CSCE 441 Computer Graphics: Keyframe Animation/Smooth Curves

1. CSCE 441 Computer Graphics: Keyframe Animation/Smooth Curves Jinxiang Chai

2. Outline • Keyframe interpolation • Curve representation and interpolation - natural cubic curves - Hermite curves - Bezier curves • Required readings: 12-6 & 14-1 14-214-3 14-4, & 14-7

3. Computer Animation • Animation - making objects moving • Compute animation - the production of consecutive images, which, when displayed, convey a feeling of motion.

4. Animation Topics • Rigid body simulation - bouncing ball - millions of chairs falling down

5. Animation Topics • Rigid body simulation - bouncing ball - millions of chairs falling down • Natural phenomenon - water, fire, smoke, mud, etc.

6. Animation Topics • Rigid body simulation - bouncing ball - millions of chairs falling down • Natural phenomenon - water, fire, smoke, mud, etc. • Character animation - articulated motion, e.g. full-body animation - deformation, e.g. face

7. Animation Topics • Rigid body simulation - bouncing ball - millions of chairs falling down • Natural phenomenon - water, fire, smoke, mud, etc. • Character animation - articulated motion, e.g. full-body animation - deformation, e.g. face • Cartoon animation

8. Animation Criterion • Physically correct - rigid body-simulation - natural phenomenon • Natural looking - character animation • Expressive - cartoon animation

9. Keyframe Animation

10. Keyframe Interpolation • Key frame interpolation in after effects (Click here)

11. Spatial Key Framing • Demo video (click here)

12. Keyframe Interpolation t=50ms t=0 IK can be used to create Key poses

13. Keyframe Interpolation t=50ms t=0 What’s the inbetween motion?

14. Outline • Process of keyframing • Key frame interpolation • Hermite and bezier curve • Splines • Speed control

15. 2D Animation • Highly skilled animators draw the key frames • Less skilled (lower paid) animators draw the in-between frames • Time consuming process • Difficult to create physically realistic animation

16. Animating a Bouncing Ball • Key frames

17. Animating Three Walking Steps • Key frames

18. Playing Basketball

19. 3D Animation • Animators specify important key frames in 3D • Computers generates the in-between frames • Some dynamic motion can be done by computers (hair, clothes, etc) • Still time consuming; Pixar spent four years producing Toy Story

20. 3D Bouncing Ball

21. 3D Jumping

22. The Process of Keyframing • Specify the keyframes • Specify the type of interpolation - linear, cubic, parametric curves • Specify the speed profile of the interpolation - constant velocity, ease-in-ease-out, etc • Computer generates the in-between frames

23. A Keyframe • In 2D animation, a keyframe is usually a single image • In 3D animation, each keyframe is defined by a set of parameters

24. Keyframe Parameters What are the parameters? • position and orientation • body deformation • facial features • hair and clothing • lights and cameras

25. Outline • Process of keyframing • Key frame interpolation • Hermite and bezier curve • Splines • Speed control

26. Inbetween Frames • Linear interpolation • Cubic curve interpolation

27. Keyframe Interpolation t=50ms t=0

28. Linear Interpolation • Linearly interpolate the parameters between keyframes x1 x x0 t0 t1 t

29. Linear Interpolation: Limitations • Requires a large number of key frames when the motion is highly nonlinear.

30. Cubic Curve Interpolation • We can use a cubic function to represent a 1D curve

31. Smooth Curves • Controlling the shape of the curve

32. Smooth Curves • Controlling the shape of the curve

33. Smooth Curves • Controlling the shape of the curve

34. Smooth Curves • Controlling the shape of the curve

35. Smooth Curves • Controlling the shape of the curve

36. Smooth Curves • Controlling the shape of the curve

37. Constraints on the cubics • How many points do we need to determine a cubic curve?

38. Constraints on the Cubic Functions • How many points do we need to determine a cubic curve?

39. Constraints on the Cubic Functions • How many points do we need to determine a cubic curve?4

40. Constraints on the Cubic Functions • How many points do we need to determine a cubic curve?4

41. Natural Cubic Curves Q(t1) Q(t2) Q(t3) Q(t4)

42. Interpolation • Find a polynomial that passes through specified values

43. Interpolation • Find a polynomial that passes through specified values

44. Interpolation • Find a polynomial that passes through specified values

45. Interpolation • Find a polynomial that passes through specified values

46. 2D Trajectory Interpolation • Each point on the trajectory is associated with a time stamp t. • Perform interpolation for each component separately • Combine result to obtain parametric curve

47. 2D Trajectory Interpolation • Each point on the trajectory is associated with a time stamp t. • Perform interpolation for each component separately • Combine result to obtain parametric curve

48. 2D Trajectory Interpolation • Each point on the trajectory is associated with a time stamp t. • Perform interpolation for each component separately • Combine result to obtain parametric curve

49. Limitation? • What’s the main limitation of interpolation using natural cubic curves?

50. Limitation? • What’s the main limitation of interpolation using natural cubic curves? - does not provide local control of the curve