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Volumetric Shaders

Assignments Please fill the dropboxes…

Still catching up on grading.

Questions.

Final exam effects Deliverables:

Research (Grads only) Shader code Documentation

Describe shader params Explain chosen implementation. List constraints. Give results.

Final exam effect Presentation:

Final exam period Thursday, May 24th 12:30 - 2:30pm ICL6

15 minutes per presentation

Announcement As promised:

THE ILLUSION OF LIFE, REVISITED Or

Dancing with the Network Sheep Ken Perlin

Thursday, May 10th @ 12 noon Golisano Building Auditorium

Plan for today This week is Volume Week!

Today: lecture Thursday: volumetric rendering lab.

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Volume Rendering From Wikipedia:

Volume rendering is a technique used todisplay a 2D projection of a 3D discretelysampled data set.

Volume Rendering

3D data Data sampled in a 3D space Voxel -- 3D equivalent of a pixel

Subdivision of space holding a single datapoint

“density function”

Examples Types of data:

CT / MRI scans Clouds Atmospheric effects Fire, smoke

Rendering Volume Data Isosurface Approach

Convert densities to geometry Render corresponding geometry Marching cubes algorithm

Direct Volume Rendering Sample density in a volume along a ray Splatting (Projection) Ray marching

Marching Cubes Volexize your space Choose threshold For each voxel vertex, determine if point

is inside or outside isosurface based onthreshold.

Create polygons for each voxel basedon status of voxel vertices.

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Marching Cubes Marching cubes

SIGGRAPH - HyperGraph

Direct Volume Rendering Splatting

SIGGRAPH - HyperGraph

Direct Volume Rendering Ray Marching

SIGGRAPH - HyperGraph

Ray marching algorithm Ray Marching algorithm Psedocode:

Calculate segment of ray on which to marchSet starting pointwhile (current point is behind final point)

call density functioncalculate light hitting pointupdate current color total and opacity totalCalculate and move to next sample point along

rayendSet surface color / opacity.

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Ray marching algorithm Said another way:

Choose step sizelen = length (I);Pcur = P - I;while (len > 0) do

sample density and light at PcurCvol += (1-Ovol) * stepsize*scatteredLightOvol += (1-Ovol) * stepsize*densityPcur += stepsize * normalize(I)len -= stepsize;

end

NOTE THERE IS AN ERROR IN THE TEXT…the above iscorrect.

Volumetric rendering isexpensive Sampling points in a volume along a ray Basic trade-off

Too few samples -- aliasing Too many samples -- takes too long.

Choose your step size well

Challenges in procedural volumetric shading

Determining the “density function” Determining the “light scattering” Efficient implementation of ray marching

algorithm

Determining density functions Empirical -- data is provided to you

CR / MRI Procedural

You calculate the density…usually usingsome form of noise

Voxelized General 3D data placed in voxel boxes.

Light scattering Scattered into the line of sight (in-

scattering)

Scattered out of the line of sight (out-scattering)

Absorbed altogether (absorption)

Determining lighting Must consider light illuminating the point Must determine how much of that light

is scattered toward the viewer Uniform scattering Mie scattering Raleigh scattering

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Light - Scattering

Light is scattered by small particles in its path (e.g. haze,smoke, etc.)

Given by fraction of light with respect to direction from particlelight impact.

Size of particles are on the order of wavelengths of light.

!r

Light -- Scattering

r << λ total absorption (no scattering) r < λ Rayleigh Scattering r ≈ λ Mie scattering r >> λ Geometric optics

!r

Light – Raleigh Scattering Raleigh scattering (smoke / dust ), the

probability that the light will scatter indirection α.

)cos1(4

3)( 2!! +=P

Light – Mie Scattering Mie Scattering (haze / fog)

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2

cos191)( !

"

#$%

& ++=

''P Sparse / hazy

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2

cos1501)( !

"

#$%

& ++=

''P

Dense / murky

Questions so far?

Uniform fog Uniform fog Ray marching with assumptions:

Density is uniform and constant. Light scattering is uniform and constant.

Can solve analytically

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Uniform fogCleave= Center - Creduce + Cincrease

WhereCleave = light leaving along a rayCenter = light entering along a ray Creduce = light absorbed due to density Cincrease = light scattered

Uniform fog Other assumptions:

0 ≤ Creduce ≤ Center Can’t reduce more light than comes in

Creduce = h Center h is uniform density.

Cincrese = h Cfog Cfog is the constant color of light scattered

toward eye due to fog.

Uniform fog So…

Cleave = (1-h)Center + hCfog

Rearranging things g = 1-h Cleave = gCenter + (1-g)Cfog

Light exiting fog is a fraction of the lightentering the fog plus 1 minus that fraction timesthe fog color

Uniform fog Apply ray marching algorithm…Let’s

assume 3 steps:

More generally for z steps:

!

