Modelingolano/class/435-08-2/modeling.pdf · From data (visualization) Through image capture (IBR)...

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Modeling

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DefinitionsDefinitions

ModelingCreating a model of an object, usually out of acollection of simpler primitives

PrimitivesA basic shape handled directly the rendering system

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Boundary Representation (Boundary Representation (BRepBRep))

Instead of representing a cube as 6 polygons,represent as 6 planes

Surfaces are represented as a hollow shell

Just the boundary

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Common PrimitivesCommon Primitives

Triangles & PolygonsMost common, usually the only choice for interactive

Patches, Spheres, Cylinders, ...Found in RenderMan

Often converted to simpler primitives within therenderer

VolumesWhat’s at each point in space?

Often with some transparent material

Few renderers handle both volume & surfacemodels

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Composing PrimitivesComposing Primitives

Collections of large numbers of primitivesSometimes called Boundary Representation (BRep)

Constructive Solid Geometry (CSG)Set operations (union, intersection, difference)

Implicit Models & BlobsSurface where f(x,y,z) = 0

Sum, product, etc. of simpler functions

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Modeling Modeling ApproachesApproaches

Manual primitive creationProceduralScan from physical objectFrom data (visualization)Through image capture (IBR)

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Manual Primitive CreationManual Primitive Creation

Text EditorHigh-level primitivesModeling Programs

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Text EditorText Editor

Display "cube.tif" "file" "rgba"Format 1024 768 1LightSource "distantlight" 1Projection "perspective"Translate 0 0 1.5Rotate 40 -1 1 0WorldBeginSurface "matte"AttributeBeginTranslate -0.5 -0.5 -0.5Scale 0.02 0.02 0.02Color [0.02 0.02 0.02]TransformBeginTranslate 0.5 0.5 0.5Scale 1 1 1TransformBeginPolygon "P" [0.5 0.5 0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 ]Rotate 90 0 1 0Polygon "P" [0.5 0.5 0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 ]Rotate 90 0 1 0Polygon "P" [0.5 0.5 0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 ]Rotate 90 0 1 0Polygon "P" [0.5 0.5 0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 ]

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Higher Level PrimitivesHigher Level Primitives

Many libraries provide higher level primitives(built atop lower level primitives)

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Modeling Modeling ProgramsPrograms

Maya, Blender, LightWave, etc...

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Constructive Solid Geometry (CSG)Constructive Solid Geometry (CSG)

Objects are solidsBoolean operations to combine objects

Union

Intersection

Difference

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Supported by the RenderMan specification viaRiSolidBegin()

RiSolidEnd ()

However, this is one of the areas where Pixie'simplementation falls short of full specificationcompliance

Currently an unimplemented feature on Pixie's “wishlist”

Liang, et al., PG’01 14

Implicit FunctionsImplicit Functions

Model as sum of implicit functionsSurface at threshold

Bloomenthal, SIGGRAPH 85 15

Hybrid Implicit & PolygonalHybrid Implicit & Polygonal

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ProceduralProcedural

Describe physical attributes though some(spatial) function

Shape

Density

Color

Texture

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Procedural ApproachesProcedural Approaches

FractalsImplicit FunctionsGrammarsSimulations

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FractalsFractals

Complex structure through self-similarity acrossscales

Iterated equations

Iterated replacement

Spectral synthesis

Created by Wolfgang Beyer 19

Fractals Fractals –– Iterated Equations Iterated Equations

Mandelbrot Set

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The Mandelbrot set is defined by a family ofcomplex quadratic polynomials

Given by (where c is a complex number)

For each c the following behavior isconsidered

Obtained by iterating (staring at z = 0)

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Thus

Denotes the nth iteration of

The Mandelbrot set is the subset which isconstrained as

Connelly Barnes 22


Mathematical depiction of the Mandelbrot setPoint c is black if it belongs to the set



Colored pictures are usually generated byassigning a color to each point whichrepresents how quickly the sequence

Diverges to infinity


Fractals Fractals –– Self Similarity Self Similarity

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Fractals Fractals –– Iterated Replacement Iterated Replacement

Koch Curve

Initiator Generator

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Fractals Fractals –– Iterated Replacement Iterated Replacement

Fractal Mountains

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Fractals Fractals –– Spectral Synthesis Spectral Synthesis

Spectral energy a function of frequencyHigher frequency, less energy

Characterizes roughness of surface

Natural phenomena tend to be 1/f

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Fractals Fractals –– Noise-Based Synthesis Noise-Based Synthesis

Band-limited Perlin noise functionMost energy between 1/2 and 1 cycle per unit

Average value is 0

Random, but repeatable

1D, 2D, 3D & 4D versions common

Sum noise octavesn(x) + n(2x) + n(4x) + ...

