Illumination Virendra

transcript

8/3/2019 Illumination Virendra

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Illumination models are also called

lighting or shading models

Virendra Singh Kushwah 1

An illumination model is operating on a pixelbasis, while surface rendering works on asurface in its whole

To get realism (summary):

perspective projection and clipping

hidden surface removal

shading/lighting aspects

color/material aspects

An illumination model is based on optical

properties of surfaces

Typical optical effects (require one or more

light sources): reflection, (can be of different types)

refraction (if transparent objects)

shadows (can be of different types)

Various optical surface properties have to be

specified, such as:

reflectivity coefficients

degree of transparency index of refraction

For simplicity, we assume opaque (non-

transparent) surfaces

Point light source

Distributed light

A cone is illustrating the light spread from a

spotlight

Illumination is primarily of two kinds:

ambient light (background light) all points on a surface have the same intensity

with only ambient light, no realism (e.g. asphere will look like a circle slice

point source light emphasizes 3D

without ambient light, like a spotlight in a darkroom

a light source in VRP => no shadows

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The intensity (I) of reflected ambient light fora point on an object surface:

I = Ib.Rb

Ib=the intensity of the ambient light

Rb=the coefficient of reflectionof ambient light for the surface(a material constant, 0-1)

Reflected light from a point source is dividedinto:

a) diffuse reflection (especially when dullsurfaces)

* the reflected color is the color of theobject surface

b) specular reflection (especially whenshiny surfaces)

Reflection is uniform

in all directions

Intensity isproportional to cos,

the angle of

incident light

(Lambert’s cosine

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Adjust the intensity formula:

I = Ib.Rb + Id

.Rd.cos

Id=the intensity of the light sourceRd=the coefficient of diffuse reflection forthe surface

.cos can also be written Id.Rd

.(L.N),

(dot product)

The intensity of light is known to decrease

with the factor 1/r2 due to energy laws,

where r is the distance from the light source

From experience, the factor 1/r2

is modified to1/(r+k) or something similar, where k is a

constant to prevent the nominator to

approach zero

The decreasing intensity factor is called the

attenuation factor

Thus, the formula is adjusted to:

I = Ib.Rb + Id.Rd.(L.N)/(r+k)

Angle of reflection =

angle of incidence

The intensity dependson the position of

the VRP (cp. the

vector V)

Described by Phong Bui Tuong, the formula nowis:

I = Ib.Rb + Id

.Rd.(L.N)/(r+k) + Id

.Rs.cosn/(r+k),

whereRs=the coefficient of specular reflection forthe surface (not really a constant but afunction of the angle, W())

cosn (in vector form (R.V)n) determines howshiny the surface is; typically 1≤n≤10000,

means from dull (chalk) to very shiny (mirror)

The understanding of the different values of

the parameter n (or ns) in the factor cosn:

The factor cosn does not follow any physical law

but is found out to be useful from experience

Rs is always independant of the color of thereflecting surface

If multiple light sources, then by index j, the

formula is extended to:

In a color model, three versions of the

formula need to be used; one for each

primary color, i.e. one for red, one for

green and one for blue in the RGB modelFurthermore, both the intensities and the

material constants in the formula have to

be given separately for each primary color

In theory, every point on an object surface

has to be computed!

Usually, several simplifications are used:

assume light sources in an infinite distance

=> parallel light rays and L is constant for all

points the attenuation factor is eliminated

V constant, i.e. VRP at an infinite distance

same model for all three primaries

An alternative way of

defining the vectors

in the model

When polygons are used to approximate curved

surfaces (e.g. a sphere), we don’t want to

identify any discontinuities at an edge

between two adjacent polygons.

On the other hand, all surfaces are not curved,

so a simple surface rendering technique may

also be fine.

1) Flat Surface Rendering - oneintensity/polygon* the selected point is often chosensomewhere in the middle of the polygon

* fast (+)* can give intensity discontinuities (-)* OK if

- the object is a polyhedron

- light sources far away- VRP far away

2) Gouraud Surface Rendering - intensityinterpolation

* linear interpolation of intensities overeach polygon

* a kind of scan-filling

* eliminates possible intensitydiscontinuities

* so called Mach bands can appear(subdivide polygons)

For each polygon:

calculate the average normal vector ineach vertex

use an illumination model to obtain theintensities in the vertices, e.g. Phong

interpolate the intensities linearly overthe surface

First, vertically along the edges Then, horizontally along each scan-line

IqI1y2 ys

y2 y1 I2

ys y1y2 y1

IrI4y3 ys

y3 y4 I3

IpIqxr xp

xr xq Ir

The normal in vertex

V is calculated as

the average of N1,N2, N3 and N4

Notice that vertex V

then will have the

same normal andintensity for all four

polygons joining in V

Illumination from point light sources

includes generating shadows, i.e. some

objects will shade other objects.

The problem of identifying shaded surfacesdirectly corresponds to the problem of

identifying hidden surfaces; those

surfaces that are hidden when viewed

from the light source position are exactlythose shaded (from that particular light

source!)

In principle, this means that those surfaces

that are invisible from the light source, but

visible from the view point (VRP), are to be

shaded

A pixel intensity is determined by following all rays

emitted from a light source (infinitely many!),

adding the intensities of those rays which are passing

through the pixel area on their way to VRP

A better idea is to start in a pixel position and

trace the rays backwards, since most rays

from the light source will not pass through

the current pixel.

Then, only those rays which are traced back to

a light source will result in a contribution of

the intensity

A ray intersecting

with a point on

an object surfaceis divided into (in

general):

* a specular

reflected ray* a refracted ray

(if transparency)

Illumination Virendra

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