Introductory logistics: Yannis

Judge for rendering competition

Remaining logistics

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• Final project reports and code due Friday 5/5, 23:59 ET.
• Report due on Canvas.
• Code due on github.

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• Programming assignment competition awards.

Take the course evaluation surveys!

•CMU's Faculty Course Evaluations (FCE): https://cmu.smartevals.com/

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•CMU's TA Evaluations: https://www.ugrad.cs.cmu.edu/ta/S23/feedback/

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•An end-of-semester survey specific to 15-468/668/868: https://docs.google.com/forms/d/e/1FAIpQLSfvVBaBAAzc009UJTTjqqR-sOJyaGjFPAXzWnlaAM1_Q3hZmw/viewform

Non-Exponential Radiative Transfer and

Position-free Monte Carlo Simulation

Shun Iwase

Non-exponential Radiative Transfer

Exponential Radiative Transfer

Non-exponential Radiative Transfer (Delta function)

Bitterli et al., A radiative transfer framework for non-exponential media, SIGGRAPH Asia 2018

Non-exponential Radiative Transfer

Four types of light transport. p and f denote particle and surface

Bitterli et al., A radiative transfer framework for non-exponential media, SIGGRAPH Asia 2018

Non-exponential Radiative Transfer

Exponential Radiative Transfer

Non-exponential Radiative Transfer (Delta function)

Bitterli et al., A radiative transfer framework for non-exponential media, SIGGRAPH Asia 2018

Comparison to traditional radiative transfer

Position-free Monte Carlo Simulation

• Only angles and z-axis of a light are considered
• Assume that incoming and outgoing locations are the same
• Beneficial for stacking multiple layered materials
• Interactions with internal media
• Add a realistic translucent color to a surface (e.g., tinted glass)
• Physically-valid reflections with dielectric coating
• Total internal reflections are considered correctly (blend of diffuse + specular doesn’t)

Assumption of small horizontal displacement

Tinted glass

Credit: Autodesk Rendering Help

Dielectric coating

Result

Dielectric coating on Lambertian BRDF (spp512)

Dielectric Coating

Lambertian BRDF

Result

Tinted glass with internal media (spp512)

Dielectric Coating

Internal Media

Dielectric Coating

Next Steps

• Spectral rendering to reproduce interference effects
• Implement BDPT for position free Monte Carlo simulation

Guillén et al., A General Framework for Pearlescent Materials, SIGGRAPH Asia 2020

Rendering Competition Image (spp4096, 6 hours)

Chen, Kris:

Position-free Monte Carlo Layered Material &&

Spectral Rendering

Position Free Monte Carlo: Layered Mats

Consider the distance between the layers are so small, we ignore the horizontal position shift of light, which give us…

Multilayer structure

Top: dielectric

Middle: any medium

Bottom: any

With Next Event Estimation

Next event points to the upper layer, instead of the light (\wo BTPT)

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Next event points to light hit-point (\w BTPT)

Results

\w NEE x10 less sample

Spectral Rendering: Dispersion

Spectrum Lighting Model and BSDF Model

Wavelength 2 RGB

Wavelength based IOR

Wavelength based rays && sampling

Spectral Rendering: challenges & Results

Rendering caustics without BTPT

Scene setup is too hard to use…

1 million samples per pixel

Rendering

Competition

Differentiable rendering of local parameters

Sally Chen

Score function and gradients

*From 15468 slides

Loss function:

Gradient update

Experiments - optimize emission (trivial case)

Iter 0 - emit.r = 0.2

Target - emit.r = 1

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Experiments - optimize blend amount

Iter 0 - blend amount 0.5 for all

Target - blend amount 0.0, 0.2, 0.4,0.6, 0.8, 1.0

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Experiments - optimize Phong material exponent

Iter 0 - exponent = 1

Target - exponent = 100

Optimized with SGD with momentum

Depth of field rendering with hexagonal aperture

• Randomly sample location on a hexagonal aperture as ray origin

Rendering competition

Bidirectional Path Tracing

and

Multiplexed Metropolis Light Transport

Ethan Chu

BDPT

s = 1 s = 0

MMLT

Parallelism

Buggy

Competition

Monte Carlo Estimation of Signed Distance

Nicole Feng

The Heat Method for Distance Computation

Idea: Recover (approximate) distance from short-time heat diffusion

Crane, Weischedel, Wardetsky, The Heat Method for Distance Computation (2013)

Diffuse data

Normalize gradient

Integrate

Vector heat diffusion

In ℝⁿ, we can solve integral equations instead

What does the source term look like?

(in ℝ²)

M

How NOT to estimate

Walk on Spheres algorithm to solve Dirichlet-Poisson problem:

Better strategy: cache samples of

Similar to e.g., photon mapping

First pass (pre-compute):

Generate & store samples of

(Metropolis sample)

Results in ℝ²

Submission for rendering competition

A 2D solution interpolated onto a background mesh.

