Raytracing: Reflection and Transparency, Slides of Computer Graphics

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Computer Graphics Raytracing (Part 4)

Reflection and Transparency

n Ray tracing also handles reflections and refraction of light well n We can easily render realistic scenes with n mirrors, n martini glasses n So, far, we have considered Local components (ambient, diffuse, specular) n Local components are contributions from light sources which are visible from hit point n To render reflection, and refraction we need to add reflection and refraction components of light

I = Iamb + Idiff + Ispec + Irefl + I tran

Reflection and Transparency

n r is given as (see eqn 4.22) as

n Transmitted component IT

is along transmitted direction t

n Portion of light coming in from

direction t is bent along dir

n IR and IT each have their own

five components (ambient, diffuse, etc)

n In some sense, point P’ along reflected

direction r serves as a light source to point Ph

r = dir − 2 ( dir • m ) m

Ph

v

r

m

s

dir

t

IR

IT

I

P’

Reflection and Transparency

n To determine reflected component

n Spawn reflected ray along direction r n Determine closest object hit

n To determine transmitted component

n Cast transmitted ray along direction t n Determine closest object hit

n So, at each hit point, local, reflected

and refracted components merge to form total contributions

Ph

v

r

m

s

dir

t

IR

IT

I

P’

Reflection and Transparency

n Tree structure suggest recursion at successive hit points

n Recurse forever? No!!

n At each point, only fraction of impinging reflected or refracted ray is lost

n Who determines fraction? Designer… sets transparency or reflectivity in SDL file.

n E.g reflectivity 0.8 means only 80% of impinging ray is reflected

n Thus, need to check reflected contribution by saying

if (reflectivity > 0.6)…

n Also check if(transparency > threshold)

n Basically, do not want to work hard for tiny contributions. Drop (terminate shade) if contribution is too small

Refraction and Transparency

n May also need to determine how many times you want to bounce (even if threshold is still high) n For example, in room with many mirrors, do you want to bounce forever (your system may cry!!) n Set recurseLevel (yup!! same as in shadows) to say how many bounces using (variable maxRecursionLevel ) n recurseLevel of 4 or 5 is usually enough to create realistic pictures n Ray from eye to first hit point has recurseLevel of 0 n All rays from first hit point have recurseLevel = 1 n Need to modify shade function to handle recursion

Recursive shade( ) skeleton

if (hit object is shiny enough) // add reflected light { get reflection direction build reflected ray, refl refl.recurseLevel = r.recurseLevel + 1; color.add(shininess * shade(refl)); } if( hit object is transparent enough) { get transmitted direction build transmitted ray, trans trans.recurseLevel = r.recurseLevel + 1; color.add(transparency * shade(trans)); } return color; }

Finding Transmitted Direction

n So far, found reflected direction ray direction as mirror direction from eye n Transmitted direction obeys Snell’s law n Snell’s law: relationship holds in the following diagram

Ph

m

t

1

1 2

sin( 2 ) sin( )

c c

faster

slower θ 2

θ 1

c 1 , c 2 are speeds of light in medium 1 and 2

Critical Angle

n There exists transmitted angle at which ray in faster medium (e.g. air) is bent along object surface n That angle ( θ 2 in figure below) is known as the critical angle n Increasing transmission angle beyond critical angle has “no effect”… transmitted ray still below object surface n Physical significance: n Underwater in pond, can see enter world through small cone of angles

Ph

m

t

faster

slower θ 2

θ 1

Transmission Angle

n Vector for transmission angle can be found as

Ph

m

t

t dir m dir  m

= + ( • )−cos( 2 )

1

2 1

c

c

c

c

Medium #

Medium # θ 2

θ 1

where dir

c

c1 (^ )

2 1

2

cos( 2 ) 1  1 −( m • dir )

c

c

References

n Hill, chapter 12