Eric Lengyel, Ph.D.

Eric Lengyel

Eric Lengyel (pronounced LENG · el, with no Y) is the founder of Terathon Software. He holds a Ph.D. in Computer Science from the University of California, Davis, and a Masters Degree in Mathematics from Virginia Tech.

Eric is the creator of the following technologies:

Eric is the author of the book series Foundations of Game Engine Development, and he is the editor for the Game Engine Gems series. Over 20 years ago, he wrote the first book focused on mathematics in games, the best-selling Mathematics for 3D Game Programming & Computer Graphics. Eric has also been a long-time member of the editorial board for the Journal of Graphics Tools, and he has been a major contributor to the successful Game Programming Gems series.

Eric is an active researcher in the field of projective geometric algebra and recently authored the book Projective Geometric Algebra Illuminated. The educational resources that he has created for this subject can be found on projectivegeometricalgebra.org.

Eric previously worked in the advanced technology group at Naughty Dog and the graphics and imaging department at Apple. Before those, he was the lead programmer for the fifth installment of Sierra Studio’s popular RPG adventure series Quest for Glory. When he’s not at his desk, Eric can usually be found running somewhere in the mountains of northern California.

Eric’s email address is lengyel at this website’s domain.

Books

PGAI Lengyel

Projective Geometric Algebra Illuminated

Terathon Software, 2024
ISBN: 979-8985358254
projectivegeometricalgebra.org

FGED1 Lengyel

Foundations of Game Engine Development, Volume 1: Mathematics

Terathon Software, 2016
ISBN: 978-0985811747
foundationsofgameenginedev.com

FGED2 Lengyel

Foundations of Game Engine Development, Volume 2: Rendering

Terathon Software, 2019
ISBN: 978-0985811754
foundationsofgameenginedev.com

Math3D Lengyel

Mathematics for 3D Game Programming & Computer Graphics, Third Edition

Cengage Learning, 2011
ISBN: 978-1435458864
mathfor3dgameprogramming.com

GEG1 Lengyel

Game Engine Gems 1

Jones and Bartlett, 2010
ISBN: 978-0763778880
gameenginegems.com

GEG2 Lengyel

Game Engine Gems 2

A K Peters, 2011
ISBN: 978-1568814377
gameenginegems.com

GEG3 Lengyel

Game Engine Gems 3

A K Peters, 2016
ISBN: 978-1498755658
gameenginegems.com

OpenGEX Lengyel

Open Game Engine Exchange Specification

Terathon Software, 2013, 2015, 2017, 2021
ISBN: 978-0985811785
opengex.org

IntroGD Lengyel

Mathematical Concepts
Introduction to Game Development, Second Edition

Cengage Learning, 2011
ISBN: 978-1584506799

Math3D Lengyel

Mathematics for 3D Game Programming & Computer Graphics, Second Edition

Cengage Learning, 2003
ISBN: 978-1584502777
mathfor3dgameprogramming.com

OpenGL Lengyel

The OpenGL Extensions Guide

Charles River Media, 2003
ISBN: 978-1584502944

Math3D Lengyel

Mathematics for 3D Game Programming & Computer Graphics

Cengage Learning, 2001
ISBN: 978-1584500377
mathfor3dgameprogramming.com

Papers and Gems

JCGT Lengyel

GPU-Centered Font Rendering Directly from Glyph Outlines
Journal of Computer Graphics Techniques
Vol. 6, No. 2

Eric Lengyel, 2017
sluglibrary.com

GEG3 Lengyel

The Open Game Engine Exchange Format
Game Engine Gems 3

Eric Lengyel, 2016
gameenginegems.com

GEG3 Lengyel

Fog with a Linear Density Function
Game Engine Gems 3

Eric Lengyel, 2016
gameenginegems.com

GEG3 Lengyel

Smooth Horizon Mapping
Game Engine Gems 3

Eric Lengyel, 2016
gameenginegems.com

GEG2 Lengyel

A Jitter-Tolerant Rigid Body Sleep Condition
Game Engine Gems 2

Eric Lengyel, 2011
gameenginegems.com

GEG2 Lengyel

Bit Hacks for Games
Game Engine Gems 2

Eric Lengyel, 2011
gameenginegems.com

GEG1 Lengyel

Motion Blur and the Velocity-Depth-Gradient Buffer
Game Engine Gems 1

Eric Lengyel, 2010
gameenginegems.com

GEG1 Lengyel

Moments of Inertia for Common Shapes
Game Engine Gems 1

Eric Lengyel, 2010
gameenginegems.com

JGT Lengyel

Transition Cells for Dynamic Multiresolution Marching Cubes
Journal of Graphics, GPU, and Game Tools
Vol. 15, No. 2

Eric Lengyel, 2010
transvoxel.org

JGT Lengyel

Unified Distance Formulas for Halfspace Fog
Journal of Graphics Tools
Vol. 12, No. 2

