Fundamentals of Computer GraphicsPart 6

Shading

prof.ing.Václav Skala, CSc.University of West Bohemia

Plzeň, Czech Republic

©2002Prepared with Angel,E.: Interactive Computer

Graphics – A Top Down Approach with OpenGL, Addison Wesley, 2001

Fundamentals of Computer Graphics 2

Shading – Light and Matter Our perception depends on:

– light directly – intensity, spectrum (color), position

– material of objects that “reflects” or “transmit” light, roughness, color of the surface

Speed of computation – significant factor

Fundamentals of Computer Graphics 3

Shading – Light and Matter Generally we do not need to

compute all, but just those rays that contribute to the final image

Methods:

• Global – ray tracing, radiosity – very slow

• Local – constant, Gouraud, Phong etc. – relatively fast

Fundamentals of Computer Graphics 4

Shading – Light and Matter Interaction between

light and materialscan be classified as

• specular surfaces –ideal mirror

• diffuse surfaces – reflected light is ideally reflected to all directions uniformly

• translucent surfaces – allow some lights to penetrate the surface – refraction – glass, watter

• optical properties – Snell’s law

Fundamentals of Computer Graphics 5

Shading – Light sources Light source – an object with a surfaceEach point (x,y,z) on the surface can emit

light with characterization:• direction of emission (,)• intensity of energy emitted at each

wavelength illumination function I(x,y,z,,,)

Basic light sources (sufficient for rendering the most simple scenes):

• ambient lighting • point sources • spotlights• distance light

Fundamentals of Computer Graphics 6

Shading – Light sources Light - an object with a surface

Each point (x,y,z) on the surface can emit light with characterization:

• direction of emission (,)

• intensity of energy emitted at each wavelength

illumination function I(x,y,z,,,)

Usually I = [ Ir , Ig , Ib ]T

is handled as a scalar value

Basic light sources - sufficient for rendering the most simple scenes:

• ambient lighting • point sources • spotlights• distance light

Fundamentals of Computer Graphics 7

Shading – Light sources Ambient light Ia- uniform light in

the space (room etc.)

Ideal point source – emits equally in all directions I(p0)

Light received at a point p

full shadow – umbrapartial shadow – penumbra

for non-point sources (d is distance)

020

01

, pIpp

ppI

12 bdbda

Fundamentals of Computer Graphics 8

Shading – Light sources Spotlights – very narrow angles of

emission, if = 180° -> point source

distribution of light within the cone – usually cose() ; e determines how rapidly intensity drops off

cos() = sT ls – vector that points

from ps to a point s on a surface

l – vector of the light direction

Fundamentals of Computer Graphics 9

Shading – Distant light sources we replace location of light sources

with their directions

p0 = [ x , y , z , 0 ]T ( 0 is correct !)

Phong Reflection Model

I = Ia + Id + Is

disadvantages

• linear model

• superposition

Fundamentals of Computer Graphics 10

Ambient, Diffuse, Specular Reflections Ambient reflection

0 ka 1

Ia = ka La global ambient term or light

Diffuse reflection

• characterized by rough surfaces

• perfectly diffuse surfaces – Lambertian surfaces

Fundamentals of Computer Graphics 11

Ambient, Diffuse, Specular Reflections Lambert’s law:

diffuse reflection 0 kd 1

if the influence of the distance is considered

dT

dd LnlkI )(

dTd

d Lnlcdbda

kI )(2

Fundamentals of Computer Graphics 12

Ambient, Diffuse, Specular Reflections Specular Reflection: 0 ks 1

as ideal specular reflection

<100 , 500> metallic surfaces

cossss LkI

Fundamentals of Computer Graphics 13

Polygonal Shading How to display surfaces with shading?

Flat (constant) shading

glShadeModel(GL_FLAT);

Mach bands

Fundamentals of Computer Graphics 14

Polygonal Shading Interpolative and Gouraud shading

Gouraud shading

glShadeModel(GL_SMOOTH);

normal in a vertex

• average normal vector

• intensity computation for a vertex

• intensity & color interpolation for a scan-line

Fundamentals of Computer Graphics 15

Polygonal Shading Phong shading

normal in a vertex

• interpolation of a normal

• normal interpolation along the scan-line

• intensity computation

Phong shading is almost always done off-line

Fundamentals of Computer Graphics 16

Light Sources in OpenGL

Study 6.6 – 6.9 on your own

Fundamentals of Computer Graphics 17

Global Rendering – Ray tracing

global versus local lightings models

Fundamentals of Computer Graphics 18

Global Rendering – Ray tracing

Algorithm complexity:O(M2 N 2k)

M – resolution of a screenN – number of objectsk – number of levels of the tree

Typical program:POV Ray – available free