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I didn’t have time to implement my own rendering functions, e.g. sphere tracing.

Bidirectional Path Tracing and GGX BRDF

Dianne Ge

Bidirectional Path Tracing

Motivation: Traditional path tracing can result in varying

images, especially if a light source is hard to reach from

a randomly generated path from the camera. With

bidirectional path tracing, we can more consistently find

paths that have some contribution to the scene.

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1. Generate two paths, one from a light source and one from the camera.
2. Looping over the lengths of each path, connect all possible paths from the light source to the camera and determine the total contribution of each path
3. Calculate the weight on the current path contribution by taking into account all the possible ways that the path could have been formed

Veach, Eric, and Leonidas Guibas. ‘Bidirectional Estimators for Light Transport’. Photorealistic Rendering Techniques, edited by Georgios Sakas et al., Springer Berlin Heidelberg, 1995, pp. 145–167.

Possible Paths

Traditional Path Tracing vs BDPT at 128 spp (no MIS)

MIS (buggy)

GGX BRDF

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Sampling: Distribution:

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Masking Shadowing Function:

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Walter, Bruce, et al. ‘Microfacet Models for Refraction through Rough Surfaces’. Proceedings of the 18th Eurographics Conference on Rendering Techniques, Eurographics Association, 2007, pp. 195–206. EGSR’07.

Results

Comparison: Beckmann

Contest Submission

Progressive Photon Mapping and a Step Towards Verified Rendering

Nathan Glover

Math Bugs - The Worst Kind of Bug

• Normalizing ray directions
• Dividing by negative or zero PDFs
• Passing the wrong input to a BSDF or a PDF
• Forgetting a cosine term
• Segfaults, accidental mutation, race conditions, and more

All of these are incredibly easy to do, and incredibly hard to catch…

If only there were a way to catch them before running the code!

Future Work on Performant, Verified Rendering

• Summer project: Type system inspired by the Lean proof assistant (take 21-321 to learn more) and CMU professor Jan Hoffman’s research
• Further strengthen the type system in my Rust raytracer

End Goal: A formally verified path tracer: Computer-checked proof that the code yields an unbiased estimate of the scene.

Progressive Photon Mapping

A biased approach to annoying light paths; precompute them and store them in a map.

Take a density estimation from the map while path tracing.

Progressive photon mapping averages this process over smaller and smaller density kernels.

Comparison (Underwater)

Path Tracing: 512 spp, 10 minutes

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Progressive Photon Mapping:

256 million photons, 64 iterations, 1 spp

4 minutes, including photon map building

Comparison (Dragon)

Path Tracing: 512 spp, 7 minutes

Progressive Photon Mapping:

64 million photons, 64 iterations, 1 spp

3 minutes, including photon map building

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Rendering Competition:

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Pet Trout

Optimizing Bounding Volume Hierarchy Traversal with Vectorized Instructions

Grey Golla

What’s a BVH?

• Tree-like structure for making ray-scene intersections O(log(n))
• Partition space into 2(?) pieces along an axis
• Intersect ray with bounding box, skip all children if ray does not
• NOT quite a tree traversal
• Ray can intersect both children
• Child bounding boxes can overlap

What are Vectorized Instructions?

• Single Instruction Multiple Data
• Hardware support for operating on small vectors
• Generally only do elementwise operations
• Add, multiply, abs, min/max, compare
• Modern vector instructions support 4/8/16 element vectors

https://www.sciencedirect.com/topics/computer-science/vectorization

Main Approach

• Widen each BVH node
• Instead of 2 children, have one child per vector slot
• Compute intersection with all children in parallel
• Sort the children by the intersection time
• Earlier intersections occlude later ones

Results

5x more intersections

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Same total runtime

8x more intersections

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3x total runtime

Discussion

• 8-wide BVH is much less efficient than “normal” 2-wide
• Need 5-8x as many intersection tests for same render
• Non-branching, non-pointer chasing intersection tests are much faster
• 2-4x faster than existing DIRT implementation
• Hand-tuning AVX2 vector instructions is a cherry on top
• 25-30% faster than compiler optimized code
• DIRT’s BVH building routine is bad
• Hard to draw good conclusion about useful speedup

Next Steps

• Make a better BVH builder
• Surface area heuristic
• Search for good split planes
• Further optimize traversal
• Switch to progressive iterative approach
• Finish coherent ray bundle tracing

https://rgl.s3.eu-central-1.amazonaws.com/media/papers/NimierDavidVicini2019Mitsuba2_7.pdf

Layered Materials

Dakota Hernandez

Approach

Lambertian vs (Dielectric <-> Homogeneous <-> Lambertian)

Final Scene

Procedural Textures

15-668 Final Project Presentation

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PSS MLT and Depth of Field

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Dakshit Agrawal

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Primary Sample Space

Metropolis Light Transport

(PSS MLT)

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Path Space

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Figure credits: Course slides

Primary Sample Space

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Figure credits: Course slides

