Modeling (01) RNDr. Martin Madaras, PhD. madaras@skeletex.xyz - - PowerPoint PPT Presentation

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Modeling (01) RNDr. Martin Madaras, PhD. madaras@skeletex.xyz - - PowerPoint PPT Presentation

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Fundamentals of Computer Graphics and Image Processing Modeling (01) RNDr. Martin Madaras, PhD. madaras@skeletex.xyz Computer Graphics Image processing Representing and manipulation of 2D images Modeling Representing and

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Fundamentals of Computer Graphics and Image Processing

Modeling (01)

  • RNDr. Martin Madaras, PhD.

madaras@skeletex.xyz

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Computer Graphics

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 Image processing

 Representing and manipulation of 2D images

 Modeling

 Representing and manipulation of 2D and 3D objects

 Rendering

 Constructing images from virtual models

 Animation

 Simulating changes over time

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  • Ask questions, please!!!
  • Be communicative
  • www.slido.com #ZPGSO01
  • More active you are, the better for you!
  • We will go into depth as far, as there are no questions

How the lectures should look like #1

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What is Modeling?

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 Representation and manipulation of objects

 Acquire  Edit  Transform  Smooth  Render  Deform  Morph  Compress  Transmit  Analyze

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What is Modeling?

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 Representation and manipulation of objects

 Acquire  Edit  Transform  Smooth  Render  Deform  Morph  Compress  Transmit  Analyze

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Modeling

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 How to represent ..

 2D and 3D objects in a computer?  Acquire computer representations of objects?  Manipulate representations of objects?

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Quick test #1

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 Describe the picture

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Quick test #2

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 Describe the picture

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Quick test #3

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 Volunteers:

Describe the image to others

 Others:

Reproduce the image

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Semantic vs. numeric

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 Humans – semantic representation

 concepts, notions, meanings, emotions...  imprecise, ambiguous

 Computers – numeric representation

 exact, mathematical, straightforward

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Detailed representation

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2D Object Representations

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 How to define 2D shapes?

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2D Object Representations

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 Let’s define these objects

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2D Object Representations

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 How to make 2D representation smooth at any scale?

Bitmaps, raster, pixels, explicit Shapes, vectors, curves, parametric, implicit

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2D Object Representations

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 Lines  Polygon (set of lines)  Curves  Vector image (set of curves)

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2D Object Representations

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 Vector Images

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3D Object Representations

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 How to represent a 3D object?

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3D Object Representations

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 Polygons…

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3D Object Representations

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 Voxels…

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3D Object Representations

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 Recreating artwork

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3D Object Representations

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 Mechanical objects

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3D Object Representations

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 Maps, Cities, Landscape

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3D Object Representations

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 Clouds, Smoke, Fog, Water

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2D Object Representations

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 Pixels

 Images

 Lines

 Curves

 Polygons

 Discrete,

Vector graphics

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3D Object Representations

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 Points

 Range Image, Point Cloud

 Surfaces

 Polygonal, Subdivision, Parametric, Implicit

 Solids

 Voxels, BSP Tree, CSG, Sweep, etc.

 Hierarchical Structures

 Scene graph, Application specific…

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Why so many representation?

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 Efficiency for different tasks

 Rendering  Acquisition  Manipulation  Animation  Analysis

 Data structures determine algorithms

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Outline

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 Points

 Range Image, Point Cloud

 Surfaces

 Polygonal, Subdivision, Parametric, Implicit

 Solids

 Voxels, BSP Tree, CSG, Sweep

 Hierarchical Structures

 Scene graph, Application specific

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Range Image

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 Set of 3D points mapping to pixels of depth image  Structured Point Cloud

 Acquired using a range scanner (eg. Kinect)

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Point Cloud

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 Unstructured set of 3D point samples

 Acquired from multiple range scans, vision, etc.

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Point Cloud Animation: Road Survey

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https://www.youtube.com/watch?v=f_ng212b-UM

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Outline

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 Points

 Range Image, Point Cloud

 Surfaces

 Polygonal, Subdivision, Parametric, Implicit

 Solids

 Voxels, BSP Tree, CSG, Sweep

 Hierarchical Structures

 Scene graph, Application specific

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Polygonal Mesh

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 Connected mesh of polygons (usually triangles)

 Most common representation, supported in OpenGL

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Subdivision Surface

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 Coarse mesh with subdivision rule  Smooth surfaces are defined as sequences of refinement

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Subdivision Surface

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 Properties

 Accurate  Concise  Intuitive specification  Local support  Affine invariant  Arbitrary topology  Guaranteed continuity  Natural parametrization  Efficient display  Efficient intersections Geri’s game, Pixar, 1997: https://www.youtube.com/watch?v=kweN7VLx-JE

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Subdivision Surfaces: Overview

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https://www.youtube.com/watch?v=ckOTl2GcS-E&t=26s

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Subdivision Surfaces: Overview

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 Subdivision surfaces

 Loop subdivision  Catmull-Clark  Butterfly, Doo-Sabin, etc.

