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Lecture_Chapter6_b

Lecture_Chapter6_b - Review of Tuesday Complex(mechanical...

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Review of Tuesday 24 ECS 175 Chapter 6: Scene Representation and Interaction Complex (mechanical) objects consist of components Kinematic chains/skeleton represented as tree Hierarchical modeling facilitates implementation of relative behavior of components Relative transformation matrices are used for animation Graphical representations can be reused representation ‘attached’ to skeleton
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Forward Kinematics 25 ECS 175 Chapter 6: Scene Representation and Interaction p = T ( dx 0 , dy 0 ) T (0 , dy 1 ) R ( α 1 ) T (0 , dy 2 ) R ( α 2 ) · 0 dy 3 p positions of points in the mechanical system dependent on parameter values p = f ( θ )
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Forward and Inverse Kinematics 26 ECS 175 Chapter 6: Scene Representation and Interaction Forward Kinematics computes the end-position of the kinematic chain dependent on parameter values Inverse Kinematics finds parameters for a desired state/ position p = f ( θ ) “Where is the hand of my robot if I choose these angles at the joints?” “What angles should I use at the joints to place my hand over there?” θ = g ( p ) ( θ = f 1 ( p ) (?))
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Inverse Kinematics 27 ECS 175 Chapter 6: Scene Representation and Interaction Inverse Kinematics Parameters hard to find (f might not have an inverse) No solutions ( “Point cannot be reached by the robot’s hand.” ) Multiple solutions ( “Robot can reach the point in several ways.” ) In animation one tries to find an ‘optimal’ solution Realistic, smooth movement Minimal movement Manual techniques ( key-framing: Specify intermediate parameters) θ = g ( p ) ( θ = f 1 ( p ) (?))
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Scene Graphs 28 ECS 175 Chapter 6: Scene Representation and Interaction Scenes are similar to complex objects They contain several (related objects) Objects can be similar/share properties Object may be grouped May contain a logical or spatial hierarchy Relative operations can be applied between related objects But: Camera is often located in the scene
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