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CSC 830 Computer CSC 830 Computer GraphicsGraphicsLecture 5Lecture 5ShadingShading

CSC 830 Computer CSC 830 Computer GraphicsGraphicsLecture 5Lecture 5ShadingShading

Course Note Credit: Some of slides are extracted from the course notes of prof. Mathieu Desburn (USC) and prof. Han-Wei Shen (Ohio State University).

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ShadingDetermining the light traveling from a point in the scene to the viewer’s eye

Images courtesy of Watt, Watt & Watt, and Foley & van Dam

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ShadingLight comes from many sources:

absorbedscattered

dtransmitte

reflectedemittedlight

scattering

absorption

reflection

transmissionemission

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Local versus Global Illumination

Global Illumination Considers

indirect illumination

Reflection Refraction Shadows

Local Illumination Only considers direct

illumination No reflection No refraction Shadows possible

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Local versus Global Illumination

2P1P

Indirect Illumination

Direct Illumination

We will do local only for this lecture…

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Local illumination• Only consider the light, the observer position,

and the object material properties

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Local versus Global Illumination

Images courtesy of Francois Sillion

To understand shading properly, we need to review some basic notions of physics…

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Basic Illumination Model• Simple and fast method for calculating surface

intensity at a given point• Lighting calculation are based on:

– The background lighting conditions– The light source specification: color, position– Optical properties of surfaces:

• Glossy OR matte• Opaque OR transparent (control refection and

absorption)

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RadianceRadiance: Power per unit projected area

perpendicular to the ray, per unit solid angle in the direction of the ray

d

dA

N),( xI

Think of it as a flux of photons leaving the surface…

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IrradianceIrradiance: Radiant energy per unit area

dxIdEE cos),(

),( xI

Think of it as a flux of photons bombarding the surface…

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BRDFBidirectional Reflection Distribution Function

Determines the fraction of light from an incoming direction reflected to an outgoing direction

),(

),(),,(

i

rri xdE

xIxf

Image courtesy of Watt, 3D Computer Graphics

Relates reflected radiance to incoming irradiance…

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Properties of the BRDFReciprocity

),,(),,( irri xfxf In photography and holography, reciprocity refers to the relationship between the intensity of the light and duration of the exposure that result in identical exposure. Within the normal range for intensity and time for the film, the reciprocity law states that exposure = intensity × time. Outside the normal range the reciprocity law breaks down, which is known as reciprocity failure.

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Properties of the BRDFAnisotropy

),,,,(),,,,( rriirrii xfxf

Anisotropy (the opposite of isotropy) is the property of being directionally dependent.In the field of computer graphics, an anisotropic surface will change in appearance as it is rotated about its geometric normal, as is the case with velvet. Anisotropic scaling occurs when something is scaled by different amounts in different directions.

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Reflectance EquationBRDF allows us to calculate outgoing light, given incoming light

),(),,(),( irirfrom xdExfxIi

Image courtesy of Watt, 3D Computer Graphics

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Splitting the BRDFIn practice, BRDF can be really funky…To simplify, we divide the BRDF into 3 components:

specularidealdiffuseldirectionadiffuseideal ffff

NL NL

MNL

M

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Reflectance• 3 forms

Slide Courtesy of Dutre et. al on SIGGRAPH 2001

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Ideal Specular Reflection

Reflection is only in the mirror direction

NL

M

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Ideal Diffuse ReflectionReflection is equal in all directions

diffuserixf ),,(NL

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Directional Diffuse Reflection

Reflection is concentrated around the mirror direction

NL

M

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Ambient LightIf a surface is visible from the eye, but not a light, it will be rendered black (if indirect light is not considered).

Ambient light is an approximation to indirect light

Difficult to compute Approximate this as a constant Or a light source at the eye

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Phong Reflection

speculardiffuseambient IIII

Assume point lights and direct illumination only

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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 (thus, Lambertian surfaces)

• The brightness of the surface is indepenent of the observer position (since the light is reflected in all direction equally)

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Lambert’s Law• How much light the surface receives from a

light source depends on the angle between its angle and the vector from the surface point to the light (light vector)

• Lambert’s law: the radiant energy ’Id’ from a small surface da for a given light source is:

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

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Phong Diffuse Component

)(

cos

LNkI

kII

dl

dldiffuse

Diffuse component depends only on incident angle.

Image courtesy of Watt, 3D Computer Graphics

Note: L and N are unit…

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Examples

Sphere diffusely lighted from various angles !

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Specular Light

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

Light reflected from the surface unequally to all directions.

The result of near total reflection of the incident light in a concentrated region around the specular reflection angle

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Specular Highlights

• Shiny surfaces change appearance when viewpoint is changed• Specularities are caused by microscopically smooth surfaces.• A mirror is a perfect specular reflector

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Phong Specular Component

nsl

nslspecular

VRkI

kII

)(

cos

Phong combines directional diffuse & ideal specular

Image courtesy of Watt, 3D Computer Graphics

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Half Vector• An alternative way of computing phong

lighting is: Is = ks * Is * (N*H)n • H (halfway vector): halfway between V and L:

(V+L)/2• Fuzzier highlight• Check

http://www.lighthouse3d.com/opengl/glsl/index.php?ogldir2 L

N H

V

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Phong Illumination

Moving Light

Change n

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Phong Ambient Component

aaambient kII

Treat it as a constant:

