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

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 on maths Integrating over a hemisphere...

Recap on maths Monte Carlo integration (almost as mighty) Expected value of a random function: Law of Large Numbers:

Recap on maths Monte Carlo integration

Recap on maths Approx. and basis functions Signal and approximation Basis function http://en.wikibooks.org/wiki/Control_Systems/Sampled_Data_Systems

Recap on maths Approx. and basis functions Calculate coefficients Reconstruct by scaling basis functions with coefficients... ... and sum up:

Some more maths Orthogonal basis function

Some more maths Associated Legendre Polynomials

Some more maths Assoc. Legendre Polynomials l - band index, m - polynomial number

Spherical Harmonics Under the hood m is Where K l normalisation factor

Spherical Harmonics The Looks http://en.wikipedia. org/wiki/Spherical_harmonics

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!

Diffuse Unshadowed Transfer

Diffuse Unshadowed Transfer

Shadowed Diffuse Transfer

Shadowed Diffuse Transfer

Shadowed Diffuse Transfer

Diffuse Interreflected Transfer

Diffuse Interreflected Transfer

Diffuse Interreflected Transfer

Other Light Sources Overcast Clear sky Partly Cloudy

Other Light Sources Artificial HDR Image

Demo

Questions?