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CSCE 441 Computer Graphics: Keyframe Animation/Smooth Curves

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

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CSCE 441 Computer Graphics: Keyframe Animation/Smooth Curves

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  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 t=50ms t=0 IK can be used to create Key poses

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

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

  13. 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

  14. 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

  15. 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

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

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

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

  19. Inbetween Frames • Linear interpolation • Cubic curve interpolation

  20. Keyframe Interpolation t=50ms t=0

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

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

  23. Cubic Curve Interpolation • We can use a cubic function to represent a 1D 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. Smooth Curves • Controlling the shape of the curve

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

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

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

  33. Constraints on the Cubic Functions • How many points 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. 2D Trajectory Interpolation • Perform interpolation for each component separately • Combine result to obtain parametric curve

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

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

  44. Constraints on the Cubic Curves • What’s the main limitation of interpolation using natural cubic curves? - does not provide local control of the curve

  45. Constraints on the Cubic Curves • What’s the main limitation of interpolation using natural cubic curves? - does not provide local control of the curve

  46. Constraints on the Cubic Curves • What’s the main limitation of interpolation using natural cubic curves? - 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

  47. Constraints on the cubic curves • What’s the main limitation of interpolation using natural cubic curves? - 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

  48. Constraints on the Cubic Curves • What’s the main limitation of interpolation using natural cubic curves? - 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

  49. Constraints on the Cubic Curves • What’s the main limitation of interpolation using natural cubic curves? - 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?

  50. Two Issues • How to select a new set of control points? • How to determine M? M?

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