Surface Rendering Methods - Hallym

Computer Graphics

Sun-Jeong Kim http://www.hallym.ac.kr/~sunkim/teach/2005/cga

Surface Rendering Methods

November 14, 2005


Content

Polygonal renderingflat shading

Gouraud shading

Phong shading

Global renderingray tracing

radiosity


Polygonal Rendering

Shading a polygonal meshflat or constant shading

interpolative, smooth, or Gouraud shading

Phong shading

polygonal mesh


Flat Shading (1)

Constant shadingflat polygon

n: constant

distant light source

l: constant

distant viewer

v: constant

One shading calculation for each polygonOne shading calculation for each polygon

In OpenGL

distant source and viewer

glShadeModel(GL_FLAT);


Flat Shading (2)

Disappointing for a smooth surfacelateral inhibition

human visual system has a remarkable sensitivity

Mach bandsperceive the increases in brightness along the edges

flat shading of polygonal mesh

We need smoother shading techniques to avoid it!!We need smoother shading techniques to avoid it!!We need smoother shading techniques to avoid it!!

perceived and actual intensities at an edge


Gouraud Shading

In OpenGL

One lighting calculation for each vertexOne lighting calculation for each vertexbilinear interpolation of colors

Defining vertex normal through interpolation

glShadeModel(GL_SMOOTH);

4321

4321

nnnn

nnnnn

++++++

=

normals near interior vertex


Example: Wireframe


Example: Flat Shading


Example: Gouraud Shading


Example: Bump Mapping


Example: Environmental Mapping


Phong Shading

Not preventing the appearance of Mach bands

If polygonal mesh is too coarse to capture illumination effects in polygon interiors?

One shading calculation for each pixelOne shading calculation for each pixel off-line

Computing vertex normal at each point

interpolate normals across each polygoninterpolate interpolate normalsnormals across each polygonacross each polygon

normals on an edge interpolation of normals

( ) ( ) BA nnn 1 ααα +−=

( ) ( ) DC nnn 1 , βββα +−=


Example: Phong Shading

Gouraud

Wireframe

Phong

Flat


Example: Shading & Subdivision

Gouraud PhongFlat

Loop SubdivisionLevel 1

Level 2

Control Mesh


Global Rendering (1)

Local lighting model cannot handle:blocking some of the light from the source from reaching the other spheres

scattering some light among spheres

global lighting model local lighting model


Global Rendering (2)

Global effectsshadows

refractions

inter-object reflections

Methodsray tracing

radiosity


Shadows

Shadow == light sources are blockedcasting ray towards each light source Li

Si = 0 if ray is blocked, Si = 1 otherwise

( ) ( )∑ ⋅+⋅++=L LL

nSDAAE ISKLNKIKII )RV(

ShadowTerm


Ray Casting

Tracing primary rays from cameradirect illumination from unblocked lights only

( ) ( )∑ ⋅+⋅++=L LL

nSDAAE ISKLNKIKII )RV(


Recursive Ray Tracing

Also tracing secondary rays from hit surfacesglobal illumination from mirror reflectionmirror reflection and transparencytransparency

( ) ( ) TTRSL LLn

SDAAE IKIKISKLNKIKII ++⋅+⋅++= ∑ )RV(


Mirror Reflection

Tracing secondary ray in direction of mirror reflection

( ) ( ) TTRSL LLn


radiancefor mirror

reflection ray


Transparency (1)

Trace secondary ray in direction of refraction

( ) ( ) TTRSL LLn


radiance forrefraction ray


Transparency (2)

Transparency coefficient is fraction transmittedKT = 1 if object is translucent

KT = 0 if object is opaque

0 < KT < 1 if object is semi-translucent

( ) ( ) TTRSL LLn


TransparencyCoefficient


Refractive Transparency (1)

For thin surfacesignoring change in direction

assuming light travels straight through surface

LT −≅


Refractive Transparency (2)

For solid objectsapplying Snell’s law:

ηr sin Θr = ηi sin Θi

Lη

ηN)coscos

η

η(T

r

iri

r

i −Θ−Θ=


Ray Tracing (1)

Extension of ray castinglooking for the visible surface for each pixel

continuing to bounce the ray around the scene

( ) ( ) TTRSL LLn



Ray Tracing (2)

Global effectsshadows

refractions

inter-object reflections

Highly realistic vs. computation time

( ) ( ) TTRSL LLn


Transparency

Reflectance

Shadow


Basic Ray Tracing Algorithm

For each pixelprimary ray

testing each surface if it is intersected

Intersected secondary rayreflection ray

transparent – refraction ray


Basic Ray Tracing Algorithm

For each pixelprimary ray

testing each surface if it is intersected

Intersected secondary rayreflection ray

transparent – refraction ray


Ray Tracing Tree (1)

Representing illumination computationone branch reflection

the other branch transmission

terminated reaching the preset maximum or striking a light source

Scene Ray Tree


Ray Tracing Tree (2)

Pixel intensity sum of intensities at root node

starting at terminal node

If no surfaces are intersected, the intensity of background

Scene Ray Tree

Iback

Iback Iback

Ipixel


Radiosity (1)

Goalsimulating diffuse inter-object reflections and shadows


Radiosity (2)

Basic ideatreating every polygon as light source


Radiosity (3)

Advantagesphysical modeling of shadows and indirect diffuse illumination

independent of any viewpoint

Equation

∑+= ijjiii FBρEB

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


Form Factors

Definitionfraction of energy leaving patch jthat arrives at patch i

Computationprojecting onto unit hemisphere

projecting onto unit circle base

dividing by area of circle

projecting scene onto hemi-cube

projecting ontounit hemisphere

projecting ontoHemi-cube


Matrix Solution Methods

Matrix formulation

Progressive refinementiterating shoot radiosity from patches

O(n2) computation – getting 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


Matrix Solution Methods

24 iterations

1 iteration

100 iterations

2 iterations


Summary

Polygonal renderingflat

Gouraud

Phong

Global renderingray Tracing

radiosity

less expensive

more accurate


Visible-Line Determination


Visible-Surface Determination with Ambient Illumination Only


Flat Shaded Polygons with Diffuse Reflection


Gouraud Shaded Polygons with Diffuse Reflection


Gouraud Shaded Polygons with Specular Reflection


Phong Shaded Polygons with Specular Reflection


Phong Shading of Curved Surfaces with Specular Reflection


Improved Illumination Model and Multiple Lights


Texture Mapping

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Surface Rendering Methods - Hallym