COMP371 COMPUTER GRAPHICS · • Color at a point on an object is decided by the properties of the...

Copyright © COMP371 Computer Graphics Instructors

COMP371 COMPUTER GRAPHICS

LECTURE 13LIGHTING AND SHADING


Lecture Overview▪Review of last class

▪Global and Local Illumination

▪Normal Vectors

▪Light Sources

▪Phong Illumination Model

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Lighting

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Without light … we don’t see our world!


Lighting and Shading

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Without light … we don’t see our world!

Without shading, objects do not look three dimensional!

Copyright © COMP371 Computer Graphics Instructors5

Illumination• Illumination is the complete description of all the light striking a

particular point on a particular surface• Color at a point on an object is decided by the properties of the

light leaving that point• Knowing the illumination and the surface physics at a point on

a surface, we can determine the properties of the light leaving that point

• In order to generate realistic images we need to understand how light interacts with the surface of objects


Interaction of light with a Solid

scatteringand absorption

refraction

incidentlight

specularreflection

diffusereflection

totalinternalreflection


Interaction of Light• There are two illumination phenomena of importance

– interaction of light with the boundaries between materials– scattering and absorption of light as it passes through the

material• Boundaries between materials are surfaces which make up

the environment• Light striking a boundary is either reflected or transmitted.

For opaque materials light is absorbed on passing through the boundary


Light Interaction in a Scene

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To simulate and calculate the precise physics of light interacting with a surface is extremely complex

Most graphics applications (including ray tracing!) use an approximation … a lighting model or an illumination model


Illumination models• A surface point could be illuminated by

– local illumination, light directly emitted by light sources– global illumination, light reflected from and transmitted

through its own and other surfaces• Illumination models express the factors which determine

the surface color at a given point on a surface• Illumination models compute the color at a point in terms

of both local and global illumination


Global Illumination

▪Ray tracing▪Radiosity▪Photon Mapping▪Follow light as it progresses

through the scene▪Accurate, but expensive (off-line)

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Tobias R. Metoc


Raytracing example

Martin Moeck,Siemens Lighting

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Radiosity ExampleRestaurant Interior. Guillermo Leal, Evolucion Visual

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Reflection Models• Illumination models used for graphics initially were often

approximate models• Main goal was to model the interaction of light with matter in

a way that appears realistic and is fast• Reflection Models are the simplest of illumination models• Reflection models assume

– local illumination only. No global illumination– light is only reflected from the surface. There is no

transmission through the object– there is no propagation media. Surfaces are in vacuum


Local Illumination

▪Approximate model▪Local interaction between light, surface, viewer▪Phong model (this lecture):▪fast, supported in OpenGL

▪GPU shaders

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Local Illumination cont’d

▪Color determined onlybased on surface normal,relative camera position,relative light positionand reflection properties at the surface.

▪What effects does this ignore?

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Normal Vectors

▪Must calculate and specify the normal vector▪Even in OpenGL!

▪Example: plane

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Method 1: Normal of a plane

▪Method 1: given by f(p) = ax + by + cz + d = 0▪Let p0 be a known point on the plane▪Let p be an arbitrary point on the plane▪Recall: u • v = 0 if and only if u orthogonal to v▪n • (p – p0) = 0 ▪Consequently n0 = [a b c]T▪Normalize to n = n0/|n0|

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Method 2: Normal of a plane

▪Method II: plane given by p0, p1, p2▪Points must not be collinear → cross product defined as 0▪Recall: u x v orthogonal to u and v▪n0 = (p1 – p0) x (p2 – p0)▪Order of cross product determines orientation▪Normalize to n = n0/|n0|

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Reflected Vector

▪Perfect reflection: angle of incidence equals angle of reflection▪Also: I, n, and r lie in the same plane → ▪Assume |l| = |n| = 1, guarantee |r| = 1

l.n = cosθ = n.rr = al + bn

(1)n.r = al.n + b = l.n(2)1 = r.r = a2+2abl.n+b2

Solution: a = ‐1 and b = 2(l‐n) → r = 2(l.n)n‐l

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Can write r as a linear combination of l and n


Light Sources and Material Properties

▪Appearance depends on▪Light sources, their locations and properties▪Material (surface) properties▪Viewer position

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Types of Light Sources

▪Ambient light: no identifiable source or direction▪Point source: given only by point position▪Directional light: given only by direction▪Spotlight: point source + direction▪Cut-off angle defines a cone of light▪Attenuation function (brighter in center)

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Point Source

▪Given by a point p0▪Light emitted equally in all directions▪Intensity decreases with square of distance

