graphics graphics lab @ korea university cgvr.korea.ac.kr creating virtual world i 김 창 헌...

Graphics

Graphics Lab @ Korea University

Creating Virtual World I

김 창 헌 Department of Computer Science

Korea University http://cgvr.korea.ac.kr/courses/2002/cse425/

CGVR


Overview

Model Construction

3D Object Representation

Subdivision Surfaces

Solid Modeling

CGVR


Model Construction

Interactive Modeling Tools CAD programs Subdivision surface editors

Scanning Tools CAT, MRI, laser, magnetic, robotic arm, etc.

Computer Vision Stereo, motion, etc.

Procedural Generation Sweeps, fractals, grammars

CGVR


Interactive Modeling Tools

User Constructs Objects with Drawing Program

CGVR


Model Construction

Interactive Modeling Tools CAD programs, subdivision surface editors

Scanning Tools CAT, MRI Laser Range Scanning Magnetic, robotic arm



CGVR


Scanning Tools

Acquire Geometry of Objects with Active Sensors CAT/MRI Laser range scanner Magnetic sensor Robotic arm Etc.

CGVR


Scanning Tools


Color

Depth

CGVR


Scanning Tools


CGVR


Model Construction

Interactive Modeling Tools CAD programs Subdivision surface editors


Computer Vision Stereo Motion


CGVR


Computer Vision

Infer 3D Geometry from Images Stereo Motion Constraints Etc.

CGVR


Model Construction

Interactive Modeling Tools CAD programs, subdivision surface editors



Procedural Generation Sweeps Fractals Grammars

CGVR


Procedural Generation

Goal: Describe 3D models algorithmically

Best for Models Resulting from ... Repeating processes Self-similar processes Random processes

Advantages: Automatic generation Concise representation Parameterized classes of models

CGVR


Sweep

Generate Different Shells by Varying Parameters

Different helico-spirals Different generating curves

CGVR


Fractal

Defining Property: Self-similar with infinite resolution

Mandelbrot Set

CGVR


Fractal

Useful for Describing Natural 3D Phenomenon Terrain Plants Clouds Water Feathers Fur Etc.

CGVR


Deterministically Self-Similar Fractal

Useful for Creating Interesting Shapes

CGVR


Statistically Self-Similar Fractal

Useful for Creating Mountains and Trees

CGVR


Grammar

Generate Description of Geometric Model by Applying Production Rules Useful for creating plants

Example:

Tree Branch Tree | Leaf

Branch Cylinder | [ Tree ]

C[CL]C[C[CL][CL]]C[[CL][CL]] C[*]C[*][*]

CGVR


Grammar

Useful for Creating Plants

CGVR


Creating Virtual World

Model Construction



Solid Modeling

CGVR


3D Object Representations

Raw Data Point cloud Range image Polygon soup

Surfaces Mesh, Subdivision, Parametric, Implicit

Solids Voxel, BSP tree, CSG, Sweep

CGVR


Point Cloud

Unstructured Set of 3D Point Samples Acquired from range finder, computer vision, etc

CGVR


Range Image

Set of 3D Points Mapping to Pixels of Depth Image Acquired from range scanner

Range Image Tessellation Range Surface

CGVR


Polygon Soup

Unstructured Set of Polygons Created with interactive modeling systems

CGVR



Raw Data Point cloud, Range image, Polygon soup

Surfaces Mesh Subdivision Parametric Implicit

Solids Voxel, BSP tree, CSG, Sweep

CGVR


Mesh

Connected Set of Polygons (Usually Triangles) May not be closed

CGVR



Coarse Mesh & Subdivision Rule Define smooth surface as limit of sequence of

refinements

CGVR


Parametric Surfaces

Tensor Product Spline Patches Careful constraints to maintain continuity

CGVR


Implicit Surface

Points satisfying: F(x,y,z) = 0

Polygonal Model Implicit Model

CGVR



Raw Data Point cloud, Range image, Polygon soup

Surfaces Mesh, Subdivision, Parametric, Implicit

Solids Voxel BSP tree CSG Sweep

CGVR


Voxels

Uniform Grid of Volumetric Samples Acquired from CAT, MRI, etc.