Primary Sample Space

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Figure credits: Course slides

MLT Integrator

• Used to estimate the rendering equation “f”

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MLT Integrator

• Used to estimate the rendering equation “f”
• Phase 1: calculate normalization constant “b = f/p”
• Sample “N” seed paths
• Pass them to the underlying path tracer and average the returned pixel values

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MLT Integrator

• Used to estimate the rendering equation “f”
• Phase 1: calculate normalization constant “b = f/p”
• Sample “N” seed paths
• Pass them to the underlying path tracer and average the returned pixel values
• Phase 2: sample via path mutations
• Generate “k” sequences of correlated samples using Metropolis-Hastings algorithm
• Pass these sequences to the underlying path tracer and accumulate pixel values

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MLT Integrator

• Used to estimate the rendering equation “f”
• Phase 1: calculate normalization constant “b = f/p”
• Sample “N” seed paths
• Pass them to the underlying path tracer and average the returned pixel values
• Phase 2: sample via path mutations
• Generate “k” sequences of correlated samples using Metropolis-Hastings algorithm
• Pass these sequences to the underlying path tracer and accumulate pixel values
• Normalize accumulated pixel value by multiplying with “b/k”

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Results

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PSS MLT with MIS Path Tracing (N=20)

Results

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Only MIS Path Tracing

Results

86

PSS MLT with N=100

Depth of Field

87

Depth of Field

88

Depth of Field

89

Figure credits: Wikipedia

Depth of Field

90

Figure credits: Wikipedia

Depth of Field

91

Figure credits: Wikipedia

Bokeh

92

Square

Bokeh

93

Diamond

Bokeh

94

Triangle

Rendering Competition Submission

95

Map the Photons

Alan Lee

Recall the process…

Direct density estimation

Spatial data structure (KD-tree)

Recall the better processes…

Caustic map

“Final gather”

i.e. path trace until hit second non-specular surface from camera

i.e. store only photons of L(S+)D paths

Photon map visualizations

+

=

Non-caustic only

Caustic only

Combined

Glass

Mirror (metal)

(2,000,000 photons)

*Distorted due to incomplete mapping to camera aperture

Parameter comparisons

(20,000 photons, basic)

10N

100N

300N

500N

Reference (MIS)

*All renders are 100 samples per pixel

Parameter comparisons

(20,000 photons, 100N)

Reference (MIS)

Improved (final gather 3S)

Basic

1.86 min

10.10 min

1.86 min

Parameter comparisons

(20,000 photons, 100N)

Basic

Final Gather 3S

Final Gather 3S + Caustic Map

Parameter comparisons

(Gather 3, 100N)

2,000 + 500

20,000 + 5,000

200,000 + 50,000

Non-caustic + Caustic photon counts

Rendering competition!

Implementation of ReSTIR algorithm

Following Bitterli et al.’s 2020 paper ¹�Loïc LESCOAT - May 4 2022

¹See paper here: https://cs.dartmouth.edu/wjarosz/publications/bitterli20spatiotemporal.html

Render above NOT made using ReSTIR²

Every frame rendered independently :(

Motivation of ReSTIR:

• Reduce cost of rendering new frame/pixel

How?

• Reuse information from previously rendered frame/other pixels in image when rendering new frame/pixel, using a Reservoir

² Visible here (in lower resolution): https://youtu.be/lMy_Y10duuo

Applying ReSTIR to our Specific Problem

• Direct lighting only
• One reservoir per (pixel, intersection point) pair: holds a point on a light source

Benefits of ReSTIR: Camera movement

If camera moves between frames: change which reservoir we look at in previous frame

Temporal reuse only

Benefits of ReSTIR: Combining Reservoirs

No spatial/temporal reuse

Spatial reuse

Temporal reuse

Rendering Competition Submission

“Wavy Forest: A Bird’s Eye View”

Image clarity made possible with ReSTIR’s temporal reuse

Visible here (in lower resolution): https://youtu.be/MmO_otHGyzc

240 frames

Contents:

• Benefits of ReSTIR: greater speed and lower variance
• Consistency of our implementation
• Extra features:
• Cube primitive
• Cylinder primitive
• Normal mapping
• Wood-like procedurally-generated texture

Annex

Benefits of ReSTIR: Greater Speed and Lower Variance

“Path_tracer_nee” integrator

(with max_bounces == 1)

Four samples per pixel

448 seconds

Our implementation

One sample per pixel

220 seconds

Benefits of ReSTIR: Reduced variance

ReSTIR improves the quality of light sampling

“Path_tracer_nee” integrator

(with max_bounces == 1)

Our implementation

Four samples per pixel

Consistency of our implementation of ReSTIR

Using temporal reuse, stationary camera, no spatial reuse

Ground truth

(“path_tracer_nee” integrator with max_bounces == 1)

Rendered using our implementation of the unbiased

algorithm

Consistency of our implementation of ReSTIR

Using temporal reuse, stationary camera, no spatial reuse

Extra Features

Normal-mapping support

No normal map: flat appearance

Normal map: relieved appearance

Extra Features

Cube primitive, cylinder primitive, and wood-like texture

Bonus: zoom-in on normal map as light moves overhead

Thank you for listening!