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Limitations of Point Sources

▪Shading and shadows inaccurate▪Example: penumbra (partial “soft” shadow)▪Similar problems with highlights▪Compensate with attenuation▪Softens lighting▪Better with ray tracing▪Better with radiosity

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q = distance |p – p0|a, b, c constants


Directional Light Source

▪Given by a direction vector▪Simplifies some calculations▪In OpenGL:▪Point source [x y z 1]T▪Directional source [x y z 0]T

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Spotlight

▪Most complex light source in OpenGL▪Light still emanates from point▪Cut-off by cone determined by angle θ

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Global Ambient Light

▪Independent of light source▪Lights entire scene▪Computationally inexpensive▪Not very interesting on its own. ▪A cheap hack to make the scene brighter.

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Phong Illumination Model

▪Calculate color for arbitrary point on surface▪Compromise between realism and efficiency▪Local computation (no inter-object visibility calculations)▪Basic inputs are material properties and l, n, v:

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l = unit vector to light sourcen = surface normalv = unit vector to viewerr = reflection of l at p(determined by l and n)


Phong Illumination Overview

1. Add contributions from each light source2. Clamp the final result to [0, 1]3. Calculate each color channel (R,G,B) separately4. Light source contributions decomposed into

▪Diffuse reflection▪Ambient reflection▪Specular reflection

(Based on ambient, diffuse, and specular lighting and material properties)

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Diffuse Reflection

▪Diffuse reflector scatters light equally to all directions▪Called Lambertian surface▪Diffuse reflection coefficient kd, 0 ≤ kd ≤ 1▪Only the angle of incoming light is important▪Models non-shiny dull matt surfaces like chalk

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Lambert’s Law

Intensity depends on angle of incoming light

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Diffuse Light Intensity Depends on Angle of Incoming Light▪Recalll = unit vector to light; n = unit surface normal; θ = angle to normal

• cos θ = l • n• Id = kd Ld (l • n)• With attenuation:

q = distance to light source,Ld = diffuse component of light

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With the diffuse reflection the part of the surface not illuminated by the light is dark.Solution (hack): Ambient lighting


Ambient Reflection

Ia = ka La▪Intensity of ambient light is uniform at every point▪Ambient reflection coefficient ka, 0 ≤ ka ≤ 1▪May be different for every surface and r,g,b▪Determines reflected fraction of ambient light▪La = ambient component of light source (can be set to different value for each light source)▪Note: Defining La, Ka in this fashion is not physically meaningful.

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Effect of ambient and diffuse reflections

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• By adding the ambient term to the diffuse reflection the illumination equation is


Specular Reflection

▪Specular reflection coefficient ks, 0 ≤ ks ≤ 1▪Shiny surfaces have high specular coefficient▪Used to model specular highlights

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Specular highlightsSpecular reflection


Specular Reflection

▪Recallv = unit vector to camerar = unit reflected vectorφ = angle between v and r

▪cos φ = v • r▪Is = ks Ls (cos φ)α▪Ls is specular component of light▪α is shininess coefficient▪Can add distance term as well

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Shininess Coefficient▪Is = ks Ls (cos φ)α▪ α is the shininess coefficient▪ maximum reflection at φ = 0▪ α controls the drop off away from R

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low α high α

incident light reflected light


Effect of adding specular reflection

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Diffuse Illumination Model Phong Illumination Model


Summary of Phong Model

▪Light components for each color:▪Ambient (La), diffuse (Ld), specular (Ls)▪Material coefficients for each color:▪Ambient (ka), diffuse (kd), specular (ks)▪Distance q for surface point from light sourcel = unit vector to lightn = surface normalr = l reflected about nv = vector to viewer

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Material Property Coeffs - Examples

©: Advanced Graphics Programming Using OpenGL by Tom McReynolds and David Blythe


BRDF

▪Bidirectional Reflection Distribution Function▪Must measure for real materials▪Isotropic vs. anisotropic▪Mathematically complex▪Programmable pixel shading

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Lighting properties of a human face werecaptured and face re-rendered;Institute for Creative Technologies


Shading• Shading is the process of determining the colors of all the

pixels covered by a surface using an illumination model• Simplest method is to

– determine surface visible at each pixel– compute normal of the surface– evaluate light intensity and color using an illumination

model• This is quite expensive. The shading methods could be

made efficient by customizing for specific surface representation


Shading Models• Shading Models give a technique to determine the colors of

all the pixels covered by a surface using appropriate illumination model

• Triangle meshes are commonly used for representing complex surfaces

• The geometric information is available only at the vertices of a triangle

• Interpolative shading models could be used to increase the efficiency substantially

