5. Outline
• Reflection • Why BSSDRF is bad?
– Diffuse reflection
– Specular reflection • Scattering model
Reflection – BRDF – Participating medium
Diffuse reflection
Specular reflection • Transmission • Absorption
BRDF
Transmission – Diffuse transmission • Emission
Diffuse transmission
– Specular transmission • In-scattering
Specular transmission
• Out-scattering
BTDF – BTDF
Scattering
– Rendering equations
BSSRDF
Dipole/Multipole
• Scattering • Airlight approximation
Plane-parallel
Empirical BSSRDF
– BSSRDF • Born series
Why BSSDRF is bad? • Dipole/Multipole • Neumann series
Scattering model
Participating medium
• Plane-parallel • M’s series
Absorption approximation
Emission • Empirical BSSRDF
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
6. Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
REFLECTION,
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
TRANSMISSION, AND
Absorption
Emission
In-scattering
Out-scattering
SCATTERING OF LIGHT
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
7. Diffuse reflection 拡散反射
• Constant
Reflection
Diffuse reflection
irradiance
Specular reflection
BRDF
Transmission
– Independent to
Diffuse transmission
Specular transmission
viewpoint
BTDF
Scattering
BSSRDF
• Pure diffuse
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
surface
Why BSSDRF is bad?
Scattering model – Lambertian
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
8. Specular reflection 鏡面反射
• Angle of reflection
– is the angle of
incidence
Reflection 𝜃
Diffuse reflection
Specular reflection
• Highlights
BRDF
Transmission
– More reflection near
Diffuse transmission
Specular transmission
to the angle of
BTDF reflection
Scattering
BSSRDF
Dipole/Multipole
• Model
Plane-parallel
Empirical BSSRDF – Phong
Why BSSDRF is bad?
Scattering model – Blinn
Participating medium
Absorption
Emission
– Cook-Trrance
In-scattering
Highlights
Out-scattering
– Trrance-Sparrow
Rendering equations
Airlight approximation
Born series
Neumann series Mirror
M’s series
9. Diffuse + Specular
Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
10. Diffuse + Specular ?
𝜔
𝜔
Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF 𝑥
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
11. BRDF
• Bidirectional
Reflectance
Distribution 𝜔
𝜔
Reflection
Diffuse reflection
Function
Specular reflection – 双方向反射率分布
BRDF
Transmission 関数
Diffuse transmission
Specular transmission • 6 parameters 𝑥
BTDF
Scattering – Point 𝑥
BSSRDF
Dipole/Multipole – angles of incidence
Plane-parallel
Empirical BSSRDF
𝜔 and reflection 𝜔
Why BSSDRF is bad?
