Game Engine Architecture

519 which is convenient. Also, while it’s prett y easy to see a diff erence in quality between a two-, three-, and even a four-j ...

520 11. Animation Systems which we’ll denote with the superscript B. At any given moment during an animation, the joint’s axes m ...

521 vector whose coordinates are expressed in joint j’s space into an equivalent set of model space coordinates. Now, consider a ...

522 11. Animation Systems We must make sure that our Bj→M and Cj→Mmatrices are calculated properly for the joint in question, u ...

523 11.5.2.4. Skinning a Vertex to Multiple Joints When a vertex is skinned to more than one joint, we calculate its fi nal posi ...

524 11. Animation Systems the sampled frames available in the animation data. We can also use temporal animation blending to smo ...

525 (qLERP) SLERP[(q ) , (q ) , ] sin((1 ) ) sin( ) (q ) (q ). sin( ) sin( ) jAj B j Aj Bj =β −β θ βθ =+ θθ (11.8b) Finally, the ...

526 11. Animation Systems times 0, Δt, 2Δt, 3Δt, and so on. To fi nd a pose at time t = (2.18)Δt, we simply fi nd the linear int ...

527 Strict mathematical continuity up to C1 or higher is oft en infeasible to achieve. However, LERP-based animation blending ca ...

528 11. Animation Systems time-synchronized, as they must be when performing a smooth transi- tion. This approach is depicted in ...

529 blend factors βstart and βend , because this yields a well-behaved curve for our purposes: start end start (^3) start (^2) s ...

530 11. Animation Systems this pivotal movement, because the person pivots about his vertical axis when he turns. Second, he can ...

531 ward and unnatural. There are a number of ways to solve this problem. One feasible approach is to defi ne two hemispherical ...

532 11. Animation Systems Targeted movement is just a special case of one-dimensional LERP blend- ing. We simply straighten out ...

533 If we know that our 2D blend involves only four animation clips, and if those clips are positioned at the four corners of a ...

534 11. Animation Systems of the skeleton corresponding to an arbitrary point b within the triangle, as illustrated in Figure 11 ...

535 and ()P 2 j, respectively. Furthermore, the barycentric coordinate (⅓, ⅓, ⅓) lies at the centroid of the triangle and gives ...

536 11. Animation Systems 11.6.4. Partial-Skeleton Blending A human being can control diff erent parts of his or her body indepe ...

537 and out of control when he or she is running than when he or she is standing still. Yet with partial blending, the right arm ...

538 11. Animation Systems pose (at a single point in time) is D = S – R. Of course, we’re dealing with joint poses, not scalar q ...