Download - 3D Object Representations (GATE-540)
1GATE-540
3D Object Representations(GATE-540)
Dr.Çağatay ÜNDEĞER
InstructorMiddle East Technical University, GameTechnologies
&
General ManagerSimBT Inc.
e-mail : [email protected]
Game Technologies Program – Middle East Technical University – Spring 2010
Reference: Thomas Funkhouser, Princeton University
2GATE-540
Outline
• 3D Objects• Raw Data Types• 3D Object Representations
– Surface models– Solid models– High-Level Structures
3GATE-540
Goals• Develop 3D Analysis Algorithms:
– Reconstruction– Segmentation– Feature Detection– Labeling– Matching – Classification– Retrielval– Recognition– Clustering Different methods are applicable
to different representations.
4GATE-540
3D Objects
• How can this simple object be represented in a computer?
5GATE-540
3D Objects
• Is representing this object similar to the previous one an effective way?
• Highly smooth curves...
6GATE-540
3D Objects
• How about this one?• A volumetric body...• Outer surface...
7GATE-540
3D Objects• How about these ones?• Has soft and hard tissue...• Has different densities...• Has Interrior...
8GATE-540
3D Objects• What about this one?• Composed of
different geometric parts / shapes...
9GATE-540
3D Objects• This one?
10GATE-540
3D Objects• How about these?• A deformable body...• Animation integration...
11GATE-540
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
12GATE-540
Point Cloud
• Unstructured set of point samples• Range finders, 3D scanners, computer vision
13GATE-540
Range Image
• Set of 3D points that maps to pixels of a depth image
• From range scanners
Range (depth) image
14GATE-540
Range Image• A kind of more structured point cloud• Generating surfaces from 3d points
15GATE-540
Polygon Soup
• Unstructures set of polygons or unconnected lines of polygons
• Mostly creates with interactive modeling sys.
16GATE-540
Surface Objects
• Mesh• Subdivision• Parametric• Implicit
17GATE-540
Mesh• Connected set of polygons (usually triangles)
18GATE-540
Subdivision Surface
• Consists of a coarse mesh and subdivision rule• Generates smooth surfaces with refinements
19GATE-540
Parametric Surface
• Bezier / spline surface patches• Defined with a parametric equation
20GATE-540
• 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
21GATE-540
Solid Objects
• Voxels• BSP Tree• Cell Complex
22GATE-540
Voxels• Uniform 3D grid of volumetric samples• Mostly acquired from CAT, MRI, etc.
23GATE-540
BSP Tree
• Binary space partition with labeled solid cells• Constructed from polygonal representations
24GATE-540
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
25GATE-540
Topology of 3D Representations
26GATE-540
High-Level Structures
• CSG (Constructive Solid Geometry)• Constraint blocks• Generative model• Skeleton• Sweep model• Scene graph
27GATE-540
CSG (Constructive Solid Geometry)
• Hierarchy of boolean set operators (union, difference, subtraction, intersection) applied to simple shapes
28GATE-540
Constraint Blocks• Set of simple shapes with geometric
constraints
29GATE-540
Generative Model• Hierarchy of modification operators on a
shape
30GATE-540
Skeleton
• A set of connected bone structures deforming shape of a 3D model
31GATE-540
Sweep Model
• A 3d model generated by sweeping a surface along a trajectory
32GATE-540
Scene Graph
• Union of objects at leaf nodes of a tree
33GATE-540
Summary• Object representation is the key for our goal