TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAA

CS 148, Summer 2012 Introduction to Computer Graphics and Imaging

Justin Solomon

http://www.futuretech.blinkenlights.nl/misc/scene_1024x768.jpg

http://www.publicdomainpictures.net/view-image.php?picture=female-photographer&image=4360&large=1 http://bloodredpencil.blogspot.com/2010/09/need-help-get-help.html

http://www.publicdomainpictures.net/view-image.php?picture=female-photographer&image=4360&large=1 http://bloodredpencil.blogspot.com/2010/09/need-help-get-help.html

http://software.intel.com/file/37491

Light source

http://software.intel.com/file/37491

Light interacts with objects in scene

http://software.intel.com/file/37491

Image plane

http://software.intel.com/file/37491

Most light doesn’t reach the camera http://software.intel.com/file/37491

??

Most light doesn’t reach the camera http://software.intel.com/file/37491

??

Many lighting effects are reversible

Trace rays from light to camera

Trace rays from light to camera

Draw viewing ray through each pixel

Intersect with geometry

Compute light ray

Evaluate shading

µ

Take closest one

Redirect ray

µ

µ

Redirect ray

µ

µ

Rasterization for (each object in scene)

drawObject();

Rasterization

Ray Tracing

for (each object in scene)

drawObject();

for (each pixel in image)

sendRay();

Rasterization

Ray Tracing

for (each object in scene)

drawObject();

for (each pixel in image)

sendRay();

for each pixel do

compute viewing ray

if (ray hits an object with t>0) then

Compute normal

Evaluate shading model

else

Set pixel color to background color

Textbook page 85

Ray

~o = origin

~d = direction

Ray

~o = origin

~d = directionDoes not have to be unit length!

Point on Ray

~o+ t~dt 2 (0;1)

t ¸ 1

Point on Ray

~o+ t~d

t < 0

Point on Ray

~o+ t~d

t < 0

Generating rays

No perspective transformation

needed!

~p0

~j

~i

~p = ~p0 + u~i+ v~ju 2 [0;w]; v 2 [0; h]

Ray-object intersection

~o+ t~d

k~x¡~ck2 = R2

Ray-object intersection

~o+ t~d k~x¡~ck2 = R2

Ray-object intersection

~o+ t~d k~x¡~ck2 = R2

k~o+ t~d¡~ck2 = R2

Ray-object intersection

~o+ t~d k~x¡~ck2 = R2

k~o+ t~d¡~ck2 = R2

(~o+ t~d¡~c) ¢ (~o+ t~d¡~c) = R2

Ray-object intersection

~o+ t~d k~x¡~ck2 = R2

k~o+ t~d¡~ck2 = R2

(~o+ t~d¡~c) ¢ (~o+ t~d¡~c) = R2

k~dk2t2 +2((~o¡~c) ¢ ~d)t+ k~o¡~ck2 =R2

Ray-object intersection CS 148, fall 2011

Normals

~x~c~N =

~x¡~c

k ¢ k

Normals http://designjk.files.wordpress.com/2011/12/teapot-decorated.png

~v1

~v2

~v3

~v2 ¡~v1

~v3 ¡~v1

~N =(~v2 ¡ ~v1)£ (~v3 ¡ ~v1)

k(~v2 ¡ ~v1)£ (~v3 ¡ ~v1)k

Light rays

~x

~l1 ¡ ~x~l2 ¡ ~x

¢ ¢ ¢

http://www.spot3d.com/vray/help/150SP1/images/examples/shadows/03_raytraced_colored.png

http://2.bp.blogspot.com/-2CpxoSdtNE8/T5nMClgobpI/AAAAAAAAAJ4/XgaZ168HpKg/s1600/P0008_I004.png

Intersect light ray with scene

abstract class surface

virtual hit-record hit(ray, t0, t1)

virtual box bounding-box()

struct hit-record

vector3d position, normal

surface hit-surface

…

abstract class material

color evaluate(in-ray, normal, pos)

…

color ray-trace(ray r)

hit-record record = intersect(r);

…

if (record.hit-surface.is-reflective)

ray reflected-ray =

reflect(r,record.normal);

color reflected-color =

ray-trace(reflected-ray);

compute-spectral-component(

reflected-color);

…

Lots of bounces Fewer bounces

CS 148, fall 2011

Save time; avoid infinite recursion

http://www.deepakantony.com/wp-content/uploads/2012/04/ambientocclusion_instancing.png http://members.optusnet.com.au/pennywyatt/Images/People.png

Deal with repeated objects

Deal with repeated objects

http://members.optusnet.com.au/pennywyatt/Images/People.png

Store object once, use often

Deal with repeated objects

Each instance stores a

transformation matrix M

(can stretch, rotate, etc!)