SGGX Microflake Distribution & Layered Material with Statistical Operator

Weisheng Li

Anisotropic RTE

Can be used for rendering cloth, hair, skin and other volumetric material that have anisotropic structures.

RTE (or volume rendering equation) we learned in class:

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Anisotropic RTE:

Microflake Theory

Analogous to the microfacet, but in a volume

SGGX Distribution

Define projected area rather than NDF

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Orthonormal Eigenvectors

Squared Projected Area

We can then use S to recover projected area and NDF

Layered Material

• BSDF Lobe:

Contains directional statistics (energy, mean and variance)

• Adding-Doubling

Combine statistics from two layers into one

Algorithm

For each layer i:

Use Adding equation to compute the statistic from layer 0 to layer i

Spawn a BSDF lobe based on the statistic

Use MIS (weighted by energy) to sample and compute PDF based on ALL BSDFs

Competition Submission

Reference

• The SGGX microflake distribution [Heitz et al. 2015]
• A radiative transfer framework for rendering materials with anisotropic structure [Jakob et al. 2010]
• Efficient Rendering of Layered Materials using an Atomic Decomposition with Statistical Operators [Laurent Belcour 2018]

GGX, Orthographic Camera, Non-Exponential Media, and BRDF Space Learning

Yehonathan Litman

GGX BRDF

Beckmann vs. GGX

Orthographic Camera Model

Non-Exponential Media

Homogeneous + Heterogeneous:

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Original:

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Mine:

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Whereas exponential radiative transfer tries to model interaction process of light with scattering particles, non-exponential radiative transfer estimates the average behavior of light in a medium

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Bitterli, B., Ravichandran, S., Müller, T., Wrenninge, M., Novák, J., Marschner, S., & Jarosz, W. (2018). A radiative transfer framework for non-exponential media. ACM Transactions on Graphics (TOG), 37, 1 - 17.

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Learning in BRDF Space

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Zhang, X., Srinivasan, P.P., Deng, B., Debevec, P.E., Freeman, W.T., & Barron, J.T. (2021). NeRFactor: Neural Factorization of Shape and Reflectance Under an Unknown Illumination. ACM Trans. Graph., 40, 237:1-237:18.

Rendering Competition Image

Specular Manifold Sampling

Shilin Ma

Manifold Next Event Estimation

Paper:https://onlinelibrary.wiley.com/doi/10.1111/cgf.12681, image: https://rgl.epfl.ch/publications/Zeltner2020Specular

Only ONE solution

Specular Manifold Sampling (unbiased)

Basin of Convergence

Results

Reference (50000 spp)

SMS (64 spp)

Importance Sampling the Environment Map

Examples

With importance sampling

No importance sampling

Renders

Competition entry

Primary Sample Space MLT

& Delayed Rejection

MAY 4^TH 2023

Yuan Meng

Implementations

• Primary Sample Space MLT(Gaussian + Large Step)
• Delayed Rejection PSSMLT(Kelemen + Wrapped Cauchy + Large Step)
• Sample time to generate motion blur picture (to sum up to 12 points)

Core: Main MLT Loop

144

Core: PSS Sampler

• Make Sampler->next1D() & Sampler->next2D() return random float after mutation. (Proposal)
• Keep the information of random numbers before mutation in case we need to reject.
• A PSS sampler can be applied to any integrator

145

Improvements on PSSMLT

• Adaptive Parameter
• Perturbations
• Gradient Based
• Delayed Rejection (kind of adaptive)
• If an aggressive step gets rejected, try with a smaller step

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146

Delayed Rejection

• Q2 Can be cancelled out if symmetric
• Q1 need special design to be cancelled out: Circular Distribution
• Treat primary samples as 2D pairs.
• Mutate two PSs at a time.

147

Comparison & Insights

Path Tracer

148

Comparison & Insights

PSSMLT

149

Comparison & Insights

PSSMLT-smaller step

150

Comparison & Insights

PSSMLT

151

Comparison & Insights

Delayed Rejection

152

Comparison & Insights

• MCMC focuses more on light regions, which makes the dark region more noisy
• MCMC takes longer time to render a same spp image

153

References

• [1] Csaba Kelemen, László Szirmay-Kalos, György Antal, and Ferenc Csonka. 2002. A Simple and Robust Mutation Strategy for the Metropolis Light Transport Algorithm. Computer Graphics Forum 21, 3 (Sept. 2002), 531–540
• [2] Damien Rioux-Lavoie, Joey Litalien, Adrien Gruson, Toshiya Hachisuka, and Derek Nowrouzezahrai. Delayed Rejection Metropolis Light Transport. ACM Transactions on Graphics, 39(3), Article 26, May 2020.�

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Progressive Photon Mapping

Bharath Raj Nagoor Kani

Overview

• I was interested in adding features to DIRT such that I could render a swimming pool realistically.
• The integrators currently available in DIRT cannot handle paths of type L(S+)D(S+).
• Unfortunately, those path types commonly occur in the scenes that I am interested in rendering.
• To overcome this issue, I added support for Photon Mapping in DIRT.

