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Computer Animation Algorithms and Techniques

Computer Animation Algorithms and Techniques. Kinematic Linkages. Hierarchical Modeling. Define motion of one object relative to another. Constrained motion - reduce dimensionality, simplify specification. Linked appendages with joints. Solar system. Motion on a surface.

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Computer Animation Algorithms and Techniques

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  1. Computer AnimationAlgorithms and Techniques Kinematic Linkages

  2. Hierarchical Modeling Define motion of one object relative to another Constrained motion - reduce dimensionality, simplify specification Linked appendages with joints Solar system Motion on a surface Local coordinate frames for simpler motion specification Data structure to facilitate keeping relative transformations

  3. Solar system http://www.earth-live.net/tag/sun-earth-moon-system/

  4. Linked appendages Joint Link End Effector

  5. Forward & Inverse Kinematics images courtesy of Domin Lee

  6. Revolute & Prismatic Joints

  7. Complex Joints

  8. Hierarchical structure

  9. Tree structure

  10. Tree structure

  11. Tree structure Static

  12. Relative movement

  13. Tree structure Changable

  14. Bifurcation in Model

  15. Bifurcating tree

  16. Traverse Tree Top to bottom traversal Accumulate transformations during traversal Transformation at node only for data Save transformation before following link Restore when traversing sibling link

  17. traverse(arcPtr,matrix) { ; get transformations of arc and concatenate to current matrix matrix = matrix*arcPtr->Lmatrix ; concatenate location matrix = matrix*arcPtr->Amatrix ; concatenate articulation ; process data at node nodePtr = arcPtr->nodePtr ; get the node of the arc push(matrix) ; save the matrix matrix = matrix * nodePtr->matrix ; ready for articulation articulatedData = transformData(matrix,dataPtr) ; articulate the data draw(articulatedData); ; and draw it matrix = pop() ; restore matrix for node’s children ; process children of node if (nodePtr->arcPtr!= NULL) { ; if not a terminal node nextArcPtr = nodePtr->arcPtr ; get first arc emanating from node while (nextArcPtr != NULL) { ; while there’s an arc to process push(matrix) ; save matrix at node traverse(nextArcPtr,matrix) ; traverse arc matrix = pop() ; restore matrix at node nextArcPtr = nextArcPtr->arcPtr ; set next child of node } } }

  18. Inverse kinematics Position and orient end effect Automatically calculate interior joint angles Only simple configurations can be solved analytically Often, solution must be iterative

  19. Inverse kinematics Analytic method Iterative: Jacobian Iterative solutions Pseudo-inverse adding more control alternative Jacobian using the transpose cyclic coordinate descent

  20. Inverse Kinematics

  21. Inverse Kinematics - Analytic

  22. Inverse Kinematics - Analytic

  23. Inverse Kinematics - Numeric Determine affect of joint i on end effector

  24. Inverse Kinematics - Numeric desired direction of end effector to goal

  25. Inverse Kinematics - Numeric joint-effect vectors: gi

  26. Singularities

  27. IK - Jacobain

  28. IK - goal out of reach Solutions with and without damping

  29. IK - with control term all joints biased to 0 top: joint 2 has higher gain bottom: joint 3 has higher gain

  30. IK - Pull goal to end effector

  31. IK - transpose of the Jacobian

  32. IK - Cyclic Coordinate Descent

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