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From these, it is simple exercise in linear algebra to determine the joint angles that gave rise tothese motions.Motion capture has the advantage of producing natural motions. Of course, it might be difficultto apply for fictitious creatures, such as flying dragons.Key-frame Generated:A design artist can use animation modeling software to specify the jointangles. This is usually done by a process calledkey framing, where the artists gives a detailedlayout of the model at certain “key” instances in over the course of the animation, calledkeyframes.(For example, when animating a football kicker, the artist might include the momentwhen the leg starts to swing forward, an intermediate point in the swing, and the point at whichthe leg is at its maximum extension.)An automated system can then be used to smoothlyinterpolate the joint angles between consecutive key frames in order to obtain the final animation.(The term “frame” here should not be confused with the use of term “coordinate frame” associatedwith the joints.)Goal Oriented/Inverse kinematics:In an ideal world, an animator could specify the desired be-havior at a high level (e.g., “a character approaches a table and picks up a book”).Then thephysics/AI systems would determine a natural-looking animation to achieve this. This is quiteSkeletal Animation and Skinning58CMSC 425
challenging.The reason is that the problem is under-specified, and it can be quite difficult toselect among an infinite number of valid solutions. Also, determining the joint angles to achievea particular goal reduces to a complex nonlinear optimization problem.Representing Animation Clips:In order to specify an animation, we need to specify how the joint anglesor generally the joint frames vary with time. This can result in a huge amount of data. Each joint thatcan be independently rotated defines adegree of freedomin the specification of the pose. For example,the human body has over 200 degrees of freedom! (It’s amazing to think that our brain can controlit all!) Of course, this counts lots of fine motion that would not normally be part of an animation,but even a crude modeling of just arms (not including fingers), legs (not including toes), torso, neckinvolves over 20 degrees of freedom.As with any digital signal processing (such as image, audio, and video processing), the standardapproach for efficiently representing animation data is to firstsamplethe data at sufficiently smalltime intervals.Then, use some form of interpolation technique to produce a smoothreconstructionof the animation.The simplest manner to interpolate values is based onlinear interpolation.Itmay be desireable to produce smoother results by applying more sophisticated interpolations, such asquadratic or cubic spline interpolations. When dealing with rotated vector quantities, it is common tousespherical interpolation.