Overview

• I experimented with improving photon mapping by:
• Using a separate caustic map
• Performing final gather
• Implementing progressive photon mapping
• I also implemented additional tiny features such as the GGX BRDF and a directional light source

Photon Mapping

• Two Pass Algorithm
• Pass 1: Trace photons from a light source and cache them in a photon map.
• Pass 2: Approximate indirect illumination using the cached photons.

Pass 1

Pass 2

Photon Mapping

• Pass 1:
• Photon location and direction is sampled from a random light source.
• Photon is scattered throughout the scene. Photon records are stored at diffuse interactions.
• Scattering is terminated using Russian Roulette.
• Once photon tracing is complete, a cache with all photon records is saved as a json file.

Photon Mapping

• Pass 1:
• When using the photon mapping integrator, photon tracing performed only if the cache does not exist on disk.
• The cache is parsed and loaded onto a KDTree for efficient nearest neighbor queries (which will be useful in Pass 2)

Photon Mapping

• Pass 2:
• Shoot a ray into the scene and recurse until a diffuse interaction is reached.
• Find all photons that exist within a pre-defined radius.
• Calculate the approximate radiance value using the density of photons.

Photon Mapping

• Experiments:

PM (without russian roulette)

PM (with russian roulette)

Photon Mapping

• Experiments:

Experimenting with changing the radius (50000 photons used for each scene)

Radius = 30

Radius = 15

Radius = 5

Radius = 3

Photon Mapping

• Experiments:

Experimenting with changing the number of photons (radius is 30 for each scene)

#Photons = 50000

#Photons = 5000

#Photons = 500

#Photons = 50

Photon Mapping

• Experiments:

MIS

PM

Photon Map Visualization

Photon Mapping

• Experiments:

MIS

PM

Photon Map Visualization

Photon Mapping

• Experiments:

MIS

PM

Photon Map Visualization

Photon Mapping++

• Enhancements:
• Use two photon maps – one caustics photon map and one global photon map.
• The caustics photon map records photons at all diffuse interactions that happen immediately after a specular interaction.
• The global photon map records photons at all diffuse interactions that DO NOT happen immediately after a specular interaction.
• Both maps are created independently.

Photon Mapping++

• Enhancements:
• Add an option to perform final gather.
• Perform ray tracing until the next diffuse interaction and then perform density estimation at that interaction.

Photon Mapping

• Experiments:

MIS

PM

PM++

Photon Mapping

• Experiments:

PM++

Caustics Photon Map Visualization

Global Photon Map Visualization

Photon Mapping

• Experiments:

MIS

PM

PM++

Photon Mapping

• Experiments:

PM++

Caustics Photon Map Visualization

Global Photon Map Visualization

Photon Mapping

• Experiments:

PM++ (without final gather)

PM++ (with final gather)

Photon Mapping

• Experiments:

MIS

PM

PM++

Photon Mapping

• Experiments:

PM++

Caustics Photon Map Visualization

Global Photon Map Visualization

Progressive Photon Mapping

• Perform N runs of photon mapping, where each run uses a different radius for density estimation.
• Each run uses the same photon map.
• The radius for some step i+1 can be obtained using the relation (here, alpha is a hyper parameter that is set by the user):
• The renders obtained using N runs are then averaged to create the final rendering.

Progressive Photon Mapping

Stacked Output

Radius = 20.00, i = 0

Progressive Photon Mapping

Stacked Output

Radius = 14.79, i = 3

Progressive Photon Mapping

Stacked Output

Radius = 9.89, i = 20

Progressive Photon Mapping

Stacked Output

Radius = 8.38, i = 40

Additional Features

• GGX BRDF

Additional Features

• Directional Light Source

Rendering Competition Submission

• Performed progressive photon mapping.
• Aggregated the results of 40 photon mapping runs.
• Alpha = 0.5, Radius of first run = 20.0
• Used separate caustic and global photon maps.
• Russian roulette was used to terminate scattering during photon tracing.
• Next slide displays the submission image in higher resolution.

Thank you!

Ruben Partono

Normal Maps

We must leverage the wealth of (free!) assets on the internet.

Normal maps are a great way to add realistic detail.

Get a local coordinate frame based on the normal, dp/du, and dp/dv vectors.

Spotlight

Add a linear falloff to emission past a certain angle.

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Useful for dramatic effect!

Rough Dielectric (Beckmann)

• Specular reflection and refraction (w/ dielectric Fresnel)
• Sample normals from the Beckmann microfacet distribution
• Be extra careful with pdf calculation!

