photo2|render - photo|render

02941 Physically Based Rendering and Material Appearance Modelling

Course description from the DTU course catalogue

Course overview

How the text book "Physically Based Rendering (3rd edition)" is used in the course

Course prerequisites and links to programming resources


Calendar dates: 1 June to 22 June (starts on a Thursday, 5 June is a holiday)
Location: Building 305, Room IT005 and Zoom (Zoom link is available on DTU Learn)
Daily schedule: Workdays 9-12 (lecture followed by exercises with an option to get help)

Afternoons (except the last day) are set off for studying and doing independent work on exercises.

The last day is set off for preparation and presentation of a slide that presents the work in your lab journal.
The slide is to be prepared in the morning and presented in the afternoon.

Lab journal and presentation slide hand-in deadline: 23:59 Friday 23 June 2023.

Textbook and Notes

The main textbook for this course is

P Pharr, M., Jakob, W., and Humphreys, G. Physically Based Rendering: From Theory to Implementation, third edition. Morgan Kaufmann/Elsevier, 2017. [webpage] [DTU Findit access]

In addition, papers will be uploaded to DTU Learn that serve sometimes as supplementary reading material sometimes as part of the curriculum (see also resources for the exercises below).


Lecture 1: Introduction and ray tracing of direct illumination.

Supplement to Lecture 1 from 02562 Rendering - Introduction: On triangle meshes, the main loop, and shading. [2022]

Lecture 2: Sun, sky, colour, and environment maps.

Lecture 3: Specular objects (reflection, transmission, and Russian roulette).

Supplement to Lecture 3 from 02562 Rendering - Introduction: On the directions of reflection and refraction. [2022]

Lecture 4: Monte Carlo integration.

Supplement to Lecture 4 on rotation of directions sampled in spherical coordinates: Combing hair and sampling directions [slides]. [2021]

Lecture 5: Path tracing.

Lecture 6: Microfacet models.

Lecture 7: Volume rendering.

Lecture 8: Material appearance modelling and the LMabs demo/code.

Lecture 9a: Overview of graphics models for acquiring the optical properties of translucent materials [slides] (EG 2020 STAR).

Lecture 9b: On the role of surface microstructure in modeling and rendering of material appearance (CIRP Winter Meetings 2021 slides).

Lecture 10: Dispersion and spectral rendering.

Lecture 11: Particle tracing and photon mapping.

Lecture 12: Subsurface scattering.

Lecture 13a: Directional dipole model for subsurface scattering. (SIGGRAPH 2015 slides)

Lecture 13b: Directional subsurface scattering.

Lecture 14: Camera and eye models. [2022]

Lecture 15: Photo-render comparison. [2022]


Worksheet 1: Ray tracing an indexed face set, direct illumination of diffuse surfaces.

Worksheet 2: Rendering with analytic sun and sky models and with environment maps.

Worksheet 3: Reflection and refraction, Russian roulette, specular surfaces (glass and metals).

Worksheet 4: Monte Carlo integration, direct illumination, ambient occlusion.

Worksheet 5: Path tracing, global illumination, splitting vs. Russian roulette.

Worksheet 6: BRDF, glossy materials, microfacet models.

Worksheet 7: Path tracing homogeneous volumes, absorption, scattering.

Worksheet 8: Material appearance modelling.

Resources for the exercises

Frisvad, J. R. Electromagnetic Radiation. In Light, Matter, and Geometry: The Cornerstones of Appearance Modelling, Chapter 4. PhD thesis, Technical University of Denmark, May 2008.

Walter, B., Marschner, S. R., Li, H., and Torrance, K. E. Microfacet models for refraction through rough surfaces. In Proceedings of Eurographics Symposium on Rendering (EGSR 2007), pp. 195-206. 2007.

Lorenz-Mie code for computing the scattering properties of participating media (Worksheet 8).

Hannemose, M., Doest, M. E. B., Luongo, A., Gregersen, S. K. S., Wilm, J., and Frisvad, J. R.. Alignment of rendered images with photographs for testing appearance models. Applied Optics 59(31), pp. 9786-9798. November 2020.

Input data for renderer in photo-render comparison (Lecture 15): H. C. Ørsted bust, cupped angel, bunny.

Glare demo for the exercise about camera and eye models.

Links to free books

Glassner, A. S. (ed.) An Introduction to Ray Tracing. Morgan Kaufmann, 1989.

Cohen, M., and Wallace, J. R. Radiosity and Realistic Image Synthesis. Academic Press, 1993.

Glassner, A. S. Principles of Digital Image Synthesis. Morgan Kaufmann, 1995.

Dutré, P. Global Illumination Compendium: The Concise Guide to Global Illumination Algorithms. August 2003.

Shirley, P. Ray Tracing in One Weekend. January 2016.

Pharr, M., Jakob, W., and Humphreys, G. Physically Based Rendering: From Theory to Implementation, third edition. Morgan Kaufmann/Elsevier, 2017. [webpage]

Haines, E., and Akenine-Möller, T. (eds.) Ray Tracing Gems. Apress, 2019.

Marrs, A., Shirley, P., and Wald, I. (eds.) Ray Tracing Gems II. Apress, 2021.

Old worksheets

Photon mapping including final gathering. (Worksheet 6, 2020)

Density estimation and photon differentials. (Worksheet 7, 2020)

Dispersion and spectral rendering. (Worksheet 8, 2020)

BSSRDF, subsurface scattering, single scattering, diffusion. (Worksheet 12, 2020)

Depth of field, glare, Fourier optics (Worksheet 13, 2018)

GPU accelerated rendering (Worksheet 2, 2012)

Ray tracing vs. real-time direct illumination (Worksheet 1, 2010)

Ray tracing vs. real-time reflections (Worksheet 2, 2010)

Ray tracing vs. real-time soft shadows (Worksheet 3, 2010)

Ray tracing vs. real-time metal and glass (Worksheet 4, 2010)

Spherical harmonics lighting (Worksheet 7, 2009, updated for 2010 but not used)

Precomputed radiance transfer and high dynamic range (Worksheet 8, 2009)


This course material was written by Jeppe Revall Frisvad, Associate Professor, DTU Compute, Technical University of Denmark.

© DTU Compute 2009-2023. All rights reserved.

Last updated 18 June 2023.