Appearance
sRGB: – HEX: –
Illuminant
Neutral
daylight
Illuminant:
–
Pigment Reflectance
380–780 nm, columns:
λ(nm), R(λ). Linear interpolation.
Custom reflectance curve
BRDF Model
Viewing Geometry
Advanced Lobes
Material Presets
Display
Contrast:
–
Realtime
Appearance Swatches
Diffuse
–
Specular
–
Shading Breakdown
sRGB: – HEX: –
Diffuse: – Specular: –
Illuminant sRGB: – N·L: –
N·V: –
L: – best text: – contrast:
–
Spectra
Illuminant
Reflectance
Product
▬ S(λ) illuminant
▬ R(λ) reflectance
▬ S·R product
Sphere Preview
Polar BRDF Lobe
BRDF Diagnostics
Metamerism table will update after render.
Color Metrics
Tristimulus
X: – Y: – Z: –
L*: – a*: – b*:
–
Perceptual (HDR)
Jz: – Az: – Bz: –
ΔE₀₀ vs ref:
–
Illuminant Quality
CRI Ra: – R9: –
TM-30 Rf: – Rg: –
Actions
Clipboard
Session & Spectra
Session JSON contains illuminants, reflectance curves, BRDF parameters, angles, and all state for full reproducibility.
Full export
Standards & Guidelines
CIE Illuminants & Colorimetry (CIE 015:2018)
CIE 015:2018 — Colorimetry, 4th edition. Defines CIE standard illuminants (A, D50, D55, D65, D75), standard observers (2° and 10°), XYZ tristimulus computation, chromaticity coordinates, and CIELAB colour space.
CIE S 014-2:2006 — CIE standard illuminant D65. Spectral power distribution for daylight simulation at 6504 K.
Planckian locus — Blackbody radiator SPD from Planck’s law for arbitrary CCT. Used for “warm” to “cool” lighting simulation.
Microfacet BRDF Theory (Cook–Torrance, GGX)
Cook & Torrance (1982) — Seminal microfacet reflectance model decomposing BRDF into distribution function D, geometry/masking G, and Fresnel F terms.
GGX / Trowbridge–Reitz (2007) — Walter et al. introduced GGX normal distribution function with extended tails, now standard in PBR pipelines (Disney, UE, Unity).
Smith height-correlated masking — Heitz (2014) showed joint masking-shadowing for microfacet models preserves energy at grazing angles.
Colour Rendering Index (CIE 13.3, IES TM-30)
CIE 13.3-1995 — Method of measuring and specifying colour rendering properties of light sources. Defines CRI Ra from 14 test colour samples (8 for general, 6 special including R9 deep red).
IES TM-30-20 — Modern alternative to CRI. Uses 99 colour evaluation samples, reports Fidelity Index Rf and Gamut Index Rg for more nuanced illuminant quality assessment.
Colour Difference (ΔE₀₀ / CIEDE2000)
CIE 142:2001 — Improvement to industrial colour-difference evaluation. CIEDE2000 (ΔE₀₀) includes lightness, chroma, hue weighting and rotation term for blue region.
Thresholds: ΔE₀₀ < 1.0 imperceptible; 1–2 perceptible upon close inspection; 2–3.5 perceptible at a glance; >5 clearly different colours.
Perceptual Colour Spaces (JzAzBz)
Safdar et al. (2017) — JzAzBz: perceptually uniform colour space for HDR and wide-gamut. Uses PQ (perceptual quantizer) transfer function from BT.2100.
Provides improved uniformity compared to CIELAB for high-dynamic-range stimuli. Suitable for HDR display colour difference and appearance modelling.
sRGB & Display Standards (IEC 61966-2-1)
IEC 61966-2-1:1999 — sRGB colour space. Defines primaries, D65 white point, gamma EOTF (piecewise linear + power 2.4), and XYZ-to-sRGB 3×3 matrix.
All rendered colours in this tool are converted to sRGB via the standard matrix and gamma-corrected for display.
