Illumination and Shading

Mengxia Zhu

Fall 2007

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Why?

What light source is used and how the object response to the light makes difference

Lighting gives you a 3D view to an object A unlit sphere looks no different from a 2D disk

To get realistic pictures, the color computation of pixels must include lighting calculations

Local and Global Illumination

Local illumination: a surface point receives light directly from all light sources in the scene. Consider in isolation

Global illumination: a point receives light after light rays interact with other objects in the scene. Shadow Refract through transparent object Reflection and transmission rays

Illumination Vs. Shading

Illumination (lighting) model: To model the

interaction of light with surfaces to determine

the final color & brightness of the surface

Shading model: applies the illumination

models at a set of points and colors the whole

image.

Local illumination Only consider the light,

the observer position, and the object material properties

L V

Types of Light Ambient

Light that’s been scattered so much by the environment that its direction is impossible to determine - it seems to come from all directions

Diffuse Light that comes from one direction, but it gets

scattered equally in all directions

Specular Light comes from a particular direction, and its

tends to bounce off the surface in a preferred direction

OpenGL Lighting Model OpenGL approximates lighting as if light can be

broken into red, green, and blue components

The RGB values for lights mean different than for materials For light, the numbers correspond to a percentage of

full intensity for each color For materials, the numbers correspond to the

reflected proportions of those colors

Ambient light (background light) The light that is the result from the light reflecting off

other surfaces in the environment A general level of brightness for a scene that is

independent of the light positions or surface directions Has no direction Each light source has an ambient light contribution, Ia For a given surface, we can specify how much ambient

light the surface can reflect using an ambient reflection coefficient : Ka (0 < Ka < 1)

Ambient Light Ambient, omni-directional light So the amount of light that the surface reflect is

therefore Ka ambient coefficient

Iamb =a aI k

Diffuse Light The illumination that a surface receives from a

light source and reflects equally in all directions This type of reflection is called Lambertian

reflection The brightness of the surface is independent of

the observer position (since the light is reflected in all direction equally)

L

Lambert’s Law Lambert’s law: the radiant energy for a given light source

is: Id * cos)

Id : the intensity of the light source is the angle between the surface normal (N) and light vector (L)

If N and L are normalized, cos) =

Surface’s material property: assuming that the surface can reflect Kd (0<Kd<1), diffuse reflection coefficient) amount of diffuse light.

( )d dI k N L N L

The Diffuse Component

Brightness is inversely proportional to the area of the object illuminated (dot product of light vector and surface normal) greatest when N and L are parallel smallest when N and L are orthogonal In calculations, max {N.L, 0} is used to avoid negative values

The total diffuse reflection = ambient + diffuse

(max{ ,0})diff a a d dI I k I k N L

Specular Light

These are the bright spots on objects (such as polished metal, apple ...)

Light reflected from the surface unequally to all directions.

Phong’s Model for SpecularBrightness depends on the angle between

reflection vector (R) and viewer vector (V), i.e, on direction of viewer

Summing the Components

Ambient + Diffuse + Specular = final

Phong Illumination Curves Specular exponents are much larger than 1, and

Values of 100 are not uncommon. The specular reflection exponent n is 1 for a slightly glossy

surface and infinity for a perfect mirror.

n : glossiness, rate of falloff

Changing Specular exponent n

Reflected Ray

LN

R

V

L N(N•L)

Project L onto N

L

2N(N•L)

Double length of vector

LR = 2N(N•L) - L

Subtract L

How to calculate R? R + L = 2(N*L) N

R = 2(N*L) N - L

Half Vector

An alternative way of computing phong lighting is:

H (halfway vector): halfway between V and L: (V+L)

LN

H

V

( )ns sI k N H

Putting It All Together

Single Light:

1 (max{ ,0})

(max{ ,0})

L a a d d

ns s

I I k I k N L

I k R V

Attenuation

Attenuation factor Light attenuates with distance from the source where d = distance between the light and object kc = constant attenuation

A light source does not give an infinite amount of light

kl = linear term kq = quadratic term

Models the theoretical attenuation from a point source

The intensity becomes

f 1

kc kld kqd2

[ (max{ ,0}) (max{ ,0}) ]nL a a d d s sI f I M I M N L I M R V

Spotlight Effect When the vertex lies inside the cone of

illumination produced by spotlight, its contribution to the light intensity is

IL fs[Ia Ma Id Md (max{N

L ,0}) IsMs(max{

R

V ,0})n ]

s (max{D

L ,0})m

Where D gives the spotlight’s direction. The intensity is maximum in the center of cone and is attenuated toward the edge of the cones is 1 if the source is not spotlightm is exponent determining the concentration of the light

The intensity of light source is

Putting All Together

1

1

[ (max{ ,0})

(max{ ,0}) ]

ni i a a d d

ni s s i

f s I k I k N L

I k R V

Multiple lighting calculation in RGB mode gives

Vertex color

Adding Lighting to the Scene

Define normal vectors for each vertex of each object

Create, select, and position one or more light sources

Create and select a lighting model Define material properties for the

objects in the scene

Creating Light Sources Properties of light sources are color, position, and direction

void glLight{if}(GLenum light, GLenum pname, TYPE param); void glLight{if}v(GLenum light, GLenum pname, TYPE

*param); Creates the light specified by light that can be GL_LIGHT0,

GL_LIGHT1, … or GL_LIGHT7 Pname specifies the characteristics of the light being set Param indicates the values to which the pname characteristic

is set

glEnable(GL_LIGHT0);