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Volume Renderer

• There were problems with the calculations for transmission times emission in our volume renderer.
• The rendering below successfully shows shadowing and scattering.

Surfaces on Volumes

Subsurface Scattering (BSSRDF)

Implementation unfinished.

Sample nearby points on a surface by casting a ray from a random point on a disk above the surface. (Done)

Calculate the Directional Dipole BSSRDF. (Unfinished).

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For more, see PBRT and the directional dipole paper.

Rendering Competition Submission

Ajax Shung

Rendering Wood

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Basic Structure - Distorting it leads to figure

[NC Brown Cen-

ter for Ultrastructure Studies, SUNY College of Environmental Sci-

ence and Forestry, Syracuse, NY]

Simple BRDF (But loses energy)

Surface BRDF +

Fresnel Factor * (diffuse + “specular”)

Better is to use SGGX microflake distribution that approximates fibers

Make out ellipsoids very long in the grain direction, then use specular flakes

Don’t have to sample BRDF and get energy conservation as a bonus so we can get rid of the random diffuse term

How to get Grain Direction?

Just make our tree a tube…

Then deform it and use jacobian of the deformation to get grain direction

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Mainly deform radially and transversally

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Knots

How do we get the grain direction now?

How do we even know what the grain should look like?

I want the tube back

Connect the rings by smoothing radial distance (aka age)

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What about dead knots? :( Discontinuity. Tree doesn’t even know what it should do :(

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Curly Figure - Highlights Move

Competition Image

Practical Path-Guiding

Gustavo Silvera

15-468 Final Project S’23

Based on papers:

[1] Practical Path Guiding for Efficient Light-Transport Simulation - Thomas Müller, Markus Gross, Jan Novak. Proceedings of EGSR 2017, vol. 36, no.4

[2] “Practical Path Guiding” in Production - Thomas Müller, SIGGRAPH 2019

What is Path Guiding?

Allow path-tracing algorithms to iteratively “learn” how to construct high-energy light paths [1]

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Goal: importance sample the integral

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Learns an approximation of incident radiance L_i and samples ω_i proportionally [2]

Combined with (standard) BSDF sampling via multiple-importance sampling (MIS) to reduce variance

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Iterative learning: Rendering is split into several passes to progressively learn incident-radiance approximations with better predictions (from the previous pass). Final pass is only inference.

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Key Terms: Data-driven, Reinforcement learning, Progressive, Unbiased

“Follow the Light”

Credits: Intel

BSDF sampling

PG sampling

How is this practical?

Primary data structure for 5D lightfield (x, y, z, phi, theta) → SD-tree

Spatial-Directional Tree:

• First partitions space (x,y,z) with adaptive KD-tree
• Leaves of the D-tree contain a quadtree for the directional domain

Enables logarithmic complexity for queries

Image credit: [2]

Scatter distribution

No path guiding

Path guiding

Path guiding (moved light)

Comparison images @ 64spp mine

Improvements (Stochastic Spatial Filter)

Integrating into Mitsuba3

Therefore, per bounce keep track of:

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Let x’ = last bounce with L(e→x’) > 0

After the path, loop and compute:

• L(x) => T(x’) / T(x)

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Finally can use x, d, & L(x)

Image credit: Mitsuba3 Docs

Mitsuba comparison mine

Mitsuba comparison mine

Mitsuba comparison mine

Final Render

Image: 1000x1000 @ 19k spp

(~1k spp for training)

Compute: ~7h @ 10c

Memory: 26 Gb

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Assets: PolyHaven, SketchFab

Made in: Blender(Using Mitsuba plugin for export)

Full credits list

Final Render (ref)

Image: 1000x1000 @ 20k spp

(no training)

Compute: ~5.5h @ 10c

Memory: 26 Gb

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Assets: PolyHaven, SketchFab

Made in: Blender(Using Mitsuba plugin for export)

Full credits list

Final scene scatter distribution comparison

Subsurface Scattering and Spectral Rendering

Jacky Sun

Subsurface Scattering with BSSRDF

• Rendering Equation

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• Separable BSSRDF

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• Precompute Profile Table (Photon Beam Diffusion Technique)

[1] Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, Pat Hanrahan. A Practical Model for Subsurface Light Transport. 2001

[2] Physically Based Rendering: From Theory To Implementation, 3rd Edition.

