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Other Rendering Techniques

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Intro

You have seen•Scanline converter (+z-buffer)•Painter’s algorithm•Radiosity

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IntroSome more…•Raytracing•Light maps•Photon-map•Reyes•Shadow maps•Sahdow volumes•PRT•BSSRF

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Raytracing

ObjectCoordinates

Modelv

iew

Matrix

Inters

ection

Data Stru

cture

Eye coo

rdinat

es

Raytracing then utilizes thisdata structure to build the image.

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Raytracing•Arthur Appel in 1968 Ray casting•Turner Whitted

“An improved illumination model for shaded display” June, 1980 Communications of the ACM.

more about illumination model

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That Pinhole Camera Model

After eyespace transformationProjection Plane at z=-d

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Raytracingcenter of projection through the center of a pixel and off into space…

What does it hit first?If it hits an object, compute the color for that point on the objectThat’s the pixel color

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RaysA Ray is a vector and a point

Point – The starting point of the rayVector – The ray directionThis describes an infinite line starting at the point and going in the ray direction

Ray t valuesA distance along the ray t=1.5

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View Plane:Pixel Grid

0

0 1 2 3 4

1

23

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Visible Surface Raytracing// width – Screen width, height – Screen height// fov – Field of view in degrees, aspect – Aspect ratiodouble ey = tan(fov / 2. * DEGTORAD); double ehit=2 * ey;double ex = ey * aspect; double ewid = 2 * ex;

for(int r=0; r<height; r++) for(int c=0; c<width; c++){

ray.start.Set(0,0,0);ray.dir.Set(-ex + ewid * (c + 0.5) / width,

-ey + ehit * (r + 0.5) / height,-1.);

ray.dir.Normalize();

// Compute color in ray direction// Save color as image pixel

}

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what will we hit?Ray intersection tests

Reduces to solving for tx = xs + t xd

y = ys + t yd

z = zs + t zd

Easiest is the sphere(x-x0)2+(y-y0)2+(z-z0)2=r2

Substitute ray equation in and solve for t

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Intersection w/ a sphere

220

20

20

000

222

2

2,1

)()()(

))()()((2

24

rzzyyxxC

zzzyyyxxxBzyxA

AACBBt

sss

sdsdsd

ddd

−−+−+−=

−+−+−=++=

−±−=

Questions: Why two t values?How do we tell if there is an intersection?

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Intersections w/ a plane

Plane equationAx+By+Cz+D=0(A,B,C) is the plane normalWe can compute the normal and, given a single point, compute D

ddd

sss

CzByAxDCzByAxt

+++++

=

Questions: Can t be negative? Zero?Why is this “more difficult” than a sphere?

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Polygon IntersectionGiven a plane intersection, the question is:

Is this point inside the polygon?

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Reduce to 2DProject the polygon for the maximum area

What is the largest component of the normal?If x: Use a Y/Z projectionIf y: Use an X/Z projectionIf z: Use an X/Y projectionWhy?

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Why “impractical”?

Suppose you do a ray for every pixel and test against very polygon:

O(WHP)Then if we allow recursion…

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Faster Intersection Tests

Grouping objects and using bounding volumes

Bounding boxes are easier to test for intersections.Your chair object could have a box around each polygon and a box around the entire object.We can create hierarchical levels of bounding boxes pretty easily (cluster tree)Spheres are a common bounding volume

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Bounding box test

Assumes: Upright boxSometimes called “generalized box”

Consider box to have 6 planesPlanes are orthogonal to some axisBox with range: (0.5, 0.7, -1) to (1.3, 2.2, -4)Ray: R((0,0,0),(1, 1, -1)) What is “t” for intersections with box planes orthogonal to the X axis?

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Ray Walking Algorithmssubdivide the space into boxestrace the ray one box after another

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Ray Walking Algorithms

Not the same as line drawing:

= line draw= extras for ray

walking

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Spatial subdivisionsUniform divisions

All boxes are equal sizedAdvantages? Disadvantages?

Non-uniform divisionsHow? Why?

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Octtree-based

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Speed-upItem buffer

A z-buffer which holds pointers to objects rather than colorsHow can this speed up ray tracing?

Also called: First-hit speedup

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color?Intersection gives a point on a polygon

Apply the color modelHow do we get

View direction?Light direction?Normal?

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How do we do?Shadows?Reflections?

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Terms to knowShadow feeler

Casting a ray in the direction of the lightIf intersection is less than distance to the light, light is shadowed

Self shadowingRoundoff errors can make us intersect ourselves

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RecursionReflections (THE point of

raytracing)Simply compute the color in the reflection direction

What does this do to the running time?

Was O(WHP)

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Adaptive Depth ControlHow deep do you recurse?

A room with mirrors?A room with only specular reflection?

Keep track of how much a ray will contribute to the final color

Falls below some threshold, don’t recurse anymore…

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How do we do?Shadows?Penumbra?Depth of field?Motion blur?Antialiasing?

