11_anim_ii_cov

11_anim_ii_cov - Computer Animation II Orientation...

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Computer Animation II Orientation interpolation Dynamics Some slides courtesy of Leonard McMillan and Jovan Popovic Lecture 13 6.837 Fall 2002
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Review from Thursday Interpolation ± Splines Articulated bodies ± Forward kinematics ± Inverse Kinematics ± Optimization ± Gradient descent ± Following the steepest slope ± Lagrangian multipliers ± Turn optimization with constraints into no constraints Lecture 11 Slide 2 6.837 Fall 2003
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Debugging Debug all sub-parts as you write them Print as much information as possible Use simple test cases When stuck, use step-by-step debugging Lecture 11 Slide 3 6.837 Fall 2003
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Grid acceleration Debug all these steps: ± Sphere rasterization ± Ray initialization ± Marching ± Object insertion ± Acceleration Lecture 11 Slide 4 6.837 Fall 2003
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Final project First brainstorming session on Thursday Groups of three Proposal due Monday 10/27 ± A couple of pages ± Goals ± Progression Appointment with staff Lecture 11 Slide 5 6.837 Fall 2003
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Computer-Assisted Animation Lecture 11 Slide 6 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
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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 ACM© 1988 “Spacetime Constraints” Lecture 11 Slide 7 6.837 Fall 2003
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Overview Interpolation of rotations, quaternions ± Euler angles ± Quaternions Dynamics ± Particles ± Rigid body ± Deformable objects Lecture 11 Slide 8 6.837 Fall 2003
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Interpolating Orientations in 3-D Rotation matrices Given rotation matrices M i and time t i , find M(t) such that M(t i )=M i . x y z u v u x v x n x u y v y n y u z v z n z M = n Lecture 11 Slide 9 6.837 Fall 2003
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Flawed Solution Interpolate each entry independently Example: M 0 is identity and M 1 is 90 o around x-axis Is the result a rotation matrix?
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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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11_anim_ii_cov - Computer Animation II Orientation...

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