[3] Habel, R., P. H. Christensen, and W. Jarosz. Photon beam diffusion: a hybrid Monte Carlo method for subsurface scattering. 2013

Sampling BSSRDF

• Sample on a disk first, and raycast back onto geometry
• Select among 3 axis
• Store all intersections within range

uniformly sample one of them

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• Sample ω_i using surface BSDF with dummy ω_o

BSSRDF Results

Lambertian

SSS

(Glossy Surface)

SSS

(Rough Surface)

Spectral Rendering

• RGB Model is physically incorrect
• Human perceive wavelengths from about 400 - 700 nm
• Use Spectral Power Distribution(SPD) instead of RGB
• Convert between RGB and SPD with CIE XYZ mapping

Spectral Rendering

• Upsampling existing material
• Perform only SPD calculations during path traversal

1 spp

32 spp

Extras - Microfacet Refractions

• Microfacet BRDF

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• Microfacet BTDF

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• BSDF = BRDF + BTDF
• GGX + Smith approximation

[2] Bruce Walter1, Stephen R. Marschner, Hongsong Li, Kenneth E. Torrance. Microfacet Models for Refraction through Rough Surfaces. 2007

Extras - Microfacet Refractions

Roughness: 0

(Specular)

Roughness: 0.2

Roughness: 0.02

Roughness: 0.5

Wavelength Dependent Refraction

• IOR can be approximated with a function of λ

The Sellmeier Equation:

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• Let rays carry wavelength sample(s), and generate path based on λ
• Stratified Wavelength Sampling
• Spectral BSDFs

Approximation:

[3] Glenn F. Evans, Michael D. McCool. Stratified Wavelength Clusters for Efficient Spectral Monte Carlo Rendering. 1999

Wavelength Dependent Refraction

• Hero Wavelength Sampling(TODO)

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• Any of them can be hero

[4] Alexander Wilkie, Sehera Nawaz, Marc Droske, Andrea Weidlich, and Johannes Hanika. Hero wavelength spectral sampling. 2014

Spectral Rendering Result

without wavelength sampling

with wavelength sampling

Problems

• Hard to obtain LSSDE spectrum
• Convergent speed is EXTREMELY slow
• Compatibility

Image for Contest

Placeholder: Wojnovich, Davis

Bi-Directional Path Tracing

• Leverage Symmetry of Light Transport
• Trace from the Sensor and Light → Deterministic step.

Veach, E., Guibas, L. (1995). Bidirectional Estimators for Light Transport. In: Sakas, G., Müller, S., Shirley, P. (eds) Photorealistic Rendering Techniques. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87825-1_11

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Results

• Able to Generate paths with zero and one light vertex
• Paths with amounts of light vertices suffer from a buggy direct connection function.

Zero Light Vertices

NEE / One Light Vertex

Arbitrary Connections (Buggy)

Render Competition

Mewtwo Model by Luca Romagnoli

https://www.cgtrader.com/yumekofigure

Mewtwo is intellectual property owned by the Pokemon Company

Depth of Field and Bidirectional Path Tracing

Wenlong Yan

Placeholder: Yan, Wenlong

Features

• Depth of Field� Objects within the target focal range to be rendered sharply. Objects outside the focal range are rendered blurred.�
• Bidirectional Path Tracing� Sample two paths starting from the camera and from the light sources, then connect two sets of paths to form complete paths of rendering

Depth of Field

• Our “camera” : puts everything in focus
• Real camera: objects that are too far or too close will lose focus

Credit: Wikipedia

Depth of Field

• Our “camera” : puts everything in focus
• Real camera: objects that are too far or too close will lose focus

Credit: Wikipedia

Results - DOF - Aperture

Aperture 10

Aperture 50

Aperture 90

Focal distance 1300

Results - DOF - Focal Distance

Focal distance 900

Focal distance 1300

Focal distance 1700

Aperture 50

BDPT-Path Generating

• Two subpaths: light and camera
• Generating subpaths
• Sample point on light source/camera lens
• Generate random ray
• Trace rest of path using BSDFs of materials
• Russian Roulette for camera subpath
• Connecting subpaths:
• Check for visibility of connecting vertices
• Check if BSDF scatters light in direction formed by connecting vertices

Result - BDPT (40spp)

Simple Path Tracing

Path Tracing With MIS

Bidirectional Path Tracing�(buggy)

Image for Contest

Placeholder: Yarlott, Lance

Polynomial Optics (and some PSSMLT)

Polynomial Optics: Overview

• Lenses affect light paths
• These effects can be explained through equations

M. Hullin et al.�Ray intersection with spherical interface

• Equation can be expanded
• Ray deflections simulated

Polynomial Optics: My Implementation

• Paper’s implementation hard-coded polynomial expansions
• I used a slightly simpler implementation, using the ray transfer matrix
• Allows for ray manipulation
• Allows for lens simulation
• Needed to convert ray dir into two separate angles
• Also needed to map to standard range
• Caused bugs
• Incomplete but close to functional for various lens types

Source: Wikipedia - Ray transfer matrix analysis

Buggy Image Lightning Round & Post Mortem

PSSMLT: What I Learned from a Failed Implementation

• It’s difficult!
• Generating arbitrary amounts of random numbers isn’t the way to go
• Leads to crashes
• Path mutations, while somewhat simple in concept, are tricky to implement

Where I could have improved:

• Carefully extract calls to samplers from path tracing functions
• Ensure that no “bad data” gets into functions (empty arrays, etc.)
• Set up a thorough error-checking pipeline before beginning
• Print statements aren’t enough sometimes

Source: Kelemen et al.