Deal with repeated objects

Object coordinates World coordinates

M 2 R3£3

Deal with repeated objects

M 2 R3£3

~o+ t~d

Deal with repeated objects

M 2 R3£3

~o+ t~dM¡1~o+ tM¡1~d

Do intersection here!

Deal with repeated objects

M 2 R3£3

~o+ t~dM¡1~o+ tM¡1~dSame t!

Deal with repeated objects

M 2 R3£3

~N ~M ~N

Binary operations for shape http://upload.wikimedia.org/wikipedia/commons/8/8b/Csg_tree.png

Binary operations for shape http://en.wikipedia.org/wiki/Constructive_solid_geometry

A B

A[B A¡B A\B

Binary operations for shape http://en.wikipedia.org/wiki/Constructive_solid_geometry

A B

A[B A¡B A\B

Store “inside intervals”

in(A) = [1; 3]

in(B) = [2; 6]

in(A \B) = [2; 3]

in(A [B) = [1; 6]

in(A¡B) = [1; 2)

A B

Store “inside intervals”

in(A) = [1; 3]

in(B) = [2; 6]

in(A \B) = [2; 3]

in(A [B) = [1; 6]

in(A¡B) = [1; 2)

A B

Store “inside intervals”

in(A) = [1; 3]

in(B) = [2; 6]

in(A \B) = [2; 3]

in(A [B) = [1; 6]

in(A¡B) = [1; 2)

A B

Store “inside intervals”

in(A) = [1; 3]

in(B) = [2; 6]

in(A \B) = [2; 3]

in(A [B) = [1; 6]

in(A¡B) = [1; 2)

A B

http://ps-2.kev009.com/CATIA-B18/basug_C2/basugbt1510.htm

http://www.hackification.com/2008/08/31/experiments-in-ray-tracing-part-8-anti-aliasing/

Scatter rays to make ray tracing less crisp.

Multiple rays per pixel

Multiple rays per pixel

Moiré pattern

http://upload.wikimedia.org/wikipedia/commons/f/fb/Moire_pattern_of_bricks_small.jpg

Remove Moiré patterns http://en.wikipedia.org/wiki/File:Moire_pattern_of_bricks.jpg

?

?

?

http://erich.realtimerendering.com/shadow_comparison.html

Hard shadows Soft shadows

http://user.online.be/felixverbelen/lunecl.jpg

Lights aren’t all point sources

Randomly sample light rays

Shadow computed per ray

Shadow computed per ray

Shadow computed per ray

http://liam887.files.wordpress.com/2010/08/weaver.jpg

Randomly sample eye positions

Square lens “Focus plane”

https://graphics.stanford.edu/wikis/cs148-11-fall/RaytracingResults http://www.baylee-online.net/Projects/Raytracing/Algorithms/Glossy-Reflection-Transmission

Randomly sample reflected rays

http://www.matkovic.com/anto/3dl-test-balls-01.jpg

Randomly sample positions

Brightness depends on nearby geometry http://en.wikipedia.org/wiki/Ambient_occlusion

Diffuse Ambient

Account for indirect lighting http://en.wikipedia.org/wiki/Global_illumination

Account for indirect lighting

Diffuse inter-reflection http://en.wikipedia.org/wiki/Global_illumination

Account for indirect lighting

Caustics http://en.wikipedia.org/wiki/Global_illumination

Rasterization:

O(bm)

Ray tracing:

O(bp)

Accelerated ray tracing:

O(p log b)

Value Variable

p Pixels on screen

b Objects in scene

m Average pixels/object

CS 148, fall 2011

Bounding Volume Hierarchy (BVH)

http://sopra.le-gousteau.de/images/2/2e/Bv_bvh_bspheres.jpg http://graphics.ucsd.edu/courses/rendering/2004/ssaha/index_files/finalbvh.jfif

Binary Space Partitioning (BSP) trees http://algorithmicarts.com/images/2008/bsptree-cutaway1269x684.png

Uniform subdivision grid http://www.cs.berkeley.edu/~sequin/CS184/IMGS/spatialSubdiv.gif

“Embarrassingly parallel,” but not SIMD? [NVIDIA, SIGGRAPH 2008]

TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAA

CS 148, Summer 2012 Introduction to Computer Graphics and Imaging

Justin Solomon

http://www.futuretech.blinkenlights.nl/misc/scene_1024x768.jpg