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Graphics: Conceptual Model

Real Object

Real Object

Human Eye

Human Eye

DisplayDevice

Graphics System

SyntheticModel

SyntheticCamera

Real Light

SyntheticLight Source

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Lights, Surfaces, and Imaging

Proj. Plane

COP

Objects

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Lights, Surfaces, and Imaging

Proj. Plane

COP

Light Source

Objects

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Modes of Interaction ofLight with Materials

SpecularSurfaceReflection

DiffuseSurfaceReflection

TranslucentSurface

Note: Any given surface can have some of all threeproperties.

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Reflection

Rough Surface:Light is reflected equally in all directions.

Smooth Surface:Light is reflected at an anglenear to the incident angle.

Diffuse

Specular

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Illuminating Surfaces

z

x

y

I(x, y, z,,, )We can define illumination function:To obtain total light, must integrate over total surface.

I( ,,)

dAddzyxII total ),,,,,()(

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Simpler Models

Exact model can easily get nasty to use! Three simplificationswill help.

1. We can consider four simplified classes of light sources

• ambient• point• spotlight• distant

2. Human color perception allows us to consider illuminationfunction in terms of the three primary colors.

3. We can (or must) neglect:

• multiple reflections• obstruction of light path by objects

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Ambient Light

Simulates situations where light sources are designed to produceuniform lighting throughout a scene. Ambient light can be thought ofas present everywhere, coming from all directions.

Characterized by a scalar intensity, Ia , that is identical at every pointin the scene.

Ia Iar

Iag

Iab

Although every surface receives the same illumination, eachsurface can reflect the light differently.

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Point Sources

An ideal point source radiates equally in all directions. It canbe characterized by:

I(p0 ) I r (p0 )

Ig (p0 )

Ib (p0 )

Intensity of illumination from a point source is proportionalto the inverse square of the distance between the point and theilluminated surface.

I(p,p0 ) 1

p p0

2 I(p0 )

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Spotlights

Spotlights are point sources for which the angle through whichlight has been emitted has been limited.

l

s

I k cose ( ) k(ls)e

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Distant Sources

Most shading calculations require the direction from the point ona surface to the light source. As light sources are moved to larger distances, this direction approaches a constant.

Therefore the point source location will be replaced by a vectorindicating the direction of the source.

p0

x

y

z

1

will be replaced by : p0

x

y

z

0

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Reflection

Rough Surface:Light is reflected equally in all directions.

Smooth Surface:Light is reflected at an anglenear to the incident angle.

Diffuse

Specular

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Vectors Used byPhong Lighting Model

n

l r

v

p is an arbitrary point on a surface.n is the unit normal to the surface at p.l is a unit vector in the direction of the light source.r is a unit vector in the direction of a perfectly (specular) reflectionv is a unit vector in thedirection of the viewer.

p

COP

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Elements of the Phong Lighting Model

L i Lira Liga Liba

Lird Ligd Libd

Lirs Ligs Libs

R i Rira Riga Riba

Rird Rigd Ribd

Rirs Rigs Ribs

I Ia Id Is La Ra Ld Rd Ls Rs

At each point p thereis an illumination matrixfrom the ith light source:

At each point p there is a reflection matrix forthe ith light source:

Assuming the calculations will be done separately foreach primary, we can sum over light sources to get:

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Elements of the Phong Lighting ModelAmbient Reflection

Ia ka La

0 ka 1

The intensity of ambient light is the same at every pointon the surface. The percentage of light reflected is givenby: Ra ka

Note that the ambient reflection terms can be differentfor red, green and blue.

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Elements of the Phong Lighting ModelDiffuse Reflection

Intensity of illumination is dependent upon the incidence angleof light from the source:

l

n

Rd cos ln

Id kd (ln)Ld

Adding a term for attenuationwith distance from source:

Id kd

a bd cd 2(ln)Ld

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Elements of the Phong Lighting ModelSpecular Reflection

For a shiny surface, most light is reflected around vector r,corresponding to a reflected angle equal to the angle of incidence.If is the angle between v and r,

Is ks Ls cos

Adding a distance term, and expressing the cosine in terms ofa dot product:

Is 1

a bd cd 2ks Ls (r v)

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The Complete Phong Model

I 1

a bd cd 2(kd Ld (l n) ks Ls (r v) ) ka La

Distance term Ambient term

Diffuse termSpecular term

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Specification of the Normal in OpenGL

Specification of the current normal is modal and associated withvertices.

glNormal3f(nx,ny,nz);glNormal3fv(pointer_to_normal_vector);

You have to calculate the normals yourself.

