10-SceneGraphs

10-SceneGraphs - Scene Graphs and Barycentric Coordinates...

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Scene Graphs and Barycentric Coordinates Jason Lawrence CS 4810: Graphics Acknowledgment: slides by Misha Kazhdan, Allison Klein, Tom Funkhouser, Adam Finkelstein and David Dobkin
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Overview • 2D Transformations Basic 2D transformations Matrix representation Matrix composition • 3D Transformations Basic 3D transformations Same as 2D • Transformation Hierarchies Scene graphs Ray casting • Barycentric Coordinates
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Transformation Example 1 • An object may appear in a scene multiple times Draw same 3D data with different transformations
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Transformation Example 1 Building Floor 4 Floor5 Floor 3 Floor 2 Floor 1 Chair K Bookshelf 1 Desk Chair Bookshelf Desk 1 Desk 2 Chair 1 Floor Furniture Office N Office 1 Office Furniture Defnitions Instances
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Transformation Example 2 Rose et al. `96 • Well-suited for humanoid characters Root LHip LKnee LAnkle RHip RKnee RAnkle Chest LCollar LShld LElbow LWrist RCollar RShld RElbow RWrist Neck Head
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Scene Graphs • Allow us to have multiple instances of a single model – providing a reduction in model storage size • Allow us to model objects in local coordinates and then place them into a global frame – particularly important for animation
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Scene Graphs • Allow us to have multiple instances of a single model – providing a reduction in model storage size • Allow us to model objects in local coordinates and then place them into a global frame – particularly important for animation • Accelerate ray-tracing by providing a hierarchical structure that can be used for bounding volume testing
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Ray Casting with Hierarchies
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Ray Casting with Hierarchies • Transform the shape ( M ) • Compute the intersection
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Ray Casting with Hierarchies • Transform the ray ( M -1 ) • Compute the intersection • Transform the intersection ( M ) • Transform the shape ( M ) • Compute the intersection
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Angel Figures 8.8 & 8.9 Ray Casting With Hierarchies • Transform rays, not primitives For each node . .. » Transform ray by inverse of matrix » Intersect transformed ray with primitives » Transform hit information by matrix Base [M 1 ] Lower Arm [M 2 ] Upper Arm [M 3 ] Robot Arm
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Applying a Transformation • Position • Direction • Normal M Affine Translate Linear M T M L
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Applying a Transformation • Position o Apply the full afFne transformation: p ʼ = M ( p )=( M T × M L )( p ) • Direction • Normal M Affine Translate Linear M T M L
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Applying a Transformation • Position • Direction o Apply the linear component of the transformation: p ʼ = M L ( p ) • Normal M Affine Translate Linear M T M L
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Applying a Transformation • Position • Direction o Apply the linear component of the transformation: p ʼ = M L ( p ) A direction vector v is deFned as the difference between two positional vectors p and q : v = p - q .
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This note was uploaded on 03/21/2010 for the course CS 4810 taught by Professor Lawrence during the Spring '10 term at UVA.

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10-SceneGraphs - Scene Graphs and Barycentric Coordinates...

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