Download PDF by Shoemake K.: Animating rotations with quaternion curves

By Shoemake K.

ISBN-10: 0897911660

ISBN-13: 9780897911665

Reliable our bodies roll and tumble via house. In laptop animation, so do cameras. The rotations of those items яге top defined utilizing a 4 coordinate approach, quaternions, as is proven during this paper. Of all quaternions, these at the unit sphere are most fitted for animation, however the query of the way to build curves on spheres has now not been a lot explored. This paper provides one solution by means of providing a brand new form of spline curve, created on a sphere, appropriate for easily in-betweening (i.e. interpolating) sequences of arbitrary rotations. either thought and scan convey that the movement generated is soft and ordinary, with out quirks present in previous tools.

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4, we cannot determine two variables (x and y components of projected motion) with only one constraint. 7) to calculate the motion field. METHOD 1: BLOCK MATCHING Along with the optical flow constraint, block matching assumes that a given neighborhood (usually, a n-by-n block) around a point moves with the same motion. Under the assumption of a constant projected motion over the neighborhood, we can determine the motion of a given neighborhood by finding the Least Square Fit to the optical flow equation.

I frames have no references to other frames and are completely intra-coded; P frames uses macroblock references from a previous (in the time of the video sequence) frame that have already been decoded; B frames uses both previous and next decoded frames. Although 3-D DCTs compressed as well as a scheme with these motion references, MPEG-1/2 standards chose the concept of P,B frames because of their simplicity [Bhaskaran and Konstantinides, 1995]. This method of coding also justifies our motion-based representation as an alternate representation of the video sequence.

Eflow underconstrains the problem; we add smoothness component as the magnitude of the gradients of u and v. 6) 40 VIDEO OBJECT EXTRACTION AND REPRESENTATION Now that we have a measure of both the smoothness and optical flow error, we can linearly combine the two metrics over the motion field of a given frame. 7) where α is a weight dependent upon the variance of intensities over the video sequence. Our motion field calculation can be described as follows. 8) To find the motion field that minimizes this function Etotal, we apply the fundamental theorem of calculus of variations and the iterative solution ∆2 u = of the∆ Gauss-Seidel.

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Animating rotations with quaternion curves by Shoemake K.

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