1. PPT7: Conics and Circles
CAP 6736
Geometric Modeling
PPT7: Conics and Circles
PPT and video are due no later than March 1
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. Various Forms of Conics
Suggested content:
Geometric definition of conics
Classification of conics

5. Various Forms of Conics
Suggested content:
Various forms of conics
ellipse
hyperbola
parabola

6. Rational Parametric Form of Conics
Suggested content:
Rational parametric form of conics
Ellipse, hyperbola and parabola

7. Maximum Area Forms of Conics
Suggested content:
Maximum area forms of conics
ellipse
hyperbola
parabola

8. Conics Forms in 3-D Suggested content: Conics in 3-D
Ellipse, hyperbola and parabola

9. Rational Bezier Conics
Suggested content:
Rational Bezier form of conics
Local coordinate frame
Equation in the local frame

10. Rational Bezier Conics
Suggested content:
Type of conics
Classification wrt. to shape invariance

11. The Shoulder Point Suggested content:
Type of conics using the shoulder point

12. Circular Arc of less than 180°
Suggested content:
Circular arc as a Bezier conic

13. Infinite Control Points
Suggested content:
Use of infinite control points

14. Semi-circle via Infinite Control Points
Suggested content:
Semi-circle defined by infinite control points

15. Nine-point Circle Suggested content: The nine-point full circle
Control points, knots and weights

16. Seven-point Circle Suggested content: The seven-point full circle
Control points, knots and weights

17. Circular Arc of 240°using Negative Weight
Suggested content:
Circular arc of 240 degrees
Control points, knots and weights

18. Circular Arc of 240° using Negative Weight and Knot Insertion
Suggested content:
Circular arc of 240 degrees
Eliminating negative weights via knot insertion

19. Semi-circle Suggested content: Semi-circle
Eliminating infinite control points via knot insertion

20. Seven-point Full Circle
Suggested content:
The seven-point full circle
Control points, knots and weights

21. Circular Arcs of Various Sweep Angles
Suggested content:
Circular arcs of various sweep angles

22. Construction of Conics
Suggested content:
Conic constructions from end points and end tangents
Parallel and non-parallel cases

23. Splitting Elliptical Arcs
Suggested content:
Splitting arcs for better convex hulls

24. Construction of Conics
Suggested content:
Conic construction examples

25. Form Conversion
Suggested content:
Form conversion
General formulas

26. Form Conversion Suggested content: Form conversion: parabola
Axis, focus and vertex

27. Form Conversion Suggested content: Form conversion: ellipse
Center, major/minor axes and axis points

28. Form Conversion Suggested content: Form conversion: hyperbola
Center, major/minor axes and axis points

29. Higher Order Circles Suggested content: Cubic circle
Degree elevate semi-circle with infinite control points
Control points, knots and weights

30. Higher Order Circles Suggested content: Cubic circle
Degree elevate 240 arc circle with negative weight
Control points, knots and weights

31. Higher Order Circles Suggested content: Degree four circle
Full circle in complex plane
Convert to Bezier with infinite control points
Control points, knots and weights

32. Higher Order Circles Suggested content: Degree five circle
Degree elevate degree four circle with infinite control points
Control points, knots and weights

33. Biarcs Suggested content: Biarcs: definition Bezier formulation
NURBS conversion: control points, knots, weights

34. Biarcs
Suggested content:
Biarcs: C-shaped and S-shaped

35. Biarcs
Suggested content:
Biarcs: parallel/anti-parallel end tangents

36. Biarc Approximation Suggested content: Biarc approximation
Curvature plot

37. Part II: Design examples

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

39. 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.

40. Geometric Modeling Lab
Suggested project:
Design shapes using simple conics
Font design using conics