From these it is simple exercise in linear algebra to determine the joint

From these it is simple exercise in linear algebra to

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From these, it is simple exercise in linear algebra to determine the joint angles that gave rise to these motions. Motion capture has the advantage of producing natural motions. Of course, it might be difficult to apply for fictitious creatures, such as flying dragons. Key-frame Generated: A design artist can use animation modeling software to specify the joint angles. This is usually done by a process called key framing , where the artists gives a detailed layout of the model at certain “key” instances in over the course of the animation, called key frames . (For example, when animating a football kicker, the artist might include the moment when the leg starts to swing forward, an intermediate point in the swing, and the point at which the leg is at its maximum extension.) An automated system can then be used to smoothly interpolate 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” associated with 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 the physics/AI systems would determine a natural-looking animation to achieve this. This is quite Skeletal Animation and Skinning 58 CMSC 425
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challenging. The reason is that the problem is under-specified, and it can be quite difficult to select among an infinite number of valid solutions. Also, determining the joint angles to achieve a 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 angles or generally the joint frames vary with time. This can result in a huge amount of data. Each joint that can be independently rotated defines a degree of freedom in 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 control it 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, neck involves over 20 degrees of freedom. As with any digital signal processing (such as image, audio, and video processing), the standard approach for efficiently representing animation data is to first sample the data at sufficiently small time intervals. Then, use some form of interpolation technique to produce a smooth reconstruction of the animation. The simplest manner to interpolate values is based on linear interpolation . It may be desireable to produce smoother results by applying more sophisticated interpolations, such as quadratic or cubic spline interpolations. When dealing with rotated vector quantities, it is common to use spherical interpolation .
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