1 L Feb-22-05 SMM009, Shading Overview Theory - Shading for 3D - - PDF document

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Feb-22-05 SMM009, Shading 1 L

INSTITUTIONEN FÖR SYSTEMTEKNIK

Shading

David Carr Virtual Environments, Fundamentals Spring 2005

Based on Slides by E. Angel

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Overview

• Theory
• Shading for 3D appearance
• Light-material interactions
• The Phong model
• OSG
• OSG methods
• Gouraud Shading

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INSTITUTIONEN FÖR SYSTEMTEKNIK

Shading Theory

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Why We Need Shading

• Model of a sphere using many polygons and color it

with a single color:

• We get something like
• But we want

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Shading

• Why does the image of a real sphere look like
• Light-material interactions cause each point to have a different

color or shade

• Need to consider
• Light sources
• Material properties
• Location of viewer
• Surface orientation

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Scattering

• Light strikes A
• Some scattered
• Some absorbed
• Some of scattered light strikes B
• Some scattered
• Some absorbed
• Some of this scattered

light strikes A and so on

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Rendering Equation

• The infinite scattering and absorption of light can be

described by the rendering equation

• Cannot be solved in general
• Ray tracing is a special case for perfectly reflecting surfaces
• Rendering equation is global and includes
• Shadows
• Multiple scattering from object to object

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Global Effects

translucent surface shadow multiple reflection

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Local versus Global Rendering

• Correct shading requires:
• Global calculation involving all objects and light sources
• Incompatible with pipeline model which shades each polygon

independently (local rendering)

• However, in computer graphics, especially real time

graphics, we are happy if things “look right”

• Many techniques for approximating global effects

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Light-Material Interaction

• Light that strikes an object is:
• Partially absorbed and
• Partially scattered (reflected)
• The amount reflected determines the color and brightness
• f the object
• A surface appears red under white light because the red

component of the light is reflected and the rest is absorbed

• The reflected light is scattered in a manner that depends
• n the smoothness and orientation of the surface

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Light Sources

• General light sources are difficult to work with because

we must integrate light coming from all points on the source

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Simple Light Sources

• Point source
• Model with position and color
• Distant source = infinite distance away (parallel)
• Spotlight
• Restrict light from ideal point source
• Ambient light
• Same amount of light everywhere in scene
• Can model contribution of many sources and reflecting

surfaces

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Surface Types

• The smoother a surface, the more reflected light is concentrated

in the direction a perfect mirror would reflected the light

• A very rough surface scatters light in all directions

smooth surface rough surface

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Phong Model

• A simple model that can be computed rapidly
• Has three components
• Diffuse
• Specular
• Ambient
• Uses four vectors
• To source
• To viewer
• Normal
• Perfect reflector

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r = 2 (l · n ) n - l

Ideal Reflector

• Normal is determined by local orientation
• Angle of incidence = angle of reflection
• The three vectors must be coplanar

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Solving for the Reflection Vector

• Note, let l, n, r be unit vectors
• The angle of incidence = the angle of reflection
• The reflection is co-planer with the normal and the vector to the light source.
• Two equations and 2 unknowns
• From the 1st, θi = θr, so cosθi = cosθr,

thus, l · n = r · n

• From the 2nd, r is a linear combination of n, l

thus, r = αl + βn

• Take the above and dot with n, solve for β

r · n = αl · n + β l · n = αl · n + β β = (α-1)(l · n )

• But, r is of unit length, so 1 = r· r = α2 + 2αβl· n + β2
• Solving gives r = 2(l· n)n - l

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Normal for Triangle

p0

p1

p2 n plane n ·(p - p0 ) = 0 n = (p2 - p0 ) ×(p1 - p0 ) normalize n ← n/ |n| p Note that right-hand rule determines outward face

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Lambertian Surface

• Perfectly diffuse reflector
• Light scattered equally in all directions
• Amount of light reflected is proportional to the vertical

component of incoming light

• reflected light ~cos θi
• cos θi = l · n if vectors normalized
• There are also three coefficients, kr, kb, kg that show how

much of each color component is reflected

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Specular Surfaces

• Most surfaces are neither ideal diffusers nor perfectly specular

(ideal reflectors)

• Smooth surfaces show specular highlights due to incoming light

being reflected in directions concentrated close to the direction

• f a perfect reflection

Specular highlight

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Modeling Specular Reflections

• Phong proposed using a term that dropped off as the

angle between the viewer and the ideal reflection increased

φ Ir ~ ks I cosαφ shininess coefficient absorption coefficient incoming intensity reflected intensity

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The Shininess Coefficient

• Values of α between 100 and 200 correspond to metals
• Values between 5 and 10 give surface that look like plastic

cosαφ φ 90

• 90

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Ambient Light

• Ambient light is the result of multiple interactions

between (large) light sources and the objects in the environment

• Amount and color depend on both the color of the

light(s) and the material properties of the object

• Add ka Ia to diffuse and specular terms

reflection coefficient intensity of ambient light

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Distance Terms

• The light from a point source that reaches a surface is

inversely proportional to the square of the distance between them

• We can add a factor of the

form 1/(a + bd +cd2) to the diffuse and specular terms

• The constant and linear terms soften

the effect of the point source

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Light Sources

• In the Phong Model, we add the results from each light

source

• Each light source has separate diffuse, specular, and

ambient terms to allow for maximum flexibility even though this form does not have a physical justification