Competition Image

Spectral Rendering

Ziwen Ye

Hero Wavelength sampling

Naive

Herowavelength

Failure cases

Spectrum light and Material

solar spectral irradiance

Copper

Spectral Tracking (Heterogeneous Medium)

Ground Truth

Delta Tracking

Spectral Tracking(Buggy)

Spectral Tracking (Chromatic Medium)

Delta

Spectral

Competition Submission

Placeholder: Zhang, Arthas

Fun with Material and Texture

Lingxi Zhang

Confidential

Customized for Lorem Ipsum LLC

Version 1.0

Worley Noise Basic Version

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Worley Noise Premium Version

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Idea

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t = c * d1

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t = c * d2

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Competition

Bump Mapping vs Displacement Mapping

Core Idea : Fake the Normals!

We want

Instead of getting the real x’

How about we just have a n’ for shading so that it looks like x’?

Some Math Work

n

dx/du

dx/dv

More Math Work

Implementations : texture!

Small problem :

Result

Result

Thank you.

Can range analysis help raycasting?

Tianyuan Zhang

Physics-based rendering course project, 2023 Spring

Range analysis for ray-casting

∈ [?, ?]

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NN

x ∈ [-1, 1]

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range tracing / interval tracing

range query

Sharp, N., & Jacobson, A. (2022). Spelunking the deep: guaranteed queries on general neural implicit surfaces via range analysis. ACM Transactions on Graphics (TOG), 41(4), 1-16.

range analysis for neural networks

x ∈ [-1, 3]

3

2

-1

2

3x

2x

y = 4x ∈ [-4, 12]

x ∈ [-1, 3]

ReLU

y = x + 0.75 𝞮; 𝞮∈ [0.25, 0.75]

auxiliary range variable

non-linear layers

linear layers

Compare sphere trace with range trace

wood

acropolis

galaxy

Range trace

Sphere trace

Computational cost

Range trace is slower and needs more iterations!

Results for inverse rendering

Range trace

Sphere trace

Range trace gives more stable and faster convergence!

Summary

Range analysis helps:

• Inverse rendering ✅
• Forward rendering ❌

Position-Free Monte Carlo Unidirectional Simulation for Layered Material

Robin Zheng

How “position-free” ?

• Position + direction -> Depth + direction
• Ignoring displacement of scattering location
• Assume layered material is locally uniform

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Why “position-free” ?

• Fast - we skip intersection check when tracing light locally
• Low variance - rolling up light throughput locally rules out geometric terms
• Free to adjust - each layer are represented independently, quite few assumptions and limitations

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Light Path Integral

Path contribution as product of vertex terms and segment terms

Light Path Integral (Cont.)

Segment terms taking depth and obtaining length measure

Then we evaluate BSDF as…

Position-Free In DIRT

sample -> now returns throughput directly after tracing a light path, equivalent to eval/pdf

pdf-> since we don’t use MIS, left blank

eval-> left blank, see evalandSampleNewDir

evalandSampleNewDir->evaluate f(w_i, w_o) and sample a new direction. Used for NEE

Multilayers are implemented recursively

Problems encountered..

• Double counting throughput..
• Forgetting jacobian…
• Highlight needs a special case!

Validation-No medium Interaction

ground truth

500 spp, with mixture sampling

6 minutes

500nd sample a new direction. Used for NEE

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Position-free Monte Caro withou NEE

3500 spp

6 minutes

500nd sample a new direction. Used for NEE

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Position-free Monte Caro with NEE

3500 spp

8 seconds

500nd sample a new direction. Used for NEE

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Validation-Medium Interaction

ground truth

500 spp, with mixture sampling

6 minutes

500nd sample a new direction. Used for NEE

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Position-free Monte Caro withou NEE

3500 spp

6 minutes

500nd sample a new direction. Used for NEE

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Position-free Monte Caro with NEE

3500 spp

8 seconds

500nd sample a new direction. Used for NEE

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Interesting results!

Contest Submission

References

Yu Guo, Miloš Hašan, and Shuang Zhao. 2018. Position-Free Monte Carlo

Simulation for Arbitrary Layered BSDFs. ACM Trans. Graph. 37, 6, Article 279

(November 2018), 14 pages. https://doi.org/10.1145/3272127.3275053

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Snake Tattoo

https://www.freepik.com/free-vector/vintage-tattoo-monochrome-concept_8136386.htm#query=dagger%20tattoo&position=3&from_view=keyword&track=ais

Designed by dgim-studio / Freepik

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Texture flower:

https://pngtree.com/freepng/floral-pattern-design_3780732.html

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Texture fish scale:

https://previews.123rf.com/images/milatoo/milatoo1607/milatoo160700037/61123985-fish-skin-repetition-texture-modern-scale-stylish-texture-repeating-geometric-background-with.jpg

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Hand model:

https://free3d.com/3d-model/hand-v3--902450.html

Thank you!