Formulas & Mathematics
Cook–Torrance Microfacet BRDF
fr = kd fLambert + ks ·
D(ωh) · G(ωi,ωo) ·
F(ωo,ωh) / (4
(N·ωi)(N·ωo))
GGX (Trowbridge–Reitz) NDF:
D(h) = α² / (π · ((N·h)²(α²−1)+1)²)
Beckmann NDF:
D(h) = exp(−tan²θh/α²) / (πα²cos⁴θh)
Smith G (height-correlated):
G(i,o) = G1(i) · G1(o)
G1(v) = 2(N·v) / ((N·v) + √(α² + (1−α²)(N·v)²))
GGX (Trowbridge–Reitz) NDF:
D(h) = α² / (π · ((N·h)²(α²−1)+1)²)
Beckmann NDF:
D(h) = exp(−tan²θh/α²) / (πα²cos⁴θh)
Smith G (height-correlated):
G(i,o) = G1(i) · G1(o)
G1(v) = 2(N·v) / ((N·v) + √(α² + (1−α²)(N·v)²))
Oren–Nayar Diffuse
fd = (1/π) · (A + B ·
max(0,cos(φi−φo)) · sinα ·
tanβ)
A = 1 − 0.5 σ²/(σ²+0.33)
B = 0.45 σ²/(σ²+0.09)
α = max(θi, θo), β = min(θi, θo)
A = 1 − 0.5 σ²/(σ²+0.33)
B = 0.45 σ²/(σ²+0.09)
α = max(θi, θo), β = min(θi, θo)
Fresnel Reflectance
Schlick approximation:
F(θ) = F0 + (1 − F0)(1 − cosθ)⁵
Dielectric F0 from IOR:
F0 = ((n−1)/(n+1))²
Water: n≈1.33 → F0≈0.02
Plastic: n≈1.5 → F0≈0.04
Glass: n≈1.52 → F0≈0.04
Diamond: n≈2.42 → F0≈0.17
Metal: F0 from complex IOR or measured spectral reflectance.
Gold F0 ≈ (1.0, 0.77, 0.34), Silver ≈ (0.97, 0.96, 0.91), Copper ≈ (0.97, 0.64, 0.54).
F(θ) = F0 + (1 − F0)(1 − cosθ)⁵
Dielectric F0 from IOR:
F0 = ((n−1)/(n+1))²
Water: n≈1.33 → F0≈0.02
Plastic: n≈1.5 → F0≈0.04
Glass: n≈1.52 → F0≈0.04
Diamond: n≈2.42 → F0≈0.17
Metal: F0 from complex IOR or measured spectral reflectance.
Gold F0 ≈ (1.0, 0.77, 0.34), Silver ≈ (0.97, 0.96, 0.91), Copper ≈ (0.97, 0.64, 0.54).
CIE XYZ Tristimulus from Spectral Data
X = k ∫ S(λ) R(λ) x̄(λ) dλ
Y = k ∫ S(λ) R(λ) ȳ(λ) dλ
Z = k ∫ S(λ) R(λ) z̄(λ) dλ
k = 1 / ∫ S(λ) ȳ(λ) dλ
CIELAB (D65):
L* = 116 f(Y/Yn) − 16
a* = 500 [f(X/Xn) − f(Y/Yn)]
b* = 200 [f(Y/Yn) − f(Z/Zn)]
Y = k ∫ S(λ) R(λ) ȳ(λ) dλ
Z = k ∫ S(λ) R(λ) z̄(λ) dλ
k = 1 / ∫ S(λ) ȳ(λ) dλ
CIELAB (D65):
L* = 116 f(Y/Yn) − 16
a* = 500 [f(X/Xn) − f(Y/Yn)]
b* = 200 [f(Y/Yn) − f(Z/Zn)]
XYZ → sRGB (IEC 61966-2-1)
Rlin = 3.2406 X − 1.5372 Y − 0.4986 Z
Glin = −0.9689 X + 1.8758 Y + 0.0415 Z
Blin = 0.0557 X − 0.2040 Y + 1.0570 Z
EOTF: c ≤ 0.0031308 → 12.92c
else 1.055 c1/2.4 − 0.055
Glin = −0.9689 X + 1.8758 Y + 0.0415 Z
Blin = 0.0557 X − 0.2040 Y + 1.0570 Z
EOTF: c ≤ 0.0031308 → 12.92c
else 1.055 c1/2.4 − 0.055
Planck’s Law (Blackbody Radiation)
B(λ, T) = (2hc² / λ⁵) · 1 /
(ehc/(λkBT) − 1)
h = 6.626×10−34 J·s (Planck)
c = 2.998×108 m/s (speed of light)
kB = 1.381×10−23 J/K (Boltzmann)
Wien’s displacement: λpeak = 2898 μm·K / T
At 6504 K: λpeak ≈ 445 nm (blue)
h = 6.626×10−34 J·s (Planck)
c = 2.998×108 m/s (speed of light)
kB = 1.381×10−23 J/K (Boltzmann)
Wien’s displacement: λpeak = 2898 μm·K / T
At 6504 K: λpeak ≈ 445 nm (blue)
CIEDE2000 (ΔE₀₀)
ΔE₀₀ = √((L′/SL)² +
(C′/SC)² + (H′/SH)² +
RT(C′/SC)(H′/SH))
SL = 1 + 0.015(L̄−50)² / √(20+(L̄−50)²)
SC = 1 + 0.045 C̄′
SH = 1 + 0.015 C̄′ T
RT = rotation for blue hue region
Reference: Sharma, Wu & Dalal (2005).