Color for a Light Source

GLfloat light_ambient[] = {0.0,0.0,0.0,1.0}; GLfloat light_diffuse[] = {1.0,1.0,1.0,1.0}; GLfloat light_specular[] = {1.0,1.0,1.0,1.0};

glLightfv(GL_LIGHT0, GL_AMBIENT, light_ambient); glLightfv(GL_LIGHT0, GL_DIFFUSE, light_diffuse); glLightfv(GL_LIGHT0, GL_SPECULAR,

light_specular);

Position of Light Source Positional light source

(x, y, z) values specify the location of the light GLfloat light_position[] = {x, y, z, w}; glLightfv(GL_LIGHT0, GL_POSITION, light_position);

Directional light source (x, y, z) values specify the direction of the light

located at the infinity No attenuation

GLfloat light_position[] = {x, y, z, 0}; glLightfv(GL_LIGHT0, GL_POSITION, light_position);

Attenuation Attenuation factor for a positional light

Needs to specify three coefficients glLightf(GL_LIGHT0, GL_CONSTANT_ATTENUATION,

2.0); glLightf(GL_LIGHT0, GL_LINEAR_ATTENUATION,

1.0); glLightf(GL_LIGHT0,

GL_QUADRATIC_ATTENUATION, 1.0);

Ambient, diffuse, and specular contributions are all attenuated

Spotlights The shape of the light emitted is restricted to a cone

glLightf(GL_LIGHT0, GL_SPOT_CUTOFF, 45.0); The cutoff parameter is set to 45 degrees

GLfloat spot_direction[] = {-1.0, -1.0, 0.0]; glLightfv(GL_LIGHT0,

GL_SPOT_DIRECTION, spot_direction); specifies the spotlight’s direction which

determines the axis of the cone of light glLightf(GL_LIGHT0, GL_SPOT_EXPONENT,

2.0); Controls how concentrated the light is

Multiple Lights You can define up to eight light sources

Need to specify all the parameters defining the position and characteristics of the light

OpenGL performs calculations to determine how much light each vertex gets from each source

Increasing number of lights affects performance

Defining Material Properties Specifying the ambient, diffuse, and specular colors, the

shininess, and the color of any emitted light void glMaterial{if}(GLenum face, GLenum pname,

TYPE param); void glMaterial{if}v(GLenum face, GLenum

pname, TYPE *param); Specifies a current material property for use in

lighting calculations Face can be GL_FRONT, GL_BACK, or

GL_FRONT_AND_BACK Pname identifies the particular material property

being set Param defines the desired values for that property

Reflectance Diffuse and ambient reflection

Gives color GLfloat mat_amb_diff[] = {0.1, 0.5,0.8,1.0}; glMaterialfv(GL_FRONT_AND_BACK,

GL_AMBIENT_AND_DIFFUSE, mat_amb_diff); Specular reflection

Produces highlights GLfloat mat_specular[] = {1.0,1.0,1.0,1.0); Glfloat low_shininess[] = {5.0}; glMaterialfv(GL_FRONT, GL_SPECULAR,

mat_specular); glMaterialfv(GL_FRONT, GL_SHININESS,

low_shininess);

Shading Models for Polygons Constant Shading (flat shading)

Compute illumination at any one point on the surface. Use face or one normal from a pair of edges. Good for far away light and viewer or if facets approximate surface well.

Per-Pixel Shading

Compute illumination at every point on the surface.

Interpolated Shading

Compute illumination at vertices and interpolate color

Constant Shading

Compute illumination only at one point on the surface

Okay to use if all of the following are true The object is not a curved (smooth) surface (e.g. a

polyhedron object) The light source is very far away (so N.L does not

change much across a polygon) The eye is very far away (so V.R does not change

much across a polygon) The surface is quite small (close to pixel size)

Un-lit

Flat Shading

Mach Band ?

Polygon Mesh Shading

Shading each polygonal facet individually will not generate an illusion of smooth curved surface

Reason: polygons will have different colors along the boundary, unfortunately, human perception helps to even accentuate the discontinuity: mach band effect

Smooth Shading

Need to have per-vertex normals Gouraud Shading

Interpolate color across triangles Fast, supported by most of the graphics

accelerator cards

Phong Shading Interpolate normals across triangles More accurate, but slow. Not widely supported by

hardware

Gouraud Shading

Normals are computed at the polygon vertices If we only have per-face normals, the normal at each

vertex is the average of the normals of its adjacent faces

Intensity interpolation: linearly interpolate the pixel intensity (color) across a polygon surface

Linear Interpolation

Calculate the value of a point based on

the distances to the point’s two neighbor points If v1 and v2 are known, then

x = b/(a+b) * v1 + a/(a+b) * v2

Linear Interpolation in a Triangle

To determine the intensity (color) of point P in the triangle,

we will do: determine the intensity of 4 by

linearly interpolating between 1 and 2

determine the intensity of 5 by linearly interpolating between 2 and 3

determine the intensity of P by linear interpolating between 4 and 5

Mach Band ?

Image

Phong Shading Model Gouraud shading does not properly handle specular

highlights, specially when the n parameter is large (small highlight).

Reason: colors are interpolated.

Solution: (Phong Shading Model)

1. Compute averaged normal at vertices.

2. Interpolate normals along edges and scan-lines. (component by component)

3. Compute per-pixel illumination.

References

Slides from Karki at LSU Jian Huang at UTK