Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr 1 Surface Rendering Methods 고려대학교 컴퓨터 그래픽스 연구실.

Graphics

cgvr.korea.ac.kr 1 Graphics Lab @ Korea University Graphics Lab @ Korea University

Surface Rendering Methods

고려대학교 컴퓨터 그래픽스 연구실

cgvr.korea.ac.kr

CGVR

2 Graphics Lab @ Korea University Graphics Lab @ Korea University

Surface Rendering: Shading

Determine a Color for Each Filled Pixel How to Choose a Color for Each Filled Pixel

Each illumination calculation for a ray from the eyepoint through the view plane provides a radiance sample

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CGVR


Shading Methods

Ray Casting Polygon Shading

Ray Tracing

Radiosity

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Ray Casting

Simplest Shading Approach Perform independent lighting calculation for every

pixel

i i

niSiiDALAE IKILNKIKII )RV(

i in

iSiiDALAE IKILNKIKII )RV(

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Polygon Shading

Can Take Advantage of Spatial Coherence Illumination calculations for pixels covered by same

primitive are related to each other

i i


i in


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Polygon Shading Algorithms

Flat Shading

Gouraud Shading

Phong Shading

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Flat Shading

Gouraud Shading

Phong Shading

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Flat Shading

Illuminated only by directional light sources Diffuse or viewed from infinitely far away

i i


i in


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Flat Shading

One Illumination Calculation per Polygon Assign all pixels inside each polygon the same color

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Flat Shading

Objects Look Like They are Composed of Polygons OK for polyhedral objects Not so good for ones with smooth surfaces

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Flat Shading

Gouraud Shading

Phong Shading

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Gouraud Shading

Smooth Surface Represented by polygonal mesh with a normal at

each vertex

i i


i in


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Gouraud Shading

One Lighting Calculation per Vertex Assign pixels inside polygon by interpolating colors

computed at vertices

Viewer Light

N1

N3N2

V1 L1

Polygon

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Gouraud Shading

Bilinearly Interpolate Colors at Vertices Down and Across Scan Lines

I1

I2I3

21 I1IA 31 I1IB

BA1I BA1I

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Gouraud Shading

Smooth Shading over Adjacent Polygons Curved surfaces Illumination highlights Soft shadows

Mesh with shared normals at vertices

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Gouraud Shading

Produces Smoothly Shaded Polygonal Mesh Piecewise linear approximation Need fine mesh to capture subtle lighting effects

Flat Shading Gouraud Shading

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Flat Shading

Gouraud Shading

Phong Shading

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Phong Shading

What if Polygonal Mesh is too Coarse to Capture Illumination Effects in Polygon Interiors?

Viewer Light

N1

N3N2

V1 L1

Polygon

i i


i in


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Phong Shading

One Lighting Calculation per Pixel Approximate surface normals for points inside

polygons by bilinear interpolation of normals from vertices

Viewer Light

N1

N3N2

V L

Polygon

N

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Phong Shading

Bilinearly Interpolate Normals at Vertices Down and Across Scan Lines

α β

21 N1NA 31 N1NB

γ

BA1N BA1N

N1

N2 N3

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Phong Shading

Gouraud

Wireframe

Phong

Flat

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Shading & Subdivision

Gouraud PhongFlat

Loop SubdivisionLevel 1

Level 2

Control Mesh

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Shading Methods


Ray Tracing

Radiosity

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Ray Tracing

Extension of Ray Casting Look for the visible surface for each pixel Continue to bounce the ray around the scene

TTRSL LLn

SDAAE IKIKISKLNKIKII )RV( TTRSL LLn

SDAAE IKIKISKLNKIKII )RV(

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Ray Tracing

Global Illumination Shadows Refractions Inter-object reflections

Highly Realistic vs. Computation Time

TTRSL LLn

SDAAE IKIKISKLNKIKII )RV( TTRSL LLn

SDAAE IKIKISKLNKIKII )RV(

Transparenc

y

Reflectanc

e

Shadow

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Basic Ray Tracing Algorithm

For Each Pixel Ray Primary ray

Test each surface if it is intersected

Intersected: Secondary ray Reflection ray Transparent – Refraction ray

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Basic Ray Tracing Algorithm

For Each Pixel Ray Primary ray

Test each surface if it is intersected

Intersected: Secondary ray Reflection ray Transparent – Refraction ray

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Ray Tracing Tree

Ray tree represents illumination computation One branch reflection The other branch transmission Terminated reach the preset maximum or strike a light

sourceScene Ray Tree

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Ray Tracing Tree

Pixel intensity Sum of intensities at root node Start at terminal node If no surfaces are intersected, the intensity of background

Scene Ray Tree

Iback

Iback Iback

Ipixel

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Shading Methods


Ray Tracing

Radiosity

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Radiosity

Goal Simulate diffuse inter-object reflections and shadows

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Radiosity

Basic Idea Treat every polygon as light source

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Radiosity

Advantages Physically models shadows and indirect diffuse

illumination Independent of any viewpoint

Equation

ijjiii FBρEB ijjiii FBρEB

Bi = Radiosity of patch iEi = Emission of patch iρi = Reflectivity of patch iFi = Form-factor between patches i and j

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Form Factors

Definition Fraction of energy leaving patch j

that arrives at patch i

Computation Project onto unit hemisphere Project onto unit circle base Divide by area of circle Project scene onto hemi-cube

Project ontounit hemisphere

Project ontoHemi-cube

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Matrix Solution Methods

Matrix Formulation

Progressive Refinement Iterate shoot radiosity from patches O(n2) computation, but get pretty good solutions

more quickly

nnnnnnnnn

n

n

n

E

E

E

E

B

B

B

B

Fρ1FρFρ

FρFρFρ

FρFρ1Fρ

FρFρFρ1

3

2

1

3

2

1

21

33323313

22222212

11121111

nnnnnnnnn

n

n

n

E

E

E

E

B

B

B

B

Fρ1FρFρ

FρFρFρ

FρFρ1Fρ

FρFρFρ1

3

2

1

3

2

1

21

33323313

22222212

11121111

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Matrix Solution Methods

24 iterations

1 iteration

100 iterations

2 iterations

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Hierarchical Radiosity

Multiresolution Computation Substructure patches into quad-tree Transfer energy using lower resolution mesh

elements if can do so within error tolerance O(n) computation

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Ray Tracing & Radiosity

Dilemma: Radiosity is good at diffuse inter-object reflection Ray tracing is good at specular inter-object reflection

Combine them Example: compute diffuse inter-object reflections in a

ray tracer Monte Carlo methods

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Summary

Ray Casting Flat Gouraud Phong

Ray Tracing

Radiosity

Less Expensive

More Accurate

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Visible-Line Determination

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Visible-Surface Determination with Ambient Illumination only

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Individually Shaded Polygons with Diffuse Reflection

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Gouraud Shaded Polygons with Diffuse Reflection

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Gouraud Shaded Polygons with Specular Reflection

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Phong Shaded Polygons with Specular Reflection

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Curved Surfaces with Specular Reflection

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Improved Illumination Model and Multiple Lights

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Texture Mapping

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Displacement Mapping

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Reflection Mapping

Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr 1 Surface Rendering Methods 고려대학교 컴퓨터 그래픽스 연구실.

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