Download rendering equation

rendering equation
computer graphics • rendering equation
© 2009 fabio pellacini • 1
physically-based rendering
synthesis algorithms that compute images by
simulation the physical behavior of light
computer graphics • rendering equation
© 2009 fabio pellacini • 2
physically-based rendering
•  advantages
–  predictive simulation
•  can be used for architecture, engineering, …
–  photorealistic
•  if simulation if correct, images will look real
•  disadvantages
–  (really) slow
•  simulation of physics is computationally very expensive
–  need accurate geometry, materials and lights
•  otherwise just a correct solution to the wrong problem
computer graphics • rendering equation
© 2009 fabio pellacini • 3
models of light
•  geometric optics
[Stam et al., 1996]
–  light particles travel in straight lines
–  light particles do not interact with each other
–  describes: emission, reflection/refraction, absorption
computer graphics • rendering equation
© 2009 fabio pellacini • 4
models of light
•  wave optics
[Gondek et al., 1997]
–  light particles interact with each other
–  describes: diffraction, interference, polarization
computer graphics • rendering equation
© 2009 fabio pellacini • 5
models of light
•  quantum optics
[Glassner et al., 1997]
–  light particles are like any other quantum particles
–  captures: fluorescence, phosphorescence
computer graphics • rendering equation
© 2009 fabio pellacini • 6
rendering equation
•  describe physical behavior of light in vacuum filled with
objects
–  based on geometric optics principles
–  can be extended to describe participating media
–  can be extended to describe wavelenght dep.
computer graphics • rendering equation
© 2009 fabio pellacini • 7
power and irradiance
•  power: energy per unit time
–  measured in Watts = Joules/sec
•  irradiance: power per unit area
–  measured in Watts/meter2
computer graphics • rendering equation
© 2009 fabio pellacini • 8
radiance
•  power per unit projected area and solid angle
[Dutré, Bekaert, Bala]
–  depends on position and direction (5D)
computer graphics • rendering equation
© 2009 fabio pellacini • 9
radiance
most sensors readings (and your eyes) are
proportional to radiance
computer graphics • rendering equation
© 2009 fabio pellacini • 10
radiance notation
•  notation follows [Dutré, Bekaert, Bala]
•  radiance leaving from point x in direction Θ
•  radiance coming to point x from direction Ψ
•  solid angle for a direction Ψ
•  in general
computer graphics • rendering equation
© 2009 fabio pellacini • 11
radiance
•  radiance is a function of wavelenght
•  in practice, write equations for RGB
–  we will use simplified notation without carry around the
wavelength explicitly
computer graphics • rendering equation
© 2009 fabio pellacini • 12
radiance
[Dutré, Bekaert, Bala]
•  formulation between two points
computer graphics • rendering equation
© 2009 fabio pellacini • 13
radiance properties
•  invariance on straight paths in vacuum
–  from energy conservation
[Shirley]
•  corollary: radiance does not change with distance
computer graphics • rendering equation
© 2009 fabio pellacini • 14
material properties
•  materials differ in the way they scatter energy
[Dutré, Bekaert, Bala]
–  need physical description of light scattering
computer graphics • rendering equation
© 2009 fabio pellacini • 15
BRDF
[Dutré, Bekaert, Bala]
•  bidirectional surface distribution function
computer graphics • rendering equation
© 2009 fabio pellacini • 16
BRDF properties
•  reciprocity
•  energy conservation
computer graphics • rendering equation
© 2009 fabio pellacini • 17
hemispherical formulation
•  need outgoing radiance in a given direction
–  from BRDF definition
–  determine reflected radiance Lr by integration over all
incoming light
computer graphics • rendering equation
© 2009 fabio pellacini • 18
hemispherical formulation
•  need outgoing radiance in a given direction
–  also consider light spontaneously emitted by surface
–  total radiance is the sum of emitted and reflected
computer graphics • rendering equation
© 2009 fabio pellacini • 19
[Dutré, Bekaert, Bala]
hemispherical formulation
computer graphics • rendering equation
© 2009 fabio pellacini • 20
[Bala]
intuition behind rendering equation
x
computer graphics • rendering equation
x
© 2009 fabio pellacini • 21
intuition behind rendering equation
integral equation
indicates radiance at equilibrium
computer graphics • rendering equation
© 2009 fabio pellacini • 22
visible point formulation
•  point visible from x in direction Ψ
•  since energy is conserved in vacuum
•  by substituting previous values in rendering eq.