CGVR


BSP Tree

Binary Space Partition with Solid Cells Labeled Constructed from polygonal representations

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Binary Spatial Partition

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BSP Tree

CGVR


CSG

Hierarchy of Boolean Set Operations (Union, Difference, Intersect) Applied to Simple Shapes

CGVR


Sweep

Solid Swept by Curve Along Trajectory

Constructing a Torus using Rotational Sweep

CGVR


Summary3D Object Representations

Taxonomy of 3D Object Representations

VoxelVoxel

Discrete Continuous

Combinational Functional

MeshSubdivision

MeshSubdivision

BSP TreeBSP Tree BezierB-Spline

BezierB-Spline

AlgebraicAlgebraic

Topological Set Membership Parametric Implicit

CGVR



Model Construction



Solid Modeling

CGVR


Subdivision

How do You Make a Smooth Curve?

CGVR



Coarse Mesh & Subdivision Rule Define smooth surface as limit of sequence of

refinements

CGVR


Loop Subdivision Scheme

How Refine Mesh? Refine each triangle into 4 triangles by splitting each

edge and connecting new vertices

CGVR


Loop Subdivision Scheme

Limit Surface Has Provable Smoothness Properties

CGVR


Subdivision Schemes

There are different subdivision schemes Different methods for refining topology Different rules for positioning vertices

Interpolating versus approximating

Face Split Vertex Split

Doo-Sabin, Midege (C1)

Biquartic (C2)Catmull-Clark (C2)

Kobbelt (C1)

Quad. Meshes

Loop (C2)

Mod. Butterfly (C1)

Triangular Meshes

Approximating

Interpolating

CGVR


Subdivision Schemes

Loop Butterfly

Catmull-Clark Doo-Sabin

CGVR


Subdivision Schemes

Loop Butterfly Catmull-Clark Doo-Sabin

CGVR


Polygon Meshes

Mesh Representations Independent faces Vertex and face tables Adjacency lists Winged-Edge

CGVR


SummarySubdivision Surface

Advantages: Simple method for describing complex surfaces Relatively easy to implement Arbitrary topology Smoothness guarantees Multiresolution

Difficulties: Intuitive specification Parameterization Intersections

CGVR



Model Construction



Solid Modeling

CGVR


Solid Modeling

Represent Solid Interiors of Objects Surface may not be described explicitly

CGVR


Solid Modeling Representation

Voxels Quadtrees & Octrees Binary Space Partitions Constructive Solid Geometry

CGVR


Voxels

Partition Space into Uniform Grid Grid cells are called a voxels (like pixels)

Store Properties of Solid Object with Each Voxel Occupancy Color Density Temperature Etc.

CGVR


Voxel Acquisition

Scanning Devices MRI CAT

Simulation FEM

CGVR


Voxel Display

Isosurface Rendering Render surfaces bounding volumetric regions of cons

tant value (e.g., density)

CGVR


Voxel Display

Ray Casting Integrate density along rays through pixels

CGVR


Voxels

Advantages Simple, intuitive, unambiguous Same complexity for all objects Natural acquisition for some applications Trivial boolean operations

Disadvantages Approximate Large storage requirements Expensive display

CGVR




CGVR


Quadtrees & Octrees

Refine Resolution of Voxels Hierarchically More concise and efficient for non-uniform objects

Uniform Voxel Quadtree

CGVR




CGVR


Binary Space Partitions (BSPs)

Recursive Partition of Space by Planes Mark leaf cells as inside or outside object

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BSP Tree

CGVR




CGVR


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Block 1 Block 2

Cylinder

Constructive Solid Geometry (CSG)

Represent Solid Object as Hierarchy of Boolean Operations Union Intersection Difference

CGVR


CSG Acquisition

Interactive Modeling Programs CAD/CAM

CGVR


CSG Display & Analysis

Ray Casting

Union

Circle Box

graphics graphics lab @ korea university cgvr.korea.ac.kr creating virtual world i 김 창 헌...

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