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: HB 8-8,8-9, 8-10

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 - character animation • Expressive - cartoon animation

9. Keyframe Animation

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

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

12. 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

13. 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 to produce Toy Story

14. 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

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

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

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

18. Inbetween Frames • Linear interpolation • Cubic curve interpolation

19. Keyframe Interpolation t=50ms t=0

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

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

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

23. Smooth Curves • Controlling the shape of the curve

24. Smooth Curves • Controlling the shape of the curve

25. Smooth Curves • Controlling the shape of the curve

26. Smooth Curves • Controlling the shape of the curve

27. Smooth Curves • Controlling the shape of the curve

28. Smooth Curves • Controlling the shape of the curve

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

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

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

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

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

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

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

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

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

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

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

40. 2D Trajectory Interpolation • Perform interpolation for each component separately • Combine result to obtain parametric curve

41. 2D Trajectory Interpolation • Perform interpolation for each component separately • Combine result to obtain parametric curve

42. 2D Trajectory Interpolation • Perform interpolation for each component separately • Combine result to obtain parametric curve

43. Constraints on the Cubic Curves • How many constraints do we need to determine a cubic curve? 4 - does not provide local control of the curve

44. Constraints on the Cubic Curves • How many constraints do we need to determine a cubic curve? 4 - does not provide local control of the curve • Redefine C as a product of the basis matrix M and the control vector G: C= MG

45. Constraints on the cubic curves • How many constraints do we need to determine a cubic curve? 4 - does not provide local control of the curve • Redefine C as a product of the basis matrix M and the control vector G: C= MG MG

46. Constraints on the Cubic Curves • How many constraints do we need to determine a cubic curve? 4 - does not provide local control of the curve • Redefine C as a product of the basis matrix M and the control vector G: C= MG M G

47. Constraints on the Cubic Curves • How many constraints do we need to determine a cubic curve? 4 - does not provide local control of the curve • Redefine C as a product of the basis matrix M and the control vector G: C= MG M? G?

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

49. Hermite Curve • A Hermite curve is determined by - endpoints P1 and P4 - tangent vectors R1 and R4 at the endpoints R1 P4 R4 P1

50. Hermite Curve • A Hermite curve is determined by - endpoints P1 and P4 - tangent vectors R1 and R4 at the endpoints • Use these elements to control the curve, i.e. construct control vector R1 P4 R4 P1 Mh Gh