SL = 1 + 0.015(L̄−50)² / √(20+(L̄−50)²)
SC = 1 + 0.045 C̄′
SH = 1 + 0.015 C̄′ T
RT = rotation for blue hue region
Reference: Sharma, Wu & Dalal (2005).
References & Citations
CIE Illuminants & Colorimetry
[1] CIE 015:2018 — Colorimetry, 4th edition. Standard illuminants, observers, XYZ
tristimulus, CIELAB.
[2] CIE S 014-2:2006 — CIE standard illuminant D65. Daylight simulation at 6504 K.
[3] CIE 15:2004 — Colorimetry (3rd edition). Observer, illuminants, chromaticity.
[2] CIE S 014-2:2006 — CIE standard illuminant D65. Daylight simulation at 6504 K.
[3] CIE 15:2004 — Colorimetry (3rd edition). Observer, illuminants, chromaticity.
Microfacet BRDF Theory
[4] Cook, R.L. & Torrance, K.E. (1982) — A Reflectance Model for Computer
Graphics. ACM TOG 1(1), 7–24.
[5] Walter, B. et al. (2007) — Microfacet Models for Refraction through Rough Surfaces. EGSR.
[6] Heitz, E. (2014) — Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. JCGT 3(2).
[7] Oren, M. & Nayar, S.K. (1994) — Generalization of Lambert’s Reflectance Model. SIGGRAPH.
[5] Walter, B. et al. (2007) — Microfacet Models for Refraction through Rough Surfaces. EGSR.
[6] Heitz, E. (2014) — Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. JCGT 3(2).
[7] Oren, M. & Nayar, S.K. (1994) — Generalization of Lambert’s Reflectance Model. SIGGRAPH.
Fresnel & Material Optics
[8] Schlick, C. (1994) — An Inexpensive BRDF Model for Physically-Based Rendering.
CGF 13(3), 233–246.
[9] Burley, B. (2012) — Physically Based Shading at Disney. SIGGRAPH Course Notes.
[9] Burley, B. (2012) — Physically Based Shading at Disney. SIGGRAPH Course Notes.
Colour Rendering & Quality
[10] CIE 13.3-1995 — Method of measuring and specifying colour rendering
properties of light sources.
[11] IES TM-30-20 — Method for evaluating light source colour rendition: Fidelity Rf, Gamut Rg.
[11] IES TM-30-20 — Method for evaluating light source colour rendition: Fidelity Rf, Gamut Rg.
Colour Difference & Perceptual Spaces
[12] Sharma, G., Wu, W. & Dalal, E.N. (2005) — The CIEDE2000 Color-Difference
Formula. CRA 30(1), 21–30.
[13] Safdar, M. et al. (2017) — Perceptually uniform color space for image signals including HDR and wide gamut (JzAzBz). Optics Express 25(13).
[13] Safdar, M. et al. (2017) — Perceptually uniform color space for image signals including HDR and wide gamut (JzAzBz). Optics Express 25(13).
Display Standards
[14] IEC 61966-2-1:1999 — sRGB default colour space. Primaries, D65 white,
piecewise gamma.
[15] Poynton, C.A. (2012) — Digital Video and HD: Algorithms and Interfaces (2nd ed.).
[15] Poynton, C.A. (2012) — Digital Video and HD: Algorithms and Interfaces (2nd ed.).
About this tool
This tool implements spectral BRDF appearance simulation with 5 microfacet models (GGX, Beckmann, Ward, Ashikhmin–Shirley, Oren–Nayar), configurable illuminants, pigment reflectance, clearcoat layers, CIE XYZ/Lab/JzAzBz colorimetry, ΔE₀₀, CRI/TM-30, sphere ray-tracer, polar BRDF lobe, batch analysis, bootstrap CIs, and session export — entirely client-side (zero network). Not a substitute for calibrated measurement or ray-tracing software.
Research & Visualization
Bootstrap ΔE Distribution
Run N random parameter perturbations and compute ΔE₀₀ vs the current render. Bootstrap histogram shows distribution and 95% confidence interval.
Click Run Bootstrap to start analysis.
Batch Illuminant Comparison
Compare appearance of the current material under multiple illuminants. Results show ΔE₀₀ relative to D65 reference.
Click Run Batch to analyse materials.
Research backend: Spectral BRDF · GGX · Beckmann ·
Ward · Ashikhmin–Shirley · Oren–Nayar · CIE XYZ ·
CIELAB · JzAzBz · ΔE₀₀ · CRI/TM-30 ·
Bootstrap CIs · Batch analysis. All computation on-device.