computer graphics • rendering equation
© 2009 fabio pellacini • 23
[Dutré, Bekaert, Bala]
visible point formulation
computer graphics • rendering equation
© 2009 fabio pellacini • 24
area formulation
[Dutré, Bekaert, Bala]
•  compute solid angle visible from x to y
computer graphics • rendering equation
© 2009 fabio pellacini • 25
area formulation
•  by changing domain from hemisphere to scene
–  and introducing explicit visibility evaluation V
computer graphics • rendering equation
© 2009 fabio pellacini • 26
[Dutré, Bekaert, Bala]
area formulation
computer graphics • rendering equation
© 2009 fabio pellacini • 27
[Dutré, Bekaert, Bala]
transport formulation
computer graphics • rendering equation
© 2009 fabio pellacini • 28
[Cornell PCG]
transport formulation
computer graphics • rendering equation
© 2009 fabio pellacini • 29
direct and indirect illum. formulation
•  direct illumination: radiance reaching a surface directly
from the light
–  often efficient to sample using area formulation
•  indirect illumination: radiance reaching a surface after
bouncing at least once on another surface
–  often efficient to sample using hemisphere formulation
computer graphics • rendering equation
© 2009 fabio pellacini • 30
direct and indirect illum. formulation
computer graphics • rendering equation
© 2009 fabio pellacini • 31
direct illumination formulation
rewrite in area formulation
computer graphics • rendering equation
© 2009 fabio pellacini • 32
indirect illumination formulation
since
computer graphics • rendering equation
© 2009 fabio pellacini • 33
hemispherical integration
•  2D square
•  2D hemisphere
computer graphics • rendering equation
© 2009 fabio pellacini • 34
materials
computer graphics • rendering equation
© 2009 fabio pellacini • 35
physically-based materials
[Cornell PCG]
•  capture realistic appearance is necessary
computer graphics • rendering equation
© 2009 fabio pellacini • 36
diffuse BRDF
[Dutré, Bekaert, Bala]
•  light is reflected equally in all directions
computer graphics • rendering equation
© 2009 fabio pellacini • 37
diffuse BRDF
•  Lambertian shading model motivation
computer graphics • rendering equation
© 2009 fabio pellacini • 38
specular BRDF
[Dutré, Bekaert, Bala]
•  light is reflected only in one direction
computer graphics • rendering equation
© 2009 fabio pellacini • 39
glossy BRDFs
•  light is reflected in many directions unequally
[Dutré, Bekaert, Bala]
–  many models exist
computer graphics • rendering equation
© 2009 fabio pellacini • 40
glossy BRDFs – Phong and Blinn models
•  Phong model
•  Blinn-Phong model
•  issues:
–  non reciprocal
–  non energy conserving
computer graphics • rendering equation
© 2009 fabio pellacini • 41
glossy BRDFs – modified Blinn-Phong
model
•  modified Blinn-Phong model
•  energy conservation
computer graphics • rendering equation
© 2009 fabio pellacini • 42
glossy BRDFs – modified Phong model
•  is modified Phong physically accurate?
Phong
accurate BRDF
[LaFortune et al., 1997]
photograph
computer graphics • rendering equation
© 2009 fabio pellacini • 43
glossy BRDFs – modified Phong model
•  is modified Phong physically accurate?
accurate
BRDF
computer graphics • rendering equation
[LaFortune et al., 1997]
Phong
© 2009 fabio pellacini • 44
glossy BRDFs – better models
•  analytic model
–  physically motivated
–  hard to capture every material
•  data-driven
–  measure light reflectance
–  encode in lookup table or fit
–  resample when rendering
computer graphics • rendering equation
© 2009 fabio pellacini • 45
extending the rendering equation
computer graphics • rendering equation
© 2009 fabio pellacini • 46
[Fedkiw et al.]
participating media
computer graphics • rendering equation
© 2009 fabio pellacini • 47
[Jensen et al.]
subsurface scattering
computer graphics • rendering equation
© 2009 fabio pellacini • 48
[Jensen]
subsurface scattering
computer graphics • rendering equation
© 2009 fabio pellacini • 49
[Jensen et al.]
subsurface scattering
computer graphics • rendering equation
© 2009 fabio pellacini • 50