Eric Lengyel, 2007

JGT Lengyel

On Faster Sphere-Box Overlap Testing
Journal of Graphics Tools
Vol. 12, No. 1

Thomas Larsson, Tomas Akenine-Möller, and Eric Lengyel, 2007

GPG5 Lengyel

Oblique View Frustums for Mirrors and Portals
Game Programming Gems 5

Eric Lengyel, 2005

JGD Lengyel

Oblique Depth Projection and View Frustum Clipping
Journal of Game Development
Vol. 1, No. 2

Eric Lengyel, 2005

GPG3 Lengyel  Best Gems Lengyel

T-Junction Elimination and Retriangulation
Game Programming Gems 3
Best of Game Programming Gems

Eric Lengyel, 2002

Gamedev Lengyel

The Mechanics of Robust Stencil Shadows
Game Developer

Eric Lengyel, 2002

GPG2 Lengyel

Applying Decals to Arbitrary Surfaces
Game Programming Gems 2

Eric Lengyel, 2001

GPG1 Lengyel

Tweaking a Vertex’s Projected Depth Value
Game Programming Gems

Eric Lengyel, 2000

GPG1 Lengyel

A Fast Cylinder-Frustum Intersection Test
Game Programming Gems

Eric Lengyel, 2000

Gamedev Lengyel

Simultaneous Cross-Platform Game Development
Game Developer

Eric Lengyel, 2000

MacTech Lengyel

3D Graphics Engine Essentials
MacTech Magazine
Vol. 15, No. 6

Eric Lengyel, 1999

Speaking

NASA Projective Geometric Algebra Lengyel

Foundations of Projective Geometric Algebra

NASA Goddard Space Flight Center 2024
Greenbelt MD

GDC 2023 Lengyel

Practical Projective Geometric Algebra

Game Developers Conference 2023
San Francisco CA

GDC 2021 Lengyel

New Developments in Projective Geometric Algebra

Game Developers Conference 2021
San Francisco CA

i3D 2018 Lengyel

GPU-Centered Font Rendering Directly from Glyph Outlines

Symposium on Interactive 3D Graphics and Games 2018
Montréal QC, Canada

i3D 2018 Lengyel

GPU Font Rendering: Current State of the Art

Blizzard Seminar 2018
Irvine CA

GDC 2018 Lengyel

Linear Algebra Upgraded

Game Developers Conference 2018
San Francisco CA

GDC 2015 Lengyel

Game Math Case Studies

Game Developers Conference 2015
San Francisco CA

GDC 2014 Lengyel

Grassmann Algebra in Game Development

Game Developers Conference 2014
San Francisco CA

GDC 2012 Lengyel

Fundamentals of Grassmann Algebra

Game Developers Conference 2012
San Francisco CA

WSCG 2012 Lengyel

A Bigger Mathematical Picture for Computer Graphics

Winter School of Computer Graphics Keynote 2012
Plzeň, Czech Republic

Visualization Colloquium 2012 Lengyel

The Return of Forgotten Mathematics in Computer Graphics

Freie Universität Berlin 2012
Berlin, Germany

Evolution Lengyel

Evolution of a Game Engine

McMaster University 2007
Hamilton ON, Canada

GDC 2007 Lengyel

Projection Matrix Tricks

Game Developers Conference 2007
San Francisco CA

GDC 2006 Lengyel

Advanced Light and Shadow Culling Methods

Game Developers Conference 2006
San Jose CA

GDC 2005 Lengyel

Advanced Stencil Shadow and Penumbral Wedge Rendering

Game Developers Conference 2005
San Francisco CA

Informational Posters

Binary Lengyel

Binary Fundamentals

Eric Lengyel, 2023

PDFPrint

Slug Lengyel

The Slug Algorithm

Eric Lengyel, 2021
sluglibrary.com

PDFPrint

C4 Engine Lengyel

The C4 Engine Architecture

Eric Lengyel, 2021
c4engine.com

PDFPrint

Transvoxel Lengyel

The Transvoxel Algorithm

Eric Lengyel, 2018
transvoxel.org

PDFPrint

OpenDDL Lengyel

Open Data Description Language

Eric Lengyel, 2020
openddl.org

PDFPrint

Projective Geometric Algebra Lengyel

Projective Geometric Algebra

Eric Lengyel, 2024
projectivegeometricalgebra.org

PDFPrint

Conformal Geometric Algebra Lengyel

Conformal Geometric Algebra

Eric Lengyel, 2024
projectivegeometricalgebra.org

PDFPrint

Dissertation and Masters Thesis

Voxel Lengyel

Voxel-Based Terrain for Real-Time Virtual Simulations

Eric Lengyel, University of California Davis, 2009
transvoxel.org

Voxel Lengyel

Hyperreal Structures Arising from an Infinite Base Logarithm

Eric Lengyel, Virginia Tech, 1996

Patents

Patent Lengyel

Method for Rendering Resolution-Independent Shapes Directly from Outline Control Points

US Patent #10373352

Patent Lengyel

Graphics Processing Apparatus, Graphics Library Module And Graphics Processing Method

US Patent #8149242

Games

QG5 Lengyel

Quest for Glory V: Dragon Fire

Yosemite Entertainment / Sierra Studios
Lead programmer, 1996–1998