Recall Our Approach To Animation We create animated behavior just like movie projectors display a sequence of still images in rapid succession creates the illusion of continuous motion typically want 30 frames sec and definitely higher than 10 Given some parameterized geometric model for every frame we calculate the correct parameter values and we draw the scene in its current state just need to figure out how to specify control these parameters Some Overall Goals in Animation Realistic motion a special case of the overall photorealism motive Flexibility Expressiveness want to support the widest possible range of animation system that can only produce a single walking motion is boring Ease of control something nigh impossible to control does us little good 1 Traditional Manual Animation Every frame created individually by a human that s 24 frames second at traditional movie speeds roughly 130 000 frames for a 1 5 hour movie Over time a general process evolved to support efficiency start with set of drawings outlining clip storyboard senior artists sketch important frames key frames typically occur when motion changes lower paid artists draw the rest of the frames in betweens all line drawings are painted on cels generally composed in layers hence the use of acetate background changes infrequently so can be reused photograph finished cel stack onto film Computer Assisted Cel Animation Cel animation has been in use for a long time e g at Disney but we can use computers to help expedite the process draw sketches with digital systems use digital paint programs for coloring can even try to automatically generate in betweens Computer assisted systems are now quite common Disney makes heavy of digital drawing painting compositing 2 D in betweening is hard to get right morphing a 2 D sketch doesn t give the impression of 3 D humans are still much better at this 2 Computer Generated Animation This is the kind of animation we re really interested in here start with some 3 D model of the scene vary parameters to generate desired pose for all objects render scene to produce one frame repeat for all 130 000 frames So how will we control these parameters manually set them for each frame key framing generate them procedurally execute behavioral scripts e g follow the fish in front of you motion capture physical simulation Key Framing We ve associated a set of parameters with our model joint angles positions etc we view each of these as a function of time In key framing we specify parameter values at specific times and let the computer interpolate the in between values t 0 t1 How do we accomplish this interpolation 3 Interpolating Motion Parameters For a given parameter we ve specified some fixed values these are the key frame values t We could try linear interpolation t Interpolating Motion Parameters For a given parameter we ve specified some fixed values these are the key frame values t t But this generally produces undesirable motion during each interpolated span we move with constant velocity and then instantaneously change at each key point but this is highly non physical What else might we try 4 Interpolating Motion Parameters For a given parameter we ve specified some fixed values these are the key frame values t t We want some higher order interpolating curve Creating Key Frames In key framing we specify parameter values at specific times and let the computer interpolate the in between values t0 t1 We discussed how to do the interpolation but what about the specification of these parameters how do I get my articulated action figure into my favorite pose 5 Forward Kinematics Position of end effector is a function of the state of all joints more formally x f 2 l1 For this simple 2D example l2 1 x position of end effector angles positions of joints x1 g 1 2 x h 2 1 2 end effector Forward Kinematics Given an articulated human how do we make him wave rotate the shoulder into position and then the elbow and wrist and finally rebalance other parts of the body This is tedious We d much rather directly move the hand we can use inverse kinematics kinematics derive motion from positions angles velocities inverse kinematics determine joint angles from positions let the user drag the tip of the hand into place 6 Inverse Kinematics Automatically derive joint angles from end effector position forward kinematics x f inverse kinematics f 1 x 2 l1 Can write formulas l2 1 end effector 1 g x1 x 2 2 h x1 x 2 for this simple 2D example Inverse Kinematics Real models are much more complex than our simple example a human has around 200 degrees of freedom parameters the mapping of parameters to effector positions is non linear inverting this function is not possible must rely on numerical methods Suppose we specify locations for end effectors we need to compute a model configuration to achieve pose there may be many possible parameter settings that work need to pick best one minimize work maintain balance similarly there may not be any parameter settings that work need to pick one that is close enough both involve some kind of optimization algorithm 7 What Key Framing Doesn t Address Control point selection how often do we need to specify a key value what precise key values work best Key value interpolation what interpolation method will give us what we want Physical constraints how do we avoid non physical motion 360 head twists infinite instantaneous accelerations how do we know that two objects don t interpenetrate how do we maintain contact at appropriate points feet must touch floor when walking Procedural Animation To specify a procedural animation sit down and write some code the animator as programmer input current time output correct parameter value usually combine lots of little procedures together one procedure for walk one for run one for hop There is a clear tradeoff between procedures interaction think of the analogy of creating a 2 D illustration if it s simple we can probably quickly do it interactively but if it s very complex regular coding is probably quicker 8 Behavioral Animation Closely related to procedural animation specify how object reacts to the world around it A common example of this approach is flocking motion of an object is directly determined by others nearby analogous to Conway s Life simple rules lead to interesting emergent behaviors very helpful for choreographing large scale action wildebeests in Lion King army of mounted soldiers in Mulan Motion Capture One of the most