
Suggested content:
Ruled surface with symbolic operators
Rational curves ruled in Euclidean space

14. Surface of Revolution Suggested content: Surfaces of revolution
Profile curve and revolution axis
Requirement of revolution

15. Surface of Revolution Suggested content:
Construction of surfaces of revolution
Revolution circle knots and weights
Surface control points
Surface weights

16. Surface of Revolution Suggested content:
Surfaces of revolution example
Control net and surface

17. Surface of Revolution Suggested content:
Surfaces of revolution examples
Sphere and torus

18. Surface of Revolution Suggested content:
Surfaces of revolution examples
Open surfaces

19. Surface of Revolution in Practice
Suggested content:
Surfaces of revolution in practice
Discrete data – profile curve – surface of revolution

20. Surface of Revolution in Practice
Suggested content:
Surfaces of revolution in practice
Circle of revolution with different degrees

21. Non-uniform Scaling of Surfaces
Suggested content:
Scaling of surfaces
Circle of revolution with different degrees
Scaling factors and center of scaling
New control points
Example: ellipsoid from sphere

22. Non-uniform Scaling of Surfaces
Suggested content:
Scaling of surfaces
Example: elliptic paraboloid

23. Three-sided Spherical Surfaces
Suggested content:
Corner surface problem
Three-sided patch as NURBS surface

24. Three-sided Spherical Surfaces
Suggested content:
Stereographic projection to parametrize the sphere
Mapping planar points onto the sphere

25. Three-sided Spherical Surfaces
Suggested content:
Creating circular boundaries for three sided patch
Convert to Bezier form

26. Three-sided Spherical Surfaces
Suggested content:
Three sided patch as degenerate Bezier surface
Control points and knots

27. Part II: Design examples

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

29. 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.

30. Geometric Modeling Lab
Suggested project:
Design common surfaces using NURBS
Design composite surfaces