Reader's Guide
How To
Links (References)
About The Graphics CodexMorgan McGuire Casual Effects
New in this Version
Bibliography
arg maxargument maximum
α
Absorption Coefficientalpha
α
Attenuation Coefficientalpha
ASCII
Greek Letters
Math Symbol Tablecross dot union intersection escape
Character Table
A* Searchstar pathfinding
ψ
Azimuth Angle Measure
Angleplanar
κ
Extinction Coefficient
BSDF
Scattering Function (BSDF)brdf btdf probability statistics
×
Cross Product
Blinn-Phong BSDF
Normalized
Ball
Volume
Surface Area
-Ray Intersection
to Ball Distance
Bayes' Ruleconditional probability statistics
Beer-Lambert Law
β
Biradiance
Cosine
Taylor Polynomial
cosh(⋅)
Hyperbolic cosh
Convolution
clamp(⋅)
Clamp
Cosine-weighted hemisphere
Cone
Random Direction Inside
Crepuscular Ray (Image)
Cross-Correlation
Cylinder
Volume
Surface Area
C/C++
printf Specification
Function Pointer
Method Pointer
Integersuint8_t int8_t uint16_t int16_t uint32_t int32_t uint64_t int64_t intptr_t uintptr_t integer short long int stdint.h limits.h inttypes.h
shared_ptrreference counted pointer weak_ptr garbage collection downcast smart
Syntax Example
det(A)
Determinant
det(A)
2×2 Matrix
det(A)
3×3 Matrix
det(A)
4×4 Matrix
dw
Differential Solid Angle
⋅
Dot Product
Dürer, Albrecht woodcut etching lithograph
Man Drawing a Lute (annotated)
Man Drawing a Lute
Perspective Woodcut
Perspective Nude
Directions
Distance
Point-Point
Euclidean
Manhattan
Point-Line
Line-Line
Sphere-Sphere
Point-Plane
Table of Useful Lengths
Electromagnetic Spectrum
Euler
e
Constant
χ
Characteristicchi
Formulacosine sine imaginary
Expected Valueprobability statistics
E(X)
of a Random Variable
of a Seriesprobability statistics
xbar
File Format
3D Models OFF IFS OBJ 3DS PLY2 MTL STL
Raster Images
Floating Point Formatssingle double quad half 32 16 64 80 nan infinity ieee
Frame Rate Tabletable useful fps ms
F(⋅)
Fresnel Coefficient
FS(⋅)
Schlick's Approximation
Fc(⋅)
for a Conductor
Fd(⋅)
for a Dielectric
F0
at Normal Incidence
F0
F0 for Selected Materials
Frequency
f
of Light
ν
of Light, Spatial
Display Refresh
Greek Alphabetalpha beta gamma delta epsilon zeta eta theta iota kappa lambda mu nu xi omicron pi rho sigma tau upsilon phi psi omega chi
Gamma Compressiongamma correction
ϕ
Golden Ratiophi
GLSL OpenGL Shading Language
Functions
Heap Sort
Hyperbolic
cosh(⋅)
Cosinecosh
||⋅||
Hausdorff Measure
S+2Hemisphere
Cosine-weighted
HTML
Greek Letter Table
Math Symbol Tablecross dot union intersection escape
HTML5 Examplecss javascript favicon style
CSS3 Selectors
CSS3 Custom Font
Human Retinaeye
Photoreceptor Density
Spectral Response
Hull Speedboat displacement friction fluid
wh
Half Vector
θ
Inclination Angle Measure
Index of Refraction
η
Real
etahat
Complex
for Selected Materials
E
Irradiance
Incoming
Li(⋅)
Light Fieldradiance
wmi
Reflection Vectoromega
wti
Refraction Vectoromega
wi
Light Vectoromega
Insertion Sort
JavaScriptjs ecmascript
Typesarray object table string number boolean null undefined function null literal
Operatorsvoid ++ -- === bitshift % [ ]
Law of Cosines
lerp(⋅)
Linear Interpolationlerp mix
L(⋅)
Light Fieldradiance
Li(⋅)
Incomingradiance
Lo(⋅)
Outgoingradiance
LuminancesRGB 709 CIE gamma
LaTeX
Greek Letter Table
Math Symbol Tablecross dot union intersection
includegraphicsscale trim angle width heigh clip
Space Command Tablehspace vspace
Size Command Tablelarge tiny small
Line
to Point Distance
to Line Distance
Metric Prefixeszetta exa peta tera giga mega kilo hecto deka deci centi milli micro nano pico fempto atto zepto
Mean
xbar
Arithmetic
E(X)
Expected Value
Geometric
Mod 3
Merge Sort
Matrix
A-1
2×2 Inverse
A-1
3×3 Inverse
det(A)
n×n Determinant
det(A)
2×2 Determinant
det(A)
3×3 Determinant
det(A)
4×4 Determinant
P
zf > -∞ Perspective Projection