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Example: Loop subdivision

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 How to refine mesh ?

 Refine each triangle into 4 triangles by splitting each edge and

connecting the vertices

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Example: Loop subdivision

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 How position new vertices?

 Choose location of the vertices as weighted average of original

vertices in local neighborhood

 Rules for extraordinary vertices and boundaries:

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Key Questions

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 How to refine mesh ?

 Aim for properties like smoothness

 How to store mesh ?

 Aim for efficiency of implementing subdivision rules

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Polygonal meshes

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 V, E, F  P, S

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Polygonal Meshes

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 Mesh Representations

 Independent faces  Vertex and face tables  Adjacency lists  Winged-Edge

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Independent Faces

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 Each face lists vertex coordinates

 Redundant vertices  No topology information

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Vertex and Face Tables

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 Each face lists vertex references

 Shared vertices  Still no topology information

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Adjacency Lists

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 Store all vertex, edge and face adjacency

 Efficient topology traversal  Extra storage

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Partial Adjacency Lists

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 Can we can store only some adjacency information and

derive others?

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Winged Edge

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 Adjacency encoded in edges

 All adjacencies in O(1) time  Little extra storage  Arbitrary polygons

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Winged Edge Example

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Parametric Surface

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 Defined using control points  Surfaces are defined using parametric functions  m × n control points  parameters u,v http://cadauno.sourceforge.net/

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Parametric Surface

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 Cubic Bezier surface, NURBS

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Implicit Surface

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 Surface satisfying function F(x,y,z) = 0

Polygonal model Implicit model

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Question

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What happens if we turn F(x,y,z) = 0 into F(x,y,z) ≤ 0 ?

surface → volume

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Outline

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 Points

 Range Image, Point Cloud

 Surfaces

 Polygonal, Subdivision, Parametric, Implicit

 Solids

 Voxels, BSP Tree, CSG, Sweep

 Hierarchical Structures

 Scene graph, Application specific

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Volumetric representation

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 not only boundary

but also the insides

  • f the object

 Medicine  Physics  Simulations  Animation

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Voxels

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 Uniform grid of volumetric samples  Acquired using CAT, MRI scans etc.  Volume elements, “3D pixels”  Discrete

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Volume Rendering Demo

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https://www.youtube.com/watch?v=uSyUCLLNtMo

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BSP Trees

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 Binary space partition

 Constructed from polygonal representations

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Constructive Solid Geometry

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 Hierarchy of boolean operations

 Union, Difference, Intersect applied to simple shapes

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Functional Representation

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 F-rep ~ generalization of CSG  More node functions – operators

 e.g. object blending

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Mesh reconstruction

 Conversion into an implicit function

 Poisson reconstruction

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Mesh reconstruction

 Isosurface extraction

 Marching cubes

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Marching cubes

 Create cubes  Classify vertices  Build indices  Lookup edge list

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Marching cubes

 Create cubes  Classify vertices  Build indices  Interpolate Triangle

Vertices

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Marching cubes

 Create cubes  Classify vertices  Build indices  Interpolate Triangle

Vertices

 Calculate normals

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Marching cubes

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Marching cubes

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Marching cubes

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Marching cubes

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Marching cubes

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Outline

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 Points

 Range Image, Point Cloud

 Surfaces

 Polygonal, Subdivision, Parametric, Implicit

 Solids

 Voxels, BSP Tree, CSG, Sweep

 Hierarchical Structures

 Scene graph, Application specific

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Scene Graph

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 Objects organized in a hierarchical structure

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Application Specific

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 Specific for given application domain

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Taxonomy of 3D representations

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Computational Differences

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 Efficiency

 Computational complexity ( O(n log n) )  Space/Time trade-off  Numerical stability/accuracy

 Simplicity

 Hardware acceleration  Ease of acquisition  Software creation and maintenance

 Usability

 Designer vs. computational engine

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Parametric vs. polygonal

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 Parametric

 smooth, reparametrizable  harder rendering  precise rendering

 Polygonal

 discrete, hard to reparametrize  faster rendering or rasterization  approximative rendering

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  • Ask questions, please!!!
  • Be communicative
  • www.slido.com #ZPGSO01
  • More active you are, the better for you!

How the lectures should look like #2

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www.skeletex.xyz madaras@skeletex.xyz

Questions ?!