Noise

​

Instructor: Christopher Rasmussen (cer@cis.udel.edu)

​

​

​

November 21, 2019 ❖ Lecture 25

Outline

• Global illumination
• Photon mapping details
• More types of photon interactions
• Noise

​

​

​

Photon Mapping (H. Jensen, 1996)

• Two-pass algorithm somewhat like bidirectional ray tracing, but photons stored differently
• Related to particle tracing approach in Marschner 23.1
• 1^st pass: Build photon map (analog of rexes)
• Shoot random rays from light(s) into scene
• Each photon carries fraction of light’s power
• Follow specular bounces, but store photons in map at each diffuse surface hit (or scattering event)
• 2^nd pass: Render scene
• Modified ray tracing: follow eye rays into scene
• Use photons near each intersection to compute light

Photon Mapping: 1^st pass (Write)

• Probabilistically decide on photon reflection, transmission, or absorption based on material properties of object hit
• Specular surface: Send new photon (with scaled-down power) in reflection/refraction direction just like ray tracing. Do not change photon map
• Diffuse surface: If at least one bounce, store photon in photon map, send new photon in random direction (usually cosine distribution as mentioned for AO -- see Marschner 14.4.1)
• Arbitrary BRDF: Use BRDF as probability distribution on new photon’s direction
• Photon map is kd-tree
• Decoupling from scene geometry allows fewer photons than scene objects/triangles (no texture maps, no meshes)

kd-trees

• Each point parametrizes axis-aligned splitting plane; rotate which axis is split at each level of tree
• Compare and contrast with BSP trees
• Example kd tree for k = 2 and N = 6:

​

​

​

​

​

​

​

images from Wikipedia

kd-trees

• Each point parametrizes axis-aligned splitting plane; rotate which axis is split
• Compare and contrast with BSP trees
• Example kd tree for k = 2 and N = 6:

​

​

​

​

​

​

• But balance is important to get O(log N) efficiency for nearest-neighbor queries

​

images from Wikipedia

Photon Map: Example

Raytraced scene (courtesy of P. Christensen)

Photon map of scene (n=500,000)�[notice nothing stored at pure specular surfaces]

WebGL path tracer (not same as photon mapping, but similar)

Photon Mapping: 2^nd pass (Read)

• For each eye ray intersection, estimate irradiance as function of nearby photons:
• Each photon stores position, power, incident direction—can treat like mini-light source
• Use filtering (cone or Gaussian) to weight nearer photons more
• Can use discs instead of spheres to only get photons from same planar surface
• For soft, indirect illumination, irradiance estimates are combined with standard local illumination calculations after final gathering (which shoots more rays to bring back irradiance estimates from other diffuse surfaces)—just like ray tracing adds reflection/refraction components to local color
• As usual, more accurate with more photons → Use multiple maps for different phenomena

Irradiance estimates based on nearby photons

Previous image combined w/ texture maps & material colors

Scene after final gathering

Raytraced scene (courtesy of P. Christensen)

Lighting Components, Reconsidered

• Break rendering equation into parts: L = L_direct + L_specular + L_indirect + L_caustic
• Can get L_direct and L_specular using ray-casting, ray-tracing respectively
• L_indirect is main reason we’re looking at photon mapping—it’s our LD*E paths
• L_caustic from special “caustic” photon map

Multiple Photon Maps

• Global map: Shoot photons everywhere for diffuse, indirect illumination
• Caustic map: Shoot photons only at specular objects (“aimed” sort of like shadow rays)
• Volume map: Photon interactions with participating media such as fog, smoke

​

Caustic map

Global map

Other kinds of interactions

• Rayleigh (air molecules) and Mie (smoke, pollution) scattering
• Simulating the colors of the sky
• GLSL implementation

​

​

Rayleigh/Mie scattering examples

Actual sky photo

Nishita sky simulation

GLSL sky simulation

Scratchapixel sky simulation

Other kinds of interactions

• Rayleigh (air molecules) and Mie (smoke, pollution) scattering
• Simulating the colors of the sky
• GLSL implementation

​

• BSSRDF (Bidirectional surface scattering RDF)
• "A Practical Model for Subsurface Light Transport", Jensen et al.

BSSRDF examples

BSSRDF examples

BRDF

BSSRDF

What is Computer Graphics? Goals

More procedural modeling

What is Computer Graphics? Goals

More procedural modeling -- noise can help with shape, motion, pattern, ...

Noise as a Texture Generator

• Easiest texture to make: Random values for texels
• noise(x, y) = random()
• If random() has limited range (e.g., [0, 1]), can control maximum value via amplitude
• a * noise(x, y)
• But the results usually aren’t very exciting visually

3-D Noise

• 3-D or solid texture has value at every point (x, y, z)
• This makes texture mapping very easy :)
• Simple solid texture generator is noise function on lattice:
• noise(x, y, z) = random()
• For points in between, we need to interpolate
• Technically, this is "value" noise -- "Perlin" noise is based on random gradients

courtesy of L. McMillan

Perlin noise is implemented in GLM library -- see this page

3-D Noise Interpolation

• f(x, y, z) can be evaluated at non-lattice points with a straightforward extension of 2-D bilinear interpolation (to trilinear interpolation)
• Other interpolation methods (quadratic, cubic, etc.) also applicable
• All of these are approximations of smoothing filters such as Gaussians

courtesy of L. McMillan

Z interpolation

X interpolation

Y interpolation

3-D Noise Texturing: Examples

Original object

Noise with trilinear smoothing

Triquadratic noise

courtesy of L. McMillan

Noise Frequency

• By selecting larger spaces between lattice points, we are increasing the magnification of the noise texture and hence reducing its frequency

Original

noise

Smoothed

noise

Smoothed noise at different magnification levels

courtesy of H. Elias

Fractal Noise (aka "turbulence", aka "fractional Brownian motion" (FBM))

• Many frequencies present, looks more natural
• Can get this by summing noise at different magnifications
• turb(x, y, z) = Σ_i a_i * noise_i(x, y, z)
• Typical (but totally adjustable) parameters:
• Magnification doubles at each level (octave)
• Amplitude drops by half

=

courtesy of H. Elias

Variations on noise

"sum" here means fractal noise as defined on previous slide

Noise Variations

from Perlin

Smoothed noise only

Turbulence (8 octaves)

Pure Perlin noise

Turbulence

Noise Variations

Turbulence with absolute

values of noise

Phase shift: sin(x + turb())

Noise in GLSL

Value noise/turbulence demo: https://www.shadertoy.com/view/4sfGzS

​

2-D Noise: Applications

• Traditional “wrappable” textures
• Clouds, water, fire, etc.
• Bump, specularity, blending maps
• ​

​

​

​

• Height maps—e.g., fractal terrain

​

Images from

http://devmag.org.za/2009/04/25/perlin-noise/

​

3-D and 4-D Noise: Applications

• 3-D
• Solid textures such as marble, wood, 3-D clouds
• Animated 2-D textures (flesh, slime, copper, mercury, stucco, amber, sparks)
• 4-D
• Animated solid textures

https://www.shadertoy.com/view/XslGRr

​

Noise: “Wobbly Chrome”

https://www.clicktorelease.com/blog/experiments-with-perlin-noise/

WebGL/GLSL examples

Seascape

GLSL programming in your browser

• http://glslsandbox.com/
• http://www.shadertoy.com
• http://pixelshaders.com