Stop add “...” when frequency is too high to see

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Perlin NoisePerlin Noise

Ken Musgrave 36

Fractals Fractals –– Fractal Landscapes Fractal Landscapes

Landscape height is a fractal function of x, y

Ken Musgrave 37


Ken Musgrave 38


Embellishments – textures, shadows,reflections

Ken Musgrave 39


Further embellishments – atmospheric haze,clouds, waves, colored light source

Ken Musgrave 40

Multi-Fractal LandscapesMulti-Fractal Landscapes

Change roughness across fractalScaling ( , , ...) becomes a function

Here, scale is a function of altitude

Perlin & Hoffert, SIGGRAPH 89 41

HypertextureHypertexture

Add noise or turbulence to functions

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Grammar Based Grammar Based ModelingModeling

Use (mostly) context-free grammars (CFG) tospecify structural change over generationsOften used to simulate a biological growthprocess

Plants

Seashells

L-Systems (Lindenmayer)

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Context Free GrammarsContext Free Grammars

A CFG G = (V, T, S, P) whereV is a set of non-terminals

T is a set of terminals

S is the start symbol

P is a set of production (rules) of the form

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Applying Grammar RulesApplying Grammar Rules

SymbolsA, B, straight line segments

[ ], branch left 90º

RulesB A[B]AA[B]

A AA

StringsB

A[B]AA[B]

AA[A[B]AA[B]]AAAA[A[B]AA[B]]

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Applying Grammar RulesApplying Grammar Rules

SymbolsA, B, straight line segments

[ ], branch left 45º

( ), branch right 45º

RulesB A[B]AA(B)

A AA

StringsB

A[B]AA(B)

AA[A[B]AA(B)]AAAA(A[B]AA(B))

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L-System ExamplesL-System Examples

Symbols[/] = push/pop

+/- = rotate left/right

A-Z = straight segment

Rules25.7º, Start=X

X F[+X][-X]FX

F FF

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L-Systems ExampleL-Systems Example

SymbolsSame as previous

Rules22.5º, Start=X

X F-[[X]+X]+F[+FX]-X

F FF

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L-Systems ExampleL-Systems Example

SymbolsSame as previous

Rules22.5º, Start=F

F FF-[-F+F+F]+[+F-F-F]

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L-Systems AdditionsL-Systems Additions

Add any/all of the following3D Structure

Randomness

Leaves

Flowers

Color

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L-SystemsL-Systems

Randomness of 50% introduced in both linesegment length and degree of rotation

Användare Solkoll 51

L-Systems WeedsL-Systems Weeds

Mitch Allen, Przemyslaw Prusinkiewicz, and Theodore DeJong 52

L-Systems PlantsL-Systems Plants

PRZEMYSLAW PRUSINKIEWICZ, JIM HANAN, MARK HAMMEL, RADOMIR MECH 53

L-Systems PlantsL-Systems Plants

Joanna L. Power, A.J. Bernheim Brush, Przemyslaw Prusinkiewicz, and David H. Salesin 54

L-Systems FlowersL-Systems Flowers

Prusinkiewicz, et al., SIGGRAPH 94 55

PruningPruning

Prusinkiewicz, et al., SIGGRAPH 94 56

PruningPruning

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SimulationsSimulations

BiologicalSimulate growth, development

PhysicalSimulate formation or erosion

Deborah R. Fowlery, Hans Meinhardt and Przemyslaw Prusinkiewicz 58

Biological SimulationsBiological Simulations

Deborah R. Fowler, Pmemyslaw Prusinkiewicz, Johannes Battjes 61


Greg Turk 62


Jacob Olsen 63

Physical SimulationsPhysical Simulations

Erosion

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Scan From ObjectsScan From Objects

General conceptFind points on surface

Connect with mesh

MechanicalTriangulation

Laser

Structured Light

Multiple Cameras

CAT/MRI scan

FARO Technologies Inc. 65

MechanicalMechanical

Touch tip to surfaceMeasure angles

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TriangulationTriangulation

Point in space at intersection of ray from A andray from B

Zhang, Curless and Seitz, 3DPVT 2002 67

Structured LightStructured Light

Point in space at intersection of color edge fromlight source/projector and ray through camerapixel

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VisualizationVisualization

DataMeasurements

Simulation

Information

Present visuallyIncrease understanding

Recognize patterns

Markus Hadwiger, Christoph Berger & Helwig Hauser 69


Can be 3D object

Markus Hadwiger, Christoph Berger & Helwig Hauser 70


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Can be 3D, but showing non-visual aspects

Jeffrey Heer & Danah Boyd 72


Can be not traditionally geometric at all

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Image-Based RenderingImage-Based Rendering

Pixels in one or more camerasColor of point in space

Color of light along one ray

IBRConstruct new novel view using only image data

Photosynth - Microsoft 74

Image Based RenderingImage Based Rendering

Modelingolano/class/435-08-2/modeling.pdf · From data (visualization) Through image capture (IBR)...

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