Spherical Harmonic Lighting Petras Sukys, Simon Ivarsson Chalmers - - PowerPoint PPT Presentation

▶
spherical harmonic lighting
SMART_READER_LITE
LIVE PREVIEW

Spherical Harmonic Lighting Petras Sukys, Simon Ivarsson Chalmers - - PowerPoint PPT Presentation

Feb 10, 2023 170 likes •439 views

Spherical Harmonic Lighting Petras Sukys, Simon Ivarsson Chalmers University of Technology 2013 Hello world Recap on maths Spherical Harmonics SH at work Some demos/examples Recap on maths Almighty lighting equation Recap

slide-1
SLIDE 1

Spherical Harmonic Lighting

Petras Sukys, Simon Ivarsson Chalmers University of Technology 2013

slide-2
SLIDE 2

Hello world

  • Recap on maths
  • Spherical Harmonics
  • SH at work
  • Some demos/examples
slide-3
SLIDE 3

Recap on maths

Almighty lighting equation

slide-4
SLIDE 4

Recap on maths

Integrating over a hemisphere...

slide-5
SLIDE 5

Recap on maths Monte Carlo integration

(almost as mighty) Expected value of a random function: Law of Large Numbers:

slide-6
SLIDE 6

Recap on maths Monte Carlo integration

slide-7
SLIDE 7

Recap on maths

  • Approx. and basis functions

Signal and approximation Basis function

http://en.wikibooks.org/wiki/Control_Systems/Sampled_Data_Systems

slide-8
SLIDE 8

Recap on maths

  • Approx. and basis functions

Calculate coefficients Reconstruct by scaling basis functions with coefficients... ... and sum up:

slide-9
SLIDE 9

Some more maths

Orthogonal basis function

slide-10
SLIDE 10

Some more maths

Associated Legendre Polynomials

slide-11
SLIDE 11

Some more maths

  • Assoc. Legendre Polynomials

l - band index, m - polynomial number

slide-12
SLIDE 12

Spherical Harmonics Under the hood

Where Kl

m is

normalisation factor

slide-13
SLIDE 13

Spherical Harmonics The Looks

http://en.wikipedia.

  • rg/wiki/Spherical_harmonics
slide-14
SLIDE 14

Spherical Harmonics The Use

  • Integration of product = multiplication of the

coefficients

  • Have another light source or shadow caster?

Almost as easy as two matrix multiplication.

  • Want to rotate light source function? A bit

trickier, but still easy with SH!

slide-15
SLIDE 15

Diffuse Unshadowed Transfer

slide-16
SLIDE 16

Diffuse Unshadowed Transfer

slide-17
SLIDE 17

Shadowed Diffuse Transfer

slide-18
SLIDE 18

Shadowed Diffuse Transfer

slide-19
SLIDE 19

Shadowed Diffuse Transfer

slide-20
SLIDE 20

Diffuse Interreflected Transfer

slide-21
SLIDE 21

Diffuse Interreflected Transfer

slide-22
SLIDE 22

Diffuse Interreflected Transfer

slide-23
SLIDE 23

Other Light Sources

Overcast Clear sky Partly Cloudy

slide-24
SLIDE 24

Other Light Sources

HDR Image Artificial

slide-25
SLIDE 25

Demo

slide-26
SLIDE 26

Questions?