10_keyfrm_ik_opt

10_keyfrm_ik_opt - Animation Lecture 10 Slide 1 6.837 Fall...

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Animation Lecture 10 Slide 1 6.837 Fall 2003
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Conventional Animation Draw each frame of the animation ± great control ± tedious Reduce burden with cel animation ± layer ± keyframe ± inbetween ± cel panoramas (Disney’s Pinocchio) ± ... Lecture 10 Slide 2 6.837 Fall 2003
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Computer-Assisted Animation Lecture 10 Slide 3 6.837 Fall 2003 Keyframing ± automate the inbetweening ± good control ± less tedious ± creating a good animation still requires considerable skill and talent Procedural animation ± describes the motion algorithmically ± express animation as a function of small number of parameteres ± Example: a clock with second, minute and hour hands ± hands should rotate together ± express the clock motions in terms of a “seconds” variable ± the clock is animated by varying the seconds parameter ± Example 2: A bouncing ball ± Abs(sin( ω t+ θ 0 ))*e -kt Image adapted from: Lasseter, John. "Principles of Traditional Animation applied to 3D Computer Animation." ACM SIGGRAPH Computer Graphics 21, no. 4 (July 1987): 35-44.
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Computer-Assisted Animation Physically Based Animation ± Assign physical properties to objects (masses, forces, inertial properties) ± Simulate physics by solving equations ± Realistic but difficult to control Motion Capture ± Captures style, subtle nuances and realism ± You must observe someone do something Lecture 10 Slide 4 6.837 Fall 2003 Image removed due to copyright considerations.
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Overview Hermite Splines Keyframing Traditional Principles Articulated Models Forward Kinematics Inverse Kinematics Optimization Differential Constraints Lecture 10 Slide 5 6.837 Fall 2003 Squash & Stretch in Luxo Jr.'s Hop Image adapted from: Lasseter, John. "Principles of Traditional Animation applied to 3D Computer Animation." ACM SIGGRAPH Computer Graphics 21, no. 4 (July 1987): 35-44.
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Keyframing Describe motion of objects as a function of time from a set of key object positions. In short, compute the inbetween frames. Lecture 10 Slide 6 6.837 Fall 2003 Image adapted from: Lasseter, John. "Principles of Traditional Animation applied to 3D Computer Animation." ACM SIGGRAPH Computer Graphics 21, no. 4 (July 1987): 35-44.
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Interpolating Positions Given positions: find curve such that (,,) , 0 ,, ii i xyt n = K = () xt t yt C = x y 0 u 000 xy 111 222 Lecture 10 Slide 7 6.837 Fall 2003
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Linear Interpolation Simple problem: linear interpolation between first two points assuming : The x-coordinate for the complete curve in the figure: 000 (,,) xy t 111 xyt 222 ) 0 1 01 0 1 10 21 12 1 2 , , () , tt xx xt +∈ −− = =0 and =1 ( ) = −+ 1 x Derivation? Lecture 10 Slide 8 6.837 Fall 2003
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Polynomial Interpolation 000 (,,) xy t 111 xyt 222 parabola An n-degree polynomial can interpolate any n+1 points. The Lagrange formula gives the n+1 coefficients of an n-degree polynomial that interpolates n+1 points. The resulting interpolating polynomials are called Lagrange polynomials. On the previous slide, we saw the Lagrange formula for n = 1.
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This note was uploaded on 12/14/2011 for the course EECS 6.837 taught by Professor Durand during the Fall '03 term at MIT.

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10_keyfrm_ik_opt - Animation Lecture 10 Slide 1 6.837 Fall...

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