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Stochastic Ray TracingProblem with ray tracing:

Point sampling

We can introduce randomness all over the place

Jitter for antialiasingLight area for penumbraDepth of field and motion blur

[Jensen07]

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Minimum distance Poisson distribution

Better matches distribution in the eye

AlgorithmGenerate a random pointIf less than specified distance to nearest point, discard, otherwise keep

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Distribution Comparisons

Poisson Uniform

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Path Tracing1) Sample each pixel with N rays2) At each intersection, trace only one ray

proportion of rays in each category should match the actual (surface) distribution

Ray Tracing Path Tracing

Reduces the amount of work deeper in the ray tree

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Adaptive samplingDetermine if number of samples is enough

If not, increase the number

Works for uniform and stochastic sampling

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Finite AperturePerturb the raysOr jitter eye position

Depth of Field

[Jensen07]

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Motion Blur

[Jensen07]

Finite shutter opening timePerturb the rays in time

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Ray tracing from the light sources

In regular ray tracing we don’t seeLighting reflected through mirrorsSurfaces lit by reflection from other surfaces

Large set of rays from each lightComputes light that hits surfacesGeneral solution for diffuse reflection?Still requires tracing from the eye as pass 2

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Lightmap

•Precomputed lighting•Implement by multitexture•Why?

Texture can be re-usedLighting unique but low-res

[Cham

bers01]

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Photon map

•Photon by light-based raytracing•Separating GI from rendering•Stored in kd-trees•Good for

Caustics, subsurface scattering,…

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Photon path

Start from light sourcesIntensity -> photon

[Jensen]

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Final Gathering

•Radiance Computation•Distributed ray tracing

[Jensen]

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Another example

[Jensen00]

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Irradiance Caching•Similar Idea to lightmap

Irradiance has lower frequency (than radiance)

[Ward]

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Reyes RenderingDeveloped by LucasfilmIn use by Pixar (Renderman)Now combined with ray-tracing on demand

One tile at a timeSubdivide geometry to pixel size

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Design GoalsNatural Coordinates

Do calculations in coordinate system most natural for it.

Support for vectorization,parallelism,etc.All objects work with common

representationsMicropolygons

LocalityGeometric and Texture locality

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Design Goals (2)Linear in model sizeLarge models (larger than memory)Textures, textures, textures

Complex shadingBump and displacement maps

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Reyes Algorithm

read model

dice

shade

visibility

picture

texture

sample

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Micropolygons

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Sampling

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Shadow Maps

Render a depth image from the light position

For each pixel in final image:1) Transform into light space2) In shadow iff zinLightSpace > zshadowMap

Shadow map =

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Shadow Maps

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Deep Shadow Maps

3D texture where each point is how much illumination we receive

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Shadow VolumesPolygons cast polyhedra of shadow volumes

Intersect polyhedra and object space

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Real-time Rendering

TransportTransportComplexityComplexity

LightingLighting

simplesimple shadowsshadows

pointpointlightslights

full full envenv..mapmap

interinter--reflectionsreflections

singlesingleareaarealightlight

[Moeller02][Moeller02]

[Blinn76][Blinn76]

[Heidrich00][Heidrich00]

[Crow77][Crow77]

[Ashikhmin02][Ashikhmin02]

PrecomputedPrecomputedRadiance Radiance TransferTransfer

[Sloan02][Ng03][Zhou05][Ren06][Sun07]

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Precomputed Radiance Transfer

( )V sr

( ) ( )i iL s l B s=∑r r%

( )( ) ( ) ( ) ( , ) ( )i i NR v l B s V s f s v H s d s= ∑∫r r r r r r r%

( ) ( ) ( ) ( , ) ( )i i NR v l B s V s f s v H s d s=∑ ∫r r r r r r r%

( ) max( ,0)NH s s N= •Preprocess for all Preprocess for all ii

vr

( ) ( ) ( ) ( , ) ( )NR v L s V s f s v H s d s= ∫r r r r r r r

( ) i iR v l t=∑r%

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Precomputed Radiance Transfer

Basis 16Basis 16

Basis 17Basis 17

Basis 18Basis 18

illuminateilluminate resultresult

......

......

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Subsurface ScatteringLighting effect

semi-translucent materialsskin, leaves, marble, milk, etc.

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BSSRDFGeneralization of BRDF

bidirectional surface scattering distribution function

entry and exit not identical

total outgoing radiance

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Subsurface ScatteringBig idea

break things down into single and multiple (diffuse) scattering eventshow does medium enter?

reduced intensity due to scatter

first order scattering as

volumetric source

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Diffusion of Lightintegrate transport equation over all

directions

two term expansion

after substitution into transport eq.

isotropic sources

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And The Winner Is?!You may now pick up your Oscar

Jensen, Marschner, Levoy, Hanrahan

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Making it Faster

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Texture Memory

Rasterization

Modern GPU Org.

Vertex ShaderGeometry

(vertex stream)

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

Pixel Shader

Frame Buffer

Tex 0

Tex 1

Tex 2

Setup

[John Hart]