Multiplicationmatmul
○
Hadamard Productarray Schur entrywise
:
Frobenius Inner Product
P
zf = -∞ Perspective Projection
T
Translation
S
Scale
R
Rotation (Roll, Yaw, Pitch)
R
Rotation from Unit Quaternion
R
Rotation from Axis and Angle
X
Skew-Symmetric
||⋅||
Measure (Hausdorff)
mirror(⋅)
Mirror Reflection Operator
cr
Microfacet Reflection Angle Cosine
Next Mod 3
S(⋅)
Normalize a Vector
Normalized Fixed-Point
O
Origin
Outgoing
Lo(⋅)
Light Field
wmo
Specular Reflection Vectoromega
wto
Refraction Vectoromega
wo
Light Vectoromega
printf Specification
Point Lights
Photoreceptor
Density, Human
Spectral Response, Human
Point
to Point Distance
to Line Distance
to Plane Distance
Photon
Q
Energy
λ
Wavelength
f
Frequency
ν
Spatial Frequency
π
pi
P
Perspective Projection Matrix
P
Infinite
Inverting
Pythagorean Theorem
h
Plank Constant
Φ
Power
Phong-like BSDFs
1973 Originalbsdf brdf
1977 Blinn-Phong BSDFbrdf
1986 Normalized Phongbrdf
2008 Normalized Blinn-Phongbrdf
L(⋅)
Plenoptic Function
Quadratic Formula
Quick Sort
Quaternion, Unit
Basis
Inverse
Multiplication
to Matrix
from Axis and Angle
slerp(⋅)
Interpolation
slerp(⋅)
Interpolation (implementation)
Verson (Unit Quaternion)
to Matrix
from Rotation Matrix
Basis
Inverse
Multiplication
from Axis and Angle
slerp(⋅)
Interpolation
slerp(⋅)
Interpolation (implementation)
L
Radiance
B
Radiosity
Radiometric Unit Table
Depicted table power radiance radiosity emittance luminance intensity time area solid angle energy biradiance
M
Radiant Exitance
M
Radiant Emittance
I
Radiant Intensity
L(⋅)
Radiance Function
Φ
Radiant Flux
Rendering Equation, The
Sphere Domain (Immel et al.)
Area Domain (Kajiya)
Reciprocity
RGB to/from sRGBgamma
RGB to Grayscalegamma
clamp(⋅)
Range Clamp
Refraction
refract(⋅)
Operator
wto
Vector (Outgoing)
wti
Vector (Incoming)
η
Index of (Real)
etahat
Index of (Complex)
ct
Angle, Microfacet Cosine of
Rodrigues' Formula
Reflection
mirror(⋅)
Operator
wmo
Vector (Outgoing)
wmi
Vector (Incoming)
cr
Angle, Microfacet Cosine of
Ray
-Triangle Intersection
-Sphere Intersection
Scattering Variables
slerp(⋅)
Slerp
slerp(⋅)
Implementation
Sphere
-Ray Intersection
S2
Unit
Volume Inside
Surface Area
to Sphere Distance
3D Model File Formats
Shallow Water EquationNavier-Stokes Witkin Miller
Spherical Coordinates
Right-handed with z=up
Right-handed with y=up
Scalar Triple Product
smoothstep
smootherstep
FS(⋅)
Schlick's Fresnel Approximation
Tetrahedron
Volume
Surface Area
Type Notationsets notation
Structural
Semantic
Transformation Matrix
T
Translation
S
Scale
R
Rotation (Roll, Yaw, Pitch)
R
Rotation from Unit Quaternion
R
Rotation from Axis and Angle
X
Skew-Symmetric
Screen Resolution Tablecommon useful table
Screenshot Keys
c0
Speed of Light (in Vacuum)constants
Solid Anglegamma
Measure of a Lat-Long Patch
Measure of a Triangle
dw
Differentialomega
Snell's Lawrefraction transmission transmit physics transparent translucent glass
Shadow Maplight shader sampler shadowmap OpenGL DX DirectX GL texture shading
Shader Pseudocode
Sortalgorithms
Insertion
Quick
Heap
Merge
Spectrum
Electromagnetic
Visible Light
Table of Useful Speeds
Simple Web Servershttp html xml chrome safari ie mozilla firefox python civet
Sine
Taylor Polynomial
Sun
Spectrum
S2
Unit Sphere
Trigonometric Identitiescosine sine csc tangent atan secant
Compressed Texture FormatsBC1 DXN PVRTC S3TC 3Dc DXT RGB sRGB OpenGL GL DirectX DX GLSL HLSL
Triangle
Solid Angle
-Ray Intersection
Area
Unproject from depth
Unicode
Greek Letter Table
Math Symbol Tablecross dot union intersection
Varianceprobability statistics
Var(X)
of a Random Variableprobability statistics
Vector
×
Cross Product
⋅
Dot Product
||⋅||
Magnitude length
XML
Greek Letters
Escape Codes
Math Symbol Tablecross dot union intersection escape