Position-Free Monte Carlo Simulation for Arbitrary Layered BSDFs

Supplemental Materials

Yu Guo¹, Miloš Hašan² and Shuang Zhao^{1 1}University of California, Irvine          ²Adobe Research

Here we show equal-spp renderings generated with our uni-directional (with nesting BSDFs) and bi-directional (with the explicit implementation) estimators. For the timings, please see Table 2 in the paper.

Unidirectional	Bidirectional

• Properties of Banches from top to bottom:
• 1. Roughness: 0.005|0.005, IOR:1.5, sigmaT=1, g=0
• 2. Roughness: 0.005|0.1, IOR:1.5, sigmaT=1, g=0
• 3. Roughness: 0.1|0.005, IOR:1.5, sigmaT=1, g=0
• 4. Roughness: 0.1|0.1, IOR:1.5, sigmaT=1, g=0

Reference	MIS (accurate pdf)	MIS (approximate pdf)	no MIS
	64spp 14min	64spp 4.1min	80spp 4.2min

Bench 1
Bench 2
Bench 3
Bench 4

1. surface-medium-surface (1)

• Roughdielectric surface: IOR:1.5, alpha=0.05
• Isotropic homogeneous Medium: sigmaT:1, albedo:(0.5,0.7,0.95), hg(g=0.5)
• Roughconductor surface: Cu, alpha=0.05

Global PT	Global BDPT	MLT	Our Unidir	Our Bidir
~10s	~10s	~10s	~10s	~10s
~100s	~100s	~100s	~100s	~100s

2. surface-medium-surface (2)

• Roughdielectric surface: IOR:1.5, alpha=0.05
• Isotropic homogeneous Medium: sigmaT:2, albedo:(0.5,0.7,0.95), hg(g=0.9)
• Roughconductor surface: Cu, alpha=0.01

Global PT	Global BDPT	MLT	Our Unidir	Our Bidir
~10s	~10s	~10s	~10s	~10s
~100s	~100s	~100s	~100s	~100s

3. surface-medium-surface (3)

• Roughdielectric surface: IOR:1.5, alpha=0.05
• Isotropic homogeneous Medium: sigmaT:5, albedo:(0.5,0.7,0.95), hg(g=0.95)
• Roughconductor surface: Cu, alpha=0.01

Global PT	Global BDPT	MLT	Our Unidir	Our Bidir
~10s	~10s	~10s	~10s	~10s
~100s	~100s	~100s	~100s	~100s

4. surface-medium-surface-medium-surface

• Roughdielectric surface: IOR:1.5, alphaU=0.05, alphaV=0.25
• Anisotropic homogeneous Medium: density:0.5, albedo:(0.5,0.7,0.95), orientation:(0.5,0.5,0), microflake(stddev=0.05)
• Roughdielectric surface: IOR:1.2/1.5, alpha=0.01
• Anisotropic homogeneous Medium: density:0.5, albedo:(0.5,0.95,0.5), orientation:(0.5,-0.5,0), microflake(stddev=0.05)
• Roughconductor surface: Cu, alpha=0.05

Global PT	Global BDPT	MLT	Our Unidir	Our Bidir
~10s	~10s	~10s	~10s	~10s
~100s	~100s	~100s	~100s	~100s

(Used in Validation 1)

Reference:
Our uni-directional:
Our bi-directional:

(Used in Validation 2)

Reference:
Our uni-directional:
Our bi-directional:

(Used in Validation 3)

Reference:
Our uni-directional:
Our bi-directional:

(Used in Validation 4)

Reference:
Our uni-directional:
Our bi-directional:

Reflection and transmittance

Reference:
Our uni-directional:
Our bi-directional:

Volume Rendering	Volume Rendering (zoom in)

Ours	Ours (zoom in)

Ours	Ours (zoom in)

• Fixed: Albedo = [0.4 1 0.8], IOR = 1.65, phase = 0.8*g(0.8) + 0.2*g(-0.8)
• Varying: sigmaT (optical density)

sigmaT = [0.1 1 0.1]	sigmaT = [1 1 0.1]	sigmaT = [5 1 0.1]	sigmaT = [10 1 0.1]
sigmaT = [0.1 1 1]	sigmaT = [1 1 1]	sigmaT = [5 1 1]	sigmaT = [10 1 1]
sigmaT = [0.1 1 5]	sigmaT = [1 1 5]	sigmaT = [5 1 5]	sigmaT = [10 1 5]
sigmaT = [0.1 1 10]	sigmaT = [1 1 10]	sigmaT = [5 1 10]	sigmaT = [10 1 10]

HG phase function

g = 0.90, sigmaT = 1.00	g = 0.93, sigmaT = 1.00	g = 0.96, sigmaT = 1.00	g = 0.99, sigmaT = 1.00
g = 0.90, sigmaT = 1.41	g = 0.93, sigmaT = 1.41	g = 0.96, sigmaT = 1.41	g = 0.99, sigmaT = 1.41
g = 0.90, sigmaT = 2.00	g = 0.93, sigmaT = 2.00	g = 0.96, sigmaT = 2.00	g = 0.99, sigmaT = 2.00
g = 0.90, sigmaT = 2.83	g = 0.93, sigmaT = 2.83	g = 0.96, sigmaT = 2.83	g = 0.99, sigmaT = 2.83

vMF phase functions

kappa = 10, sigmaT = 1.00	kappa = 14, sigmaT = 1.00	kappa = 25, sigmaT = 1.00	kappa = 100, sigmaT = 1.00
kappa = 10, sigmaT = 1.41	kappa = 14, sigmaT = 1.41	kappa = 25, sigmaT = 1.41	kappa = 100, sigmaT = 1.41
kappa = 10, sigmaT = 2.00	kappa = 14, sigmaT = 2.00	kappa = 25, sigmaT = 2.00	kappa = 100, sigmaT = 2.00
kappa = 10, sigmaT = 2.83	kappa = 14, sigmaT = 2.83	kappa = 25, sigmaT = 2.83	kappa = 100, sigmaT = 2.83

Isotropic

η (1.1~1.7): α1 (0.01~0.1): α2 (0.01~0.1): σt (0.6~1.5): g (0~0.9):	η (1.1~1.7): α1 (0.01~0.1): α2 (0.01~0.1): σt (0.6~1.5): g (0~0.9):

Anisotropic

α1U (.01): α1V (.01): α2U (.01~.22): α2V (.01~.22): Ori (0~150): Std (.01~.07):	α1U (.01): α1V (.01): α2U (.01~.22): α2V (.01~.22): Ori (0~150): Std (.01~.07):