Scattering model • If isotropic and
Participating medium
Absorption homogeneous
Emission
In-scattering – 3 parameters
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
14. Refraction 回折 Transmission 透過
• Transmitted light
– Translucent
Reflection materials
Diffuse reflection
Specular reflection
BRDF
– All non-metals
Transmission
Diffuse transmission
Specular transmission
• Refraction
BTDF
Scattering
BSSRDF
– Snell’s low
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
15. Specular Transmission 鏡面透過
• Angle of refraction
– depends on
Reflection • the angle of
Diffuse reflection
Specular reflection incidence
BRDF
Transmission • the indexes of
Diffuse transmission
Specular transmission refraction of two
BTDF
Scattering
materials
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
16. Diffuse transmission 拡散透過
• Constant
irradiance
Reflection
Diffuse reflection
– Independent to
Specular reflection
BRDF
viewpoint inside
Transmission
Diffuse transmission
the material
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
18. BTDF
• Bidirectional
Transmittance
Reflection
Diffuse reflection
Distribution
Specular reflection
BRDF Function
Transmission
Diffuse transmission
Specular transmission
– 双方向透過率分布
BTDF
Scattering
関数
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
19. Reflection + Transmission
• Reflection
– BRDF
Reflection
Diffuse reflection • Transmission
Specular reflection
BRDF
Transmission
– BTDF
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
20. Subsurface scattering 表面下散乱
Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
21. Subsurface scattering
• Scattering
– Inside medium
Reflection
Diffuse reflection
– Some come the
Specular reflection
BRDF
surface
Transmission
Diffuse transmission – Some absorbed
Specular transmission
BTDF
Scattering
BSSRDF
• Outgoing light
Dipole/Multipole
Plane-parallel – From a point
Empirical BSSRDF
Why BSSDRF is bad? different from the
Scattering model
Participating medium
Absorption
incident point
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
65. Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
BSSRDF,
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
A WRONG MODEL
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
66. BRDF
• 6 parameters
– Point 𝑥 𝜔
𝜔
Reflection
Diffuse reflection
– angles of incidence
Specular reflection
BRDF
𝜔 and reflection
Transmission
Diffuse transmission
𝜔
Specular transmission
BTDF 𝑥
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
67. BRDF, OK!
• BRDF
– Works for a point 𝜔
on a curved 𝜔
Reflection
Diffuse reflection
Specular reflection surface
BRDF
Transmission
Diffuse transmission – Angles relative to
Specular transmission
BTDF the normal of the 𝑥
Scattering
BSSRDF point
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
68. BSSRDF
• 8 parameters
– Points of incidence 𝜔
Reflection 𝑥 and outgoing 𝑥 ,
Diffuse reflection
Specular reflection angles of incidence 𝜔
BRDF
Transmission
Diffuse transmission
𝜔 and outgoing
Specular transmission
BTDF
𝜔 𝑥 𝑥
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
69. BSSRDF ?
• 8 parameters
– Points of incidence 𝜔
Reflection 𝑥 and , NG : curved surface
Diffuse reflection
Specular reflection angles of incidence 𝜔
BRDF
Transmission
Diffuse transmission
𝜔 and outgoing
Specular transmission
BTDF
𝜔 𝑥 𝑥
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
70. BSSRDF ?
• 8 parameters
– Points of incidence 𝜔
Reflection 𝑥 and , NG : curved surface
Diffuse reflection
Specular reflection angles of incidence 𝜔
BRDF
Transmission
Diffuse transmission
𝜔 and outgoing
Specular transmission
BTDF
𝜔 𝑥 𝑥
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations NG : transmission
Airlight approximation
Born series
Neumann series
M’s series
73. Curvature dependent BRDF
• Light is reflected
– Even when
𝜃 > 180°
𝜃 = 180°
Hiroyuki Kubo, Yoshinori Dobashi, and Shigeo Morishima. 2010. Curvature-dependent reflectance function for rendering translucent materials. In ACM SIGGRAPH 2010
Talks (SIGGRAPH '10). ACM, New York, NY, USA, , Article 46 , 1 pages. DOI=10.1145/1837026.1837086 http://doi.acm.org/10.1145/1837026.1837086
久保 尋之, 土橋 宜典, 森島 繁生, "半透明物体の高速描画に向けた曲率に依存する反射関数の近似式", Visual Computing / グラフィクスと CAD 合同シンポジウム
2010, 2010.
74. Curvature dependent BRDF
• Light is reflected
– Even when
𝜃 > 180°
𝜃 > 180°
Hiroyuki Kubo, Yoshinori Dobashi, and Shigeo Morishima. 2010. Curvature-dependent reflectance function for rendering translucent materials. In ACM SIGGRAPH 2010
Talks (SIGGRAPH '10). ACM, New York, NY, USA, , Article 46 , 1 pages. DOI=10.1145/1837026.1837086 http://doi.acm.org/10.1145/1837026.1837086
久保 尋之, 土橋 宜典, 森島 繁生, "半透明物体の高速描画に向けた曲率に依存する反射関数の近似式", Visual Computing / グラフィクスと CAD 合同シンポジウム
2010, 2010.
75. Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
SCATTERING,
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
A CORRECT WAY
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
76. BSSRDF
• Subsurface
scattering 𝜔
Reflection
Diffuse reflection
Specular reflection 𝜔
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
𝑥 𝑥
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission Translucent material
In-scattering 半透明物質
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
77. Scattering model
• Volumetric
scattering
Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission Participating medium
In-scattering 関与媒質
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
78. Scattering model
• Volumetric
scattering
Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission Participating medium
In-scattering 関与媒質
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
79. Scattering model
Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF Backward scattering
Dipole/Multipole
Plane-parallel
Empirical BSSRDF Forward scattering
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations Phase function
Airlight approximation
Born series
Neumann series
M’s series
80. Scattering model
Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations Phase function
Airlight approximation
Born series
Neumann series
M’s series
81. Rendering by ray marching
Reflection
Diffuse reflection
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Numerical integration along
Empirical BSSRDF the line of sight
Why BSSDRF is bad?
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Rendering equations
Airlight approximation
Born series
Neumann series
M’s series
82. Light in participating medium
Absorption 吸収
Reflection Attenuation 減衰
Diffuse reflection Out-scattering
Specular reflection
BRDF
Transmission
Diffuse transmission
Specular transmission
BTDF
Scattering
BSSRDF
Dipole/Multipole In-scattering
Plane-parallel
Empirical BSSRDF
Why BSSDRF is bad?
Multiple scattering
Scattering model
Participating medium
Absorption
Emission
In-scattering
Out-scattering Emission 発光
Rendering equations
Airlight approximation
Born series
Usually ignored
Neumann series
M’s series
83. Absorption
𝐿 𝐿
Reflection
Diffuse reflection
Specular reflection 𝑑
BRDF
Transmission
𝐿
Diffuse transmission
(Macroscopic) Beer-Lambert Law log = 𝜀𝐶𝛽𝑑
Specular transmission
BTDF
𝐿
Scattering
BSSRDF
Dipole/Multipole モル吸光係数
Plane-parallel
Molar absorption coefficient path length
Empirical BSSRDF
Why BSSDRF is bad? (thickness)
Scattering model モル濃度
光路長,厚さ
Participating medium molarity
Absorption
Emission
In-scattering
光路長補正項
Out-scattering
Rendering equations 透明溶液 𝛽 = 1
Airlight approximation
Born series
混濁溶液 𝛽 ≠ 1
Neumann series
M’s series 田村守, 「生体分光学の基本原理とその医学応用」,非侵襲・可視化技術ハンドブック, 小川誠二, 上野照剛 監修, NTS, pp.253-266, 2007.
102. Mukaigawa series
Neumann series of volume rendering equation
𝐿= 𝑇 𝐿
Reflection
Diffuse reflection
Specular reflection Continuous Linear operator
BRDF
Transmission light (integral)
Diffuse transmission
Specular transmission
distribution
BTDF
Scattering
BSSRDF
Dipole/Multipole
Plane-parallel
Mukaigawa series of light transport (CVPR2010, MIRU2010)
Empirical BSSRDF
Why BSSDRF is bad?
Scattering model 𝐿= 𝑇 𝐿
Participating medium
Absorption
Emission
In-scattering
Out-scattering
Discretized Light transport
Rendering equations light field matrix
Airlight approximation
Born series
Neumann series
M’s series