1 7M836 Animation & Rendering Animation Jakob Beetz Joran Jessurun

2 Next Week Subject: Virtual Reality When: June 2 nd Where: Design Systems Lab. (Vertigo 9.16)

3 Animation History of cartoon and computer animation Extensive description of techniques and algorithms Rick Parent Computer Animation, Algorithms and Techniques How to make an animation Examples

4 Animation –“To give live to” –Make objects change over time according to scripted actions –By showing a sequence of fast changing images Series images (frames) –Film 24 fps –Video 30 fps=> 1 hour animation frames

5 What can be animated? Position and orientation of objects Geometry (shape) and scaling of objects Illumination Reflection Camera In fact, everything!

6 Animation process - traditional Storyboard –The story –Sequence of images with descriptions Key frames –Draw a number of important images (key frames) –Motion-based description Inbetweens –Draw the rest of the frames Painting –Redraw frames onto cels –Color them in Put animation onto film

7 Computer animation Computer animation pipeline –3D modeling –Motion specification –Motion simulation –Rendering –Post-processing Key framing

8 Keyframe animation Each “keyframe” specified by a number of key-parameters (state) Inbetweening: Interpolate these parameters

9 Keyframe animation For each key parameter, specify value at “important” frames Computer creates path for each parameter by interpolating this key parameter for inbetween frames

10 Interpolation Linear interpolation –Usually discontinuities –Not a smooth movement

11 Interpolation Spline interpolation –Smooth transitions –Beware of unwanted side effects

12 Interpolation – speed control Include velocity of interpolation –It is often more realistic to start a movement slowly, then speed up, and end it again slowly –Use speed curve Speed curve relates time with position on interpolation spline Position on interpolation spline determines interpolated key parameter value

13 Interpolation – speed control

14 Keyframing summarized Specification of key frames/parameters –Determine key parameters and their values at certain important points in time –Specify type of interpolation Specify speed curve for interpolation Computer generates inbetween frames

15 Animation of articulated structures Articulated structure: –Object consists of a number of (sub-)objects (links) connected by joints –Each joint is specified by at least one (key-)parameter –Movement of object described by changing parameter values

16 Examples of joints Constraints on joints

17 Articulated structure Skeleton consists of 14 joints Each joint has 2 or 3 degrees of freedom Some parameters constrained

18 Kinematics Kinematics is the study of movement of (hierarchical) objects –Position, orientation, velocity, acceleration –Without taking into account dynamic properties (forces) (dynamics) Forward kinematics Inverse kinematics

19 Forward kinematics Animator sets parameter values for joints Computer computes positions/orientations for links links:

20 Forward kinematics Animation by specification / interpolation of joint parameters

21 Forward kinematics

22 Forward kinematics

23 Forward kinematics

24 Kinematics What to do when animation knows the desired end- position of the (sub-)object? –E.g. to grab something?

25 Inverse kinematics Animator specifies position (and orientation) within scene at wich link (end-effector) has to be positioned Computer computes joint parameter values to get link at desired position: After that. computer computes positions of all links by applying these joint parameter values for all joints

26 Inverse kinematics

27 Inverse kinematics Animation by specification / interpolation of end-effector position Or animation by interpolation of joint parameter values at start and end frame

28 Inverse kinematics Problems –Often more than one solution Extra requirements to solution –Result not always desired path (e.g. collisions) –What to do when end-effector position specified outside operation area of object?

29 Inverse kinematics Inverse kinematics is also used to compute dependency of joint parameter values –E.g. for object with closed loops

30 Kinematics summarized Forward kinematics –Animator controls through joint parameters –Direct control over object state –Often many parameters to control Inverse kinematics –Animator controls through position/orientation end- effector –Simpler specification of movements Less parameters Better feeling for positions in scene –Complex computations

31 Rigid Body Simulation Rigid bodies Joints Contact and collisions Friction Springs Mechanical systems that have: Examples: BridgeRope Robot arm Vehicle Human Tower of cards

32 Rigid Body Simulation Physical process Model Simulation algorithm Computer program

33 Simulating position

34 Simulating rotational movement Angular velocity Torque Inertia Tensor is the angular equivalent of mass Inertia Tensor is dependent on the orientation of the body

35 Springs Spring Force Dampers

36 Collision Detecting the occurrence of collision Computing the response to those collisions

37 Friction Static friction Kinetic friction

38 Constraints Hard constraints Soft constraints Joints are constraints Point-spline constraint

39 Flexible objects Spring-Mass-Damper model Each vertex is a point mass Between vertices a spring Add interior springs to create stability

40 3D Max Reactor examples Demo1 – pencils fall out of cup Demo2 – shoot cannon ball against wall that fractures Demo3 – create box on a rope and let it swing Demo4 – create a piece of cloth, let the wind blow and drop something on it Demo5 – vehicle down a ramp and a simple roller coaster