animation

1 .Animation CMSC 435/634

2 .Keyframe Animation From hand drawn animation Lead animator draws poses at key frames Inbetweener draws frames between keys Computer animation Can have separate keys for different attributes Interpolate between values at key frames

3 .How to Interpolate Linear interpolation Value V 0 at time T 0 , V 1 at time T 1 Fraction of the way from T 0 to T 1 Lerp/mix equation

4 .Spline Set of polynomials 1 constraint per coefficient Positions Velocities Acceleration

5 .All constraints from control points : Resulting equations: Bezier Spline

6 .Bezier Basis Functions Computing position

7 .Bezier Basis Functions Group by t i : coefficients

8 .Bezier Basis Functions Group by p i : Basis Functions

9 .Bezier Basis Functions Cubic Bezier basis functions

10 .Constraints Resulting equations: Catmull -Rom Spline

11 .Catmull -Rom Basis Functions

12 .What to Interpolate What controls to artists need? How to convert those into transformations?

13 .Position and Orientation Objects can move! Keys: Separate control of position and orientation Never interpolate matrices! They won’t do what you want. Quaternions interpolate better than Euler angles But angles make a better animation interface Can still convert to and interpolate as quaternion Possible to use directly for rotation, or convert to matrix

14 .Squash and Stretch Defining the rigidity and mass of an object by distorting its shape during an action Examples: Ball flattening during bounce Facial animation – cheeks squash during smile

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18 .Squash and Stretch Keys Volume constant Different materials respond differently Need not deform Use stretching to eliminate strobing from fast action Method Can use scale to conserve volume (up in one dimension down in others)

19 .Anticipation The preparation for an action Examples: Pull back foot to kick ball Luxo : big lamp looks off stage before Jr. ’ s entrance

20 .Anticipation The preparation for an action Examples: Pull back foot to kick ball Luxo : big lamp looks off stage before Jr. ’ s entrance

21 .Anticipation Keys Direct attention to upcoming action Anticipation can allow faster action

22 .Slow In and Out The spacing of the in between frames to achieve subtlety of timing and movement Example: Moving from place to place: start and end slow

23 .Slow In and Out The spacing of the in between frames to achieve subtlety of timing and movement Example: Moving from place to place: start and end slow

24 .Slow In and Out The spacing of the in between frames to achieve subtlety of timing and movement Example: Moving from place to place: start and end slow

25 .Slow In and Out The spacing of the in between frames to achieve subtlety of timing and movement Example: Moving from place to place: start and end slow

26 .Slow In and Out Keys Think about continuity of second and third order motion Reparameterize time

27 .Arcs The visual path of action for natural movement Examples: Thrown ball Keys Arc movements are more natural than lines

28 .Character Animation Control Hierarchical model Forward kinematics Inverse kinematics Motion capture Rendering Skinning Blend Shapes Deformation

29 .Forward Kinematics Given a set of joint angles, where’s the hand? (or foot or head or …) End effector Just apply nested transforms We know how to do that!