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Calculation of Normals

Normal exists at every point for mathematically defined smooth surfaces.

Exists for each polygon in surface defined by flat polygons.What about the shared lines?

Polygonal Case:

p0

p1

p2

n

n (p1 p0 ) (p2 p0 )

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Shading in OpenGL:Flat Shading

OpenGL uses the current normal and calculates thecolor at the first vertex of a polygon. This color is used for the entire polygon.

Requested by: glShadeModel(GL_FLAT);

Flat shading exaggerates the visual effect of the boundaries between polygons due to the Mach band effect.

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Mach Band Effect(Mach, 1865)

Color Science, Concepts and MethodsWyszecki, Stiles

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Mach Band Effect

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Mach Band Effect

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Shading in OpenGL:Smooth Shading

Requested by: glShadeModel(GL_SMOOTH);

Lighting calculations will be done at each vertex using thematerial properties, and the vectors v and l calculated forthat vertex.

Bilinear interpolation is used to determine color values inthe interior of the polygon.

Gouraud Shading:

Normal at a vertex is the normalized average of the normals of the polygons that share that vertex.

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Gouraud Shading

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Specifying Light Sources in OpenGL

General form: glLightf(source, parameter, value);glLightfv(source, parameter, *array);

source is one of at least eight lights: GL_LIGHTi

Parameters:

GL_AMBIENT contains four values that specify the ambient RGBAintensity of the light. Default is (0.0, 0.0, 0.0, 1.0).

GL_DIFFUSE contains four values that specify the diffuse RGBAintensity of the light. Default is (1.0, 1.0, 1.0, 1.0).

GL_SPECULAR contains four values that specify the secular RGBAintensity of the light. Default is (1.0, 1.0, 1.0, 1.0).

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Specifying Light Sources in OpenGl

GL_POSITION specifies the position of the light in homogeneousobject coordinates. If the w component is zero, the lightis treated as a directional source.

GL_SPOT_DIRECTION specifies the direction of the light in homogeneous object coordinates. Default is (0.0, 0.0, -1.0)

GL_SPOT_EXPONENT spotlight exponent, default 0.0

GL_SPOT_CUTOFF spot cutoff angle in [0,90] or (default) 180.

GL_CONSTANT_ATTENUATION constant atten. factor, default 1.0

GL_LINEAR_ATTENUATION linear atten. factor, default 0.0

GL_QUADRATIC_ATTENUATION quadratic atten. factor, default 0.0

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Enabling the Lights and Lighting

Enabling a light source: glEnable(GL_LIGHTi );

Enabling lighting: glEnable (GL_LIGHTING);

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Specifying Materials in OpenGL

General form: glMaterialf(face, parameter,value);glMaterialfv(face, parameter,*array);

face is GL_FRONT, GL_BACK, GL_FRONT_AND_BACK

parameter 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

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Lighting ChecklistLighting = Lights + Materials + Model

0 Lights- Color of lights is set as desired.

=Recommended: all lights set to white for diffuse, specular, and ambient

- Lights are positioned correctly.=Remember lights are positioned with current

MODELVIEW transformation at time of calling glLightfv() + GL_POSITION.

=Remember position (point) vs. direction (vector).- Remember: Lights are objects and retain properties.- Required lights are enabled.- Lighting is enabled.

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Lighting ChecklistLighting = Lights + Materials + Model

0 Materials- Color of materials is set as desired.

=Recommended: Set ambient color to zero initially until lighting is working perfectly. Use ambient with care!

=Remember: Material properties are modal and there is only one current material. Therefore set all properties that are required and keep track of current state.

- Be sure the proper normal is set for every polygon drawn. =Make sure the normal is of unit magnitude. You can

use glEnable(GL_NORMALIZE).=Remember: Normals are modal, like materials.

- Do not use glcolor3f() with lighting. Do not use glColorMaterial() in submissions for this class.

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Lighting ChecklistLighting = Lights + Materials + Model

0 Model- glShadeModel() determines where lighting is calculated

=GL_SMOOTH calculates at each polygon vertex and interpolates (default)

=GL_FLAT calculates at first vertex and uses one color

- glLightModel() sets global properties of lighting=GL_LIGHT_MODEL_TWO_SIDE reverses normals for

back facing polygons. This is the only argument that we should ever require.

=Do not use this function unless you really understand what the effects are.