• Separate red, green and blue components
• Hence, 9 coefficients for each point source
• Idr, Idg, Idb, Isr, Isg, Isb, Iar, Iag, Iab

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Material Properties

• Material properties match light source properties
• Nine absorption coefficients

+kdr, kdg, kdb, ksr, ksg, ksb, kar, kag, kab

• Shininess coefficient α

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Adding up the Components

• For each light source and each color component, the

Phong model can be written (without the distance terms) as I =kd Id l · n + ks Is (v · r )α + ka Ia

• For each color component

we add contributions from all sources

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Example

• Only differences in

these teapots are the parameters in the Phong model

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INSTITUTIONEN FÖR SYSTEMTEKNIK

Shading in OSG

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Steps in OSG Shading

• Specify material properties
• setDiffuse,setSpecular, setAmbient

+ Take a 4D vector, RGBα + For RGB 1.0=100% reflectivity, 0.0=0% + For α, 1.0=opaque, 0.0=transparent

• setShininess, bigger gives smaller specular highlights
• Specify normal vectors
• Default for OSG primitive objects
• In OSG the normal vector is part of the drawable
• Usually bound per vertex

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Steps in OSG Shading

• Specify lights, point sources
• setLightNum, different for each source, limited but at least 8
• setPosition, 4D vector,

w=1 for finite distance, 0 for infinite

• setDirection, 3D vector pointing in light’s direction
• setDiffuse, setSpecular, setAmbient

+ 4D vectors RBGα, α is used for blending

• Construct StateSet for
• Materials, attached to objects (drawables, Geodes)
• Root, gets the lights
• Stick the lights in a LightSource and enable

LightSource.setStateSetModes();

• See LightDemo.java

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Video with Commentary

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Notes on Lights

• Spotlights
• Model cone
• Variable intensity
• Proportional to cosaf
• Global Ambient Light
• Ambient light depends on color of light sources
• A red light in a white room will cause a red ambient term that

disappears when the light is turned off

θ −θ

φ

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Moving Light Sources

• Light sources are geometric objects whose positions or

directions are affected by their position in the scene graph

• Depending on where we place them, we can
• Move the light source(s) with the object(s)
• Fix the object(s) and move the light source(s)
• Fix the light source(s) and move the object(s)
• Move the light source(s) and object(s) independently

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Front and Back Faces

• The default is shade only front faces which works correct for

convex objects

• If we set two sided lighting, OSG will shaded both sides of a

surface

• Each side can have its own properties which are set by using

MATERIALFace.FRONT_AND_BACK, MATERIALFace.FRONT, MATERIALFaceBACK when setting the material

back faces not visible back faces visible

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Notes on Materials

• Emissive Term
• We can simulate a light source in OSG by giving a material

an emissive component

• This color is unaffected by any sources or transformations
• Transparency
• Material properties are specified as RGBα values
• The α value can be used to make the surface translucent
• The default is that all surfaces are opaque regardless of α
• Later we will enable blending and use this feature

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INSTITUTIONEN FÖR SYSTEMTEKNIK

Other Aspects of Shading

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Polygonal Shading

• Shading calculations are done for each vertex
• Vertex colors become vertex shades
• By default, vertex colors are interpolated across the

polygon

• gl.glShadeModel(GL.GL_SMOOTH);
• If we use gl.glShadeModel(GL.GL_FLAT); the

color at the first vertex will determine the color of the whole polygon

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INSTITUTIONEN FÖR SYSTEMTEKNIK

Gouraud Shading

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Polygon Normal Vectors

• Polygons have a single normal
• Shades at the vertices as computed by the Phong model can

be almost same

• Identical for a distant viewer (default)
• r if there is no specular component
• Consider model of sphere
• Want different normal vectors at

each vertex even though this concept is not quite correct mathematically

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Smooth Shading

• We can set a new normal at

each vertex

• Easy for sphere model
• If centered at origin n = p
• Now smooth shading works
• Note silhouette edge

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Mesh Shading

• The previous example is not general because we knew

the normal at each vertex analytically

• For polygonal models, Gouraud proposed we use the

average of normal vectors around a mesh vertex

| n | | n | | n | | n | n n n n n

4 3 2 1 4 3 2 1

+ + + + + + =

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Gouraud and Phong Shading

• Gouraud Shading
• Find average normal at each vertex (vertex normal vectors)
• Apply Phong model at each vertex
• Interpolate vertex shades across each polygon
• Phong shading
• Find vertex normal vectors
• Interpolate vertex normal vectors across edges
• Find shades along edges
• Interpolate edge shades across polygons

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Comparison

• If the polygon mesh approximates surfaces with a high

curvatures, Phong shading may look smooth while Gouraud shading may show edges

• Phong shading requires much more work than

Gouraud shading

• Usually not available in real time systems
• Both need data structures to represent meshes so we

can obtain vertex normal vectors

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Questions?