Where is the ambient light in the scene.aI

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Adding Color

bsbl

gsgl

rsrln

bdbl

gdgl

rdrl

baba

gaga

rara

b

g

r

kI

kI

kI

HN

kI

kI

kI

LN

kI

kI

kI

I

I

I

,,

,,

,,

,,

,,

,,

,,

,,

,,

)()(

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Adding Lights

lightsll

nsdaa

lightslbsbl

gsgl

rsrln

bdbl

gdgl

rdrl

babal

gaga

rara

b

g

r

IHNkLNkIkI

kI

kI

kI

HN

kI

kI

kI

LN

kI

kI

kI

I

I

I

)()(

)()(

,,

,,

,,

,,

,,

,,

,,

,,

,,

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Phong Reflection

Image courtesy of Watt, 3D Computer Graphics

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Aluminium

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Bronze

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Chrome

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Stainless Steel

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OpenGL Materials

GLfloat white8[] = {.8, .8, .8, 1.}, white2 = {.2,.2,.2,1.},black={0.,0.,0.}; GLfloat mat_shininess[] = {50.}; /* Phong exponent */ glMaterialfv( GL_FRONT_AND_BACK, GL_AMBIENT, black);

glMaterialfv( GL_FRONT_AND_BACK, GL_DIFFUSE, white8);

glMaterialfv( GL_FRONT_AND_BACK, GL_SPECULAR, white2);

glMaterialfv( GL_FRONT_AND_BACK, GL_SHININESS, mat_shininess);

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OpenGL Lighting

GLfloat white[] = {1., 1., 1., 1.}; GLfloat light0_position[] = {1., 1., 5., 0.}; /* directional light (w=0) */

glLightfv(GL_LIGHT0, GL_POSITION, light0_position); glLightfv(GL_LIGHT0, GL_DIFFUSE, white); glLightfv(GL_LIGHT0, GL_SPECULAR, white); glEnable(GL_LIGHT0);

glEnable(GL_NORMALIZE); /* normalize normal vectors */ glLightModeli(GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE);/* two-sided lighting*/

glEnable(GL_LIGHTING);

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Vertex Normals vs. Face Normals

What are the normals to the surface?

Each polygonal face has a normal.

We call these face normals.

a

c

b

N = (b - a) x (c - b)

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Flat ShadingAssume a constant color across the polygon

Uses face normalsEquivalent to single point sampling…

a

c

b

Polygon mesh is only an approximation.Can we do better?

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Vertex Normals vs. Face Normals

Should use the actual surface’s normals

Usually stored at the vertices of the objectCan calculate as averages of face normals

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Mach Band ?

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Mach Band ?

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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

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Interpolation

Gouraud Interpolation Phong Interpolation

Given vertex normals, how to color the interior:

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Un-lit

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Flat Shading

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Gouraud Interpolation – Interpolated Shading

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Phong Interpolation – Per pixel Shading

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Gouraud InterpolationCalculate the color at each vertex

Interpolate the colors

C(a)

C(c)

C(b)

C(a)

C(c)

C(b)

C = t C(b) + (1 – t) C(c)

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Gouraud Interpolation Problems

Misses some highlights

light

Shading is not linear

shading will be constant!

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Phong InterpolationInterpolate the normals, then compute the colors

light

Interpolation is usually done component-wise

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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.

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Interpolation

Image courtesy of Watt & Watt, Advanced Animation and Rendering Techniques

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Interpolated Shading - Problems

Problems at shared vertices – shared by right polygons and not by one on left and hence discontinuity

Incorrect Vertex normals – no variation in shade

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Shade Trees

dot

N L

dot

N H

*

Il

*

Il pow

n

+

Phong Shade Tree:

Ia

*

ka

kd

ks

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Shading LanguageA language for implementing shading models

State is passed to/from the shader by global variablesCi – Outgoing ray colorOi – Outgoing ray opacity

Cs – Surface colorOs – Surface opacityP – Surface pointN - Surface normalI - Direction of viewing (eye ray)L - Direction to the light source

I N

L

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Shading Languagesurfaceplastic(float Ks = .5, float Kd = .5, float Ka = 1,

float roughness = .1, color specularColor = 1){ point Nf = faceforward(N,I);

Oi = Os; Ci = Os*(Cs*(Ka*ambient()+Kd*diffuse(Nf)

+ specularColor*Ks*specular(Nf,-I,roughness);}

Phong Surface Shader:

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Light Sources• Point light source• Directional light source: e.g. sun

light• Spot light

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Spot Light

• To restrict a light’s effects to a limited area of the scene• Flap: confine the effects of the light to a designed range in

x, y, and z world coordinate• Cone: restrict the effects of the light using a cone with a

generating angle

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Light Source Attenuation

• Takes into account the distance of the light from the surface

I’L = I L * fatt (d)

I’L: the received light after attenuation

I L: the original light strengthfatt: the attenuation factord: the distance between the light source

and the surface point

• fatt = max ( 1/(c1 + c2*d + c3*d2) , 1) • C1, C2, C3 are user defined constants

associated with each light source

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Hints for HW4• Shading can be done in easily in view space or in

world space where all light, view, & surface normal vectors are described in same coordinate space. – how can you achieve this effect?

• For normal transformation, use only 3x3 rotation matrix out of the 4x4 transformation & inverse transpose of it – remember normal transformation from the lecture 2?

• For Phong shading, interpolate normal & compute shading for each pixel. For Gouraud shading, compute shading at only vertex and interpolate the color.