Cleave = g3Center + (1" g

3)Cfog

!

Cleave = gzCenter + (1" g

z)Cfog

!

Ceye = gzCobject + (1" g

z)Cfog

Uniform fog Recall exponentials:

Exp and log base 2 are quick

Final equation

Where: z is fog distance h is fog density

!

gz

= exp2(log2(g)z)

!

Ceye = fCobject + (1" f )Cfog

f = exp2("dz)

d = "log2(1" h)

break

Hypertexture [Perlin89] Extension of procedural textures Between surface + texture, i.e., spatial

filling/volumetric Objects modeled as distribution of density

hard region - objects completely solid soft region - object shape is malleable using a toolkit of

shaping functions and CSG style operators to combineshapes

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Hypertexture D(x) - Object Density Function over R3

D (x) for all points x in 3D space [0,1] Density of 3D shape D (x) = 0 for all points outside the surface D (x) = 1 for hard region of the object 0 < D (x) < 1 for soft region of the object

(fuzzy region)

Hypertexture Toolbox of base DMFs

Bias – up / down control Gain – controls gradiant Noise (controlled randomness)

Won Ken an Academy Award! Turbulence

Sum of noise at variety of frequencies

Mathematical functions

Bias Used to bend the density upwards or

downwards over [0,1] Properties:

biasb (0.00) = 0 biasb (0.5) = b biasb (1.00) = 1

Definition:

!

biasb(t) = t

ln(b )

ln(0.5)

Bias

Bias0.25 Bias0.5 Bias0.75

Gain

used to help shape how fast themidrange of an objects soft region goesfrom 0 to 1. Properties:

gaing (0.0) = 0.0; gaing (0.25) = 0.5 - g/2; gaing (0.5) = 0.5; gaing (0.75) = 0.5 + g/2; gaing (1.0) = 1.0;

Gain Definition

!

gaing (t) = if (t > 0.5) then bias1"g (2t)

2 else

2 " bias1"g (2 " 2t)

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Gain

gain0.25 gain0.5 gain0.75

Noise Noise resembles a sin wave but with

“random” bumps: For hypertexture we use 3D noise

fBm / Turbulence fBm -- fractional Brownian motion. 1/f noise

Sum of noise functions Contribution of each is proportional to the

inverse of the frequencyfloat value = 0;

for (f = MINFREQ; f < MAXFREQ; f *=2)

value += snoise (P * f) / f;

return value;.

fBm / Turbulence Turbulence

Like fBm but absolute value of noise issummed

Both are useful for “natural” effects

float value = 0;

for (f = MINFREQ; f < MAXFREQ; f *=2)

value += abs (snoise (P * f)) / f;

return value;.

fBm / Turbulence

fBm turbulence

Hypertexture Noise Examples

2* frequency, 1/2 amplitude

[Perlin89]High Amplitude, Noisy Sphere

Noisy

Fractal, noise - Σ many f’s

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Hypertexture Example - Fire

)))(1()( xturbulencesphere(xxD +=[Perlin89]

Red = low density

Yellow = high

Hypertexture Example - Fur/Hair

[Perlin89]Tribble

Here noise displaces

x before projecting;

uses variable to control

curliness

Rendering hypertextures Use a basic ray marching algorithm A priori knowlegde of shape being

shaded E.g. for sphere

Define inner_raidus (where D = 1) Define outer_radius (outside of which D = 0) Ray march from inner to outer.

Hypertexture clouds Set inner radius = 0.0

Entire interior region is “fuzzy”

See Perlin paper for more details/usesof hypertextures.

Questions?

Volume Rendering inRenderMan volume shader

Defines how light, passing through a volume isaffected.

Global variables: P - origin of ray I - incident vector (direction of ray) E - eye point Ci / Oi -- surface color / opacity (output variables)

Volume Rendering inRenderMan From the spec:

A volume shader is not associated with a surface,but rather attenuates a ray color as it travelsthrough space. As such, it does not have accessto any geometric surface parameters, but only tothe light ray I and its associated values. Theshader computes the new ray color at the rayorigin P-I. The length of I is the distance traveledthrough the volume from the origin of the ray to thepoint P.

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Volume Rendering inRenderMan Three places where volume shaders can be

bound: Interior -- for volume within a primitive

Interior shaders are often implemented as surfaceshaders.

Exterior -- for volume between light and primitive(can sample lights using illuminance)

Atmospheric -- for volume between primitive andcamera.

Implementation in Cg Once again…

In Cg, there are only vertices andfragments.

Volume effects are achieved by explicitmodification of lighting paths in eitherfragment or vertex program.

Real time ray marching is a very recentadvancement.

Questions? In the lab…

Basic fog Ray marching Hypertextures or Mie Scattering