1. The document discusses different types of parametric curves used for modeling shapes, including Bezier curves, B-splines, and Catmull-Rom splines. 2. It explains how these curves work and their properties, such as continuity conditions and degree of smoothness between curve segments. 3. Key approaches covered are using B-splines to achieve smoothness while allowing local control, and Catmull-Rom splines which preserve interpolation but only provide continuous derivatives.

1. Parametric Curves 고려대학교 컴퓨터 그래픽스 연구실

10. Example: Bezier Curves

12. Example: 2D Bezier Curves

15. Example: Explicit Formulation

18. Explanation

33. C 3 Continuity V 0 V 1 V 2 V 3

34. C 3 Continuity V 0 V 1 V 2 V 3 W 0 W 1 W 2 W 3

35. C 3 Continuity V 0 V 1 V 2 V 3 W 0 W 1 W 2 W 3

36. C 3 Continuity V 0 V 1 V 2 V 3 W 0 W 1 W 2 W 3

37. C 3 Continuity V 0 V 1 V 2 V 3 W 0 W 1 W 2 W 3

47. B-Spline Construction n+1 control points polynomials of degree d-1