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3D Object Representations(GATE-540)

Dr.Çağatay ÜNDEĞER

InstructorMiddle East Technical University, GameTechnologies

&

General ManagerSimBT Inc.

e-mail : cagatay@undeger.com

Game Technologies Program – Middle East Technical University – Spring 2010

Reference: Thomas Funkhouser, Princeton University

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Outline

• 3D Objects• Raw Data Types• 3D Object Representations

– Surface models– Solid models– High-Level Structures

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Goals• Develop 3D Analysis Algorithms:

– Reconstruction– Segmentation– Feature Detection– Labeling– Matching – Classification– Retrielval– Recognition– Clustering Different methods are applicable

to different representations.

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3D Objects

• How can this simple object be represented in a computer?

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3D Objects

• Is representing this object similar to the previous one an effective way?

• Highly smooth curves...

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3D Objects

• How about this one?• A volumetric body...• Outer surface...

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3D Objects• How about these ones?• Has soft and hard tissue...• Has different densities...• Has Interrior...

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3D Objects• What about this one?• Composed of

different geometric parts / shapes...

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3D Objects• This one?

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3D Objects• How about these?• A deformable body...• Animation integration...

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3D Object Representations

• Raw Data– Point cloud– Range image– Polygon soup– ...

• Surfaces– Mesh– Subdivision– Parametric– Implicit

• Solids– Voxels– BSP Tree– Cell Complex

• High-Level Structures– CSG– Constraint blocks– Generative model– Skeleton– Sweep model– Scene graph

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Point Cloud

• Unstructured set of point samples• Range finders, 3D scanners, computer vision

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Range Image

• Set of 3D points that maps to pixels of a depth image

• From range scanners

Range (depth) image

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Range Image• A kind of more structured point cloud• Generating surfaces from 3d points

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Polygon Soup

• Unstructures set of polygons or unconnected lines of polygons

• Mostly creates with interactive modeling sys.

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Surface Objects

• Mesh• Subdivision• Parametric• Implicit

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Mesh• Connected set of polygons (usually triangles)

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Subdivision Surface

• Consists of a coarse mesh and subdivision rule• Generates smooth surfaces with refinements

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Parametric Surface

• Bezier / spline surface patches• Defined with a parametric equation

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• Many smooth and deformable objects are difficult or inefficient to represent with basic primitives, even with bezier/spline surfaces.

• Field functions with control points, line segments and/or polygonally bounded planes are used to define shapes in space.

Implicit Surface

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Solid Objects

• Voxels• BSP Tree• Cell Complex

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Voxels• Uniform 3D grid of volumetric samples• Mostly acquired from CAT, MRI, etc.

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BSP Tree

• Binary space partition with labeled solid cells• Constructed from polygonal representations

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Cell Complex

• A topological space, an arrangement of polyhedral cells with adjacent cells linked and solid cells labeled

• e.g. Adjacency graph of BSP leaf cells

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Topology of 3D Representations

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High-Level Structures

• CSG (Constructive Solid Geometry)• Constraint blocks• Generative model• Skeleton• Sweep model• Scene graph

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CSG (Constructive Solid Geometry)

• Hierarchy of boolean set operators (union, difference, subtraction, intersection) applied to simple shapes

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Constraint Blocks• Set of simple shapes with geometric

constraints

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Generative Model• Hierarchy of modification operators on a

shape

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Skeleton

• A set of connected bone structures deforming shape of a 3D model

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Sweep Model

• A 3d model generated by sweeping a surface along a trajectory

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Scene Graph

• Union of objects at leaf nodes of a tree

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Summary• Object representation is the key for our goal