COL859: Advanced Computer Graphics

COL859: Advanced Computer GraphicsPrem Kalra

[email protected]://www.cse.iitd.ac.in/~pkalra/col859

Department of Computer Science and EngineeringIndian Institute of Technology Delhi

mailto:[email protected]

http://www.cse.iitd.ac.in/~pkalra/col859

Advanced Computer Graphics http://www.cse.iitd.ac.in/~pkalra/col859

Online PlatformMicrosoft TeamMoodleImpartusCourse webpage

http://www.cse.iitd.ac.in/~pkalra/col859

Time SlotE (10-10:50 AM Tuesday, Wednesday, Friday)

Course Administration


EvaluationAssignments (30)

ProgrammingReading

Term Paper Presentation (20)Project (30)Exam (20)

Course Administration

Should have done COL781 (Introduction to Computer Graphics)or its equivalent.

OR Instructors approval

Eligibility


ModelingParametric curves and surfacesTriangle meshesSubdivision

RenderingGlobal illuminationRendering equationPhysically based rendering

AnimationCharacter animation – Kinematics, SkinningPhysics based animation

Augmented/Virtual Reality

Contents


[1] Tabellion, E. “Ray Tracing vs. Point-Based GI for Animated Films”. SIGGRAPH 2010 Course: “Global Illumination Across Industries”.

Recap: Ray Tracing


• VisibilityWhat objects or parts in the scene are visible?

Clipping (with respect to the view frustum)Done

Occlusion (with respect to the objects in the scene) Hidden surface elimination

• IlluminationReflection, Refraction, Transparency, Shadows, etc.

Issues

Recap: Ray Tracing


Forward Ray TracingModeling interaction of light with the objects/surfaces

Problem:Many rays will not contribute to the image!

Recap: Ray Tracing


Backward Ray Tracing

Rays from camera (viewer) through each pixel to the scene

Recap: Ray Tracing


Backward Ray Tracing

A

B

CE

F

D

View Plane

Viewer

Primary and Secondary Rays

Recap: Ray Tracing


Backward Ray TracingShadow Rays

Visibility check with respect to the light source

Recap: Ray Tracing


Backward Ray TracingShadow Rays

Visibility check with respect to the light source

Recap: Ray Tracing


Ray TracingTwo IssuesRay-object intersection

Visibility test: Closest to the viewer

Pixel color determination (shading)Illumination model

Recap: Ray Tracing


Ray TracingTwo Issues

A

B

CE

F

D

View Plane

Viewer

Light

Recap: Ray Tracing


Ray Object Intersection

Ro

Rd

0

1][][

222

>+=

=++==

t tRRR(t)Form Parametric

ZYXDirection) (Ray Z Y XROrigin) (Ray Z Y XR

do

ddd

dddd

oooo

Center Sc = [ Xc Yc Zc ] Radius SrSurface Point [ Xs Ys Zs ]

2222 )()()( rcscscs SZZYYXX =-+-+-

Implicit FormSphereRay

2222 )()()( rcdocdocdo SZtZZYtYYXtXX =-++-++-+

Solve for t

Recap: Ray Tracing


Illumination Model

å=

•+•+=

•+•+=++=

++=

m

i

niisiidaa

nlsldaa

nlsldaa

total

VRIkNLIkIk

VRIkNLIkIkαIkθIkIk

reflection specular reflection diffuse reflection ambientI

1)()(

)()(coscos

NL q q

R

Va

Recap: Ray Tracing


Recursive Ray Tracing

A

B

CE

F

D

View Plane

Eyeeye-ray

R1

T1

R2

T2

Recap: Ray Tracing


Recursive Ray TracingEye

C

DR1 T1

R2 T2

Different Rays

Eye ray (primary ray)

Reflected rayTransmitted rayShadow ray

(secondary rays)

Recap: Ray Tracing


Recursive Ray TracingReflected Ray

NL

Rqrqi L

N

R

-L

NNL )(2 •

LNNLR -•= )(2

Recall Reflection Vector

Recap: Ray Tracing


Recursive Ray TracingRefracted Ray

Snell’s Law

i

t

t

i

ηη

θθ

=sinsin

NθNθIηηT

Nθθ

NθIθT

NθMθTθ

NθIM

tit

i

ti

it

tt

i

i

)(cos))(cos(

)(cossin

))(cos(sin)(cos)(sin

sin)(cos

-+=

-+

=

-=

+=N

qt

qiI

T

Nθi )(cos

M

Recap: Ray Tracing



When to stop ?

When ray leaves the sceneWhen the contribution to the overall intensity is small

Recap: Ray Tracing



Documents

COL859: Advanced Computer Graphics