Copyright © COMP371 Computer Graphics Instructors 47

Constant (Flat) Shading• It is the simplest of the shading models• Also called as faceted shading or flat shading• One polygon receives only one intensity value• Illumination model is applied only once for each polygon• Makes the following assumptions

– light source is at infinity, so is constant across a polygon face

– viewer is at infinity, so is constant across the polygon face

– polygon represents the actual surface being modeled


Gouraud Shading Model

• “Fixed Pipeline” OpenGL implements Gouraud Shading• Phong Lighting is computed per-vertex• The result is then interpolated on the whole Triangle• Specular highlights are typically blurry, a high tessellation

is required for good lighting• It can be completely implemented in a Vertex Shader

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Gouraud Shading

• I1, I2 and I3 are computed using Phong Illumination.

• Intensity Ip at a point is calculated as:

I1

I3

I2

Ia IbIp

y1

y

y2

y3

xa xbx

Might miss specular highlights, if the highlight doesn’t fall at the vertex


Gouraud Shading

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Low Poly Count High Poly Count


Phong Shading

• Is typically implemented per Fragment (pixel)• It provides “sharp” specular highlights even with low polygon count

since lighting is calculated for each pixel individually.• It is implemented on both the Vertex and Fragment Shader• The Vertex Shader Transforms the Lighting Data to View Space• The Fragment Shader calculates the Phong Shading Equation

(Ambient + Diffuse + Specular)

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Phong Model Implementation with GLSL

• Light Properties and Material Properties are implemented as Shader Uniform Variables

• Be careful from which Coordinate System the Light Positions are sent to the Shaders

• Typically, lighting is computed in View Space– Normals must be converted– Eye, Light vectors must be converted

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Phong Shading in GLSL

Vertex Shader• Transform vertex positions

to Clip Space• Transform lighting data to

View Space

Fragment Shader• Calculate and add

ambient, diffuse and specular components

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Phong Shading in GLSL• Vertex Shader• Uniforms

• Light position• Transformation Matrices

• Input– Vertex Data(pos, normal, color)

• Output– Normal (N)– Light Vector (L)– Eye Vector (V)– Vertex Color

• Fragment Shader• Uniforms

– Material Coefficients(ka, kd, ks, n)– Light Coefficients(Color, Attenuation const)

• Inputs in View Space– Normal (N)– Light Vector (L)– Eye Vector (V)

• Output– Fragment Color

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Phong Shading in GLSL Multiple Light Sources

• Use arrays for light parameters in your Shaders to support multiple light sources.

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Review

▪Global and Local Illumination▪Normal Vectors▪Light Sources▪Phong Illumination Model▪Gouraud and Phong Shading

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Next Lecture

▪ Rasterization Techniques

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Studying Support Slides


Lighting in OpenGL

Steps of specifying lighting in OpenGL• Define normal vectors for each vertex of every object.• Create, position, and enable one or more light sources.• Select a lighting model.• Define material properties for the objects in the scene.


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Lights in OpenGL

• glLightfv(Light #, Property, Array of Vals)– Light # = One of GL_LIGHTi– Property, one of

• GL_AMBIENT• GL_DIFFUSE• GL_SPECULAR• GL_POSITION = where is the light?

– Array of values = value for the property


Specifying Materials in OpenGLGeneral form: glMaterialf(face, parameter, value);

glMaterialfv(face, parameter,*array);

face is GL_FRONT, GL_BACK, GL_FRONT_AND_BACKparameter is:GL_AMBIENT four values that specify the ambient RGBA reflectance of the material. (0.2,0.2,0.2,1.0)GL_DIFFUSE four values that specify the diffuse RGBA reflectance of the material. (0.8,0.8,0.8,1.0)GL_SPECULAR four values that specify the ambient RGBA reflectance of the material. (0.0,0.0,0.0,1.0)GL_SHININESS specifies the specular reflectance exponent of the material. 0.0


Problems with Interpolated Shading

• Polygon silhouette : The silhouette edge of the mesh is always a polygon

• Solution :– finer subdivision for the

entire surface– finer subdivision only along

silhouette (view dependent)



• Perspective distortionSolution : – smaller polygons by

finer subdivision– interpolate in world space

• Orientation dependence Solution :– decomposing polygons into

triangles– rotation invariant interpolation in

object space

0 0 0 00

255 255255 255 255 255

128 128 128

A

B

C

DP

A

B

C

D

P



• Problems at shared vertices– avoid such cases

• Unrepresentative vertex normals– subdividing the polygons before calculating normals

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