1. Maths & Technologies for Games Animation: Practicalities CO3303 Week 3

2. Today’s Lecture 1.Animation Issues 2.Transformation Decomposition 3.Keyframes 4.Interpolation Revisited 5.Playing Animations 6.Blending Multiple Animations 7.Motion Extraction

3. Animation Issues We have seen a method to interpolate a model’s pose between keyframes Surely we can now build an animation system? No –Several major practicalities to deal with –Need further refinements to the previous theory

4. Animation Issues Assume our game has: –30 characters with 64 bones, 60 animations each –Animations are 5 seconds long, store 8 keyframes / s Memory usage = 30*64*60*5*8* sizeof(keyframe) If our keyframe is a 4x4 matrix then = 295Mb If a quaternion, position and scaling, then = 184Mb –Too much memory used Implies poor cache performance Can improve on this

5. Animation Issues Sometimes need to play more than one animation at the same time –E.g. Character running and firing a gun –Or character standing and firing –Would like to blend the firing animation with the character’s other motion – 2 animations at once –Simple interpolation insufficient Also, how to combine movement in the scene with movement in the animation? Will look briefly at several practical animation techniques to address these issues

6. Transformation Decomposition Each bone in a model has a separate transform –Each relative to its parent, forming a hierarchy Last year we used matrices for this hierarchy Now we have seen that matrices are not a good choice for animation in general –Expensive to interpolate & too much storage So we decompose the transform into: –Rotation, translation, scale etc. Use vectors for translation and scale Quaternions for rotation

7. Transformation Decomposition Can write a quaternion-based transformation class –With the same functionality as a matrix class –But able to interpolate rotations efficiently Use for current transformations of animated models – one for each bone in hierarchy However, when storing keyframes, we can remove uneeded elements –E.g. no scaling – don’t store scaling Will reduce the storage by 40% or so

8. Key frames authored by artists –Based on needs of animation Must make sure it suits our needs too: –Rotations small enough for interpolation method (e.g. nlerp) –No unsupported components (e.g. shear) All bones key-framed at once or independently Key Frames Might pre-process keyframes: –Precalculate values (e.g. sin θ ) –Add extra frames to improve motion when using approximations

9. Interpolation Revisited Choices with interpolation: –Use lerp or normalised lerp (nlerp) always –Or use slerp sometimes –Or use slerp approximations (sometimes) First choice can be the best –Unless there are large angular movements in your animation (rare) Less than 5% inaccurate for < 45 degrees nlerp

10. Higher Order Interpolation We may wish to use more complex interpolations: –To produce smooth curves Higher order interpolation needs less key frames –Up to ten times less –Only a little extra data –Overall greatly aids our memory problem Example: cubic Bezier curve formula Use as a replacement for linear interpolation –Needs extra points to define curve

11. Playing Animations Each animation has a length –Usually measured in seconds Within that time there will be several key frames –Around 0.5 to 8 per second - may not be evenly spread Our model will know its current animation position –E.g. 1.2 seconds into an 2 second walk animation Need a fast method to extract the which key frames are needed at this point –Need the frame before, the frame after and the interpolation value t

12. Playing Animations For each animation store a single structure: –Number of bones in animation –Length (in seconds) –Key frame data When a model plays an animation it stores an additional structure: –Pointer to the animation it is using –Current position (time) in the animation Can be converted to key frames + t value –Speed of playback This way several models can use the same animation at the same time

13. Blending Animations Game characters often do several things at once: –E.g. Running and shooting Many animations only use part of the body –E.g. A waving animation Like to use different animations at the same time And/or apply them only to parts of the body Possible with further linear interpolation of several animations: –A first lerp to get pose 1, a second lerp to get pose 2 –Then a final lerp to blend these two together

14. Multiway Blending Can add weightings to the animations: FinalPose = Pose1 * w1 + Pose2 * w2 –If w1>w2, then Pose1 is more prominent –Almost identical to quaternion and vector linear interpolation from last week Can blend more than two animations too This is called multiway blending Uses: –Smoothly changing from a run to a walk –Different animations for legs and upper body –Separate facial animations –All of the above happening at the same time

15. Bone Masks Can also have per-bone weights for blending animations - called a bone mask For a waving animation, the bones in the arm would have a weight of 1.0 –The animation fully affects the arm The rest of the body would have 0.0 –No effect on the body –Don’t need to store key frames for these parts The shoulder would have a weight of 0.5 –Blending the waving animation with any underlying animation

16. Motion Extraction A run animation actually moves the character in the scene – even if our model is stationary How to match the motion stored in the animation and the position of our models? Use motion extraction techniques, generally: –Analyse movement of a root bone in the animation –Subtract that motion from the animation – so the animation doesn’t move –Replicate the movement onto our actual scene model The result will look the same, but with the scene model tracking the animation root

17. Animation Summary Many aspects to a full animation system –A very intricate areas of games development Only able to touch upon the issues in the time available here –Matrices, quaternions, interpolation are just the building blocks Look at simple, but functional system in the labs In the real world you will find more complex systems in use –But with the same principles