-------------------------------------------------------------------------------

	   CS 99D - Light and shadow lecture #1 - February 13, 2001

				  Marc Levoy
			      Stanford University
				   (c) 2001

		      (with corrections, March 14, 2003)

-------------------------------------------------------------------------------

			     *** Introduction ***

o more complicated than linear perspective
	o appearance of surfaces has many different causes
		o geometric, chemical/physical
	o many causes are microscopic in origin
		o Jansen compound microscope (1595)
	o requires understanding the nature of light
		o Newton's Optiks (1704)
	o visual perception plays a more subtle role
		o Helmholz (mid-1800's)

o science (of light and shadow) came later than perspective
	o Age of Enlightenment
	o artists were no longer scientists
	o transfer from science to art was less direct

Errors in Leonardo:
	o attenuation of point source is 1/d (p. 91)
		(wrong - 1/d^2)
	o illumination falls off as (90-theta)/90 (p. 93)
		(wrong - cos(theta))
	o the (cloudy?) sky is equally bright in all directions
	  ("luminous hemisphere") (p. 95)
		(ok for foggy, but wrong for cloudy, L falls off as cos theta)
	o shadows lighten with increasing distance from the occluder
	  (p. 98, 103)
		(wrong - this is a penumbra effect)
	o shadow of large source by small occluder is a double pyramid (p. 105)
		(wrong - he is mixing up the umbra and penumbra)
	o shadows are tinged by the color of the shadowing object (p. 110)
		(wrong - this is an interreflection effect)
	o darkest part of shadow is at shadow horizon
		(wrong - this is a perceptual effect)

Summary of reasons for Leonardo's errors:
	o lack of rigorous geometry - intuitions are sometimes wrong
	o lack of a comprehensive physical model (e.g. of colored shadows)
	o inability to distinguish physical from perceptual effects

-------------------------------------------------------------------------------

			     *** Light sources ***

Light sources:
	o size (point versus area) and directionality
		-> taxonomy using light field position & direction into 0D-4D,
		   Langer and Zucker, What is a Light Source",
		   Proc. CVPR '97, p. 172, and illustrations
	o number and placement - lighting design is an art
		-> Professional Photographic Illustration, p. 16, 152
	o brightness:
		o relative to human range
		o relative among lights
	o color - spectral variation
		-> Maxfield Parrish's yellow key and blue fill

Point light sources:
	o Kepler (1571-1630) - attenuation of point source is 1/d^2
		o light does not weaken with distance; it merely spreads out
		o twice the distance -> twice the height -> four times the area
		o total illumination on surface of a growing sphere is constant
		o area of sphere grows as radius squared (area = 4 pi r^2)

			==> Demonstrate using photometer and desk lamp
			    (incident mode, with dome, plot several distances)

	o units of luminous intensity of a point source
		o candelas = lumens / sr (Cohen, p.27)
		o lumen (power) = talbot (energy) / sec  (optional)
		o originally defined by the intensity of Bouguer's candles
		o 1 sr = solid angle s.t. area subtended on sphere = radius^2
		o area of sphere = 4 pi r^2, so 1 sr = r^2 / (4 pi r^2) = ~1/12
		o radiometry versus photometry
		o radiant intensity is in watts / sr
		o watt (power) = joule (energy) / sec  (optional)

Area light sources:
	o attenuation of an area light source
			==> Demonstrate using photometer and white wall
			    (spot mode, through viewfinder)

		o as distance increases:
			o light from each point on wall drops as d^2,
			o but area seen increases as d^2,
			o so illuminance stays the same!

	o units of luminance of an area source
		o nits = candelas / m^2 = lumens / m^2 sr (projected)
		o projected area = area x cos theta
		o Examples:  (Minneart, p. 102)
			o disk of sun:  100,000 cd / cm^2
			o white surface illuminated by sun:  2 cd / cm^2
				(sun:surface = 50,000:1)
			o black surface illuminated by sun:  0.04 cd / cm^2
				(white:black = 50:1)
			o disk of moon: 0.3 cd / cm^2
				(sun:moon = 300,000:1)
				(moon's reflectivity is gray)
			o white surface illuminated by moon, black,...
			o cloud = 10 x blue sky

Illumination of surfaces:
	o Pierre Bouguer (1760) - illumination falls off as cos(theta)
		==> Demonstrate using point or area source far away, a
		    rotating flat plane, and a photometer

	o units of illuminance on a surface
		o lux = lumens / m^2  (energy / sec / unit area)
		o British unit is footcandle = 1 candela at 1 foot
		o Example:  (Minneart, p. 100)
			o from bright star = 1 candle at 900m = 1/810,000 lux
			o luminance of disk of sun = 300,000 x of blue sky,
			  but sun takes up only a small fraction of the sky,
			  so illumination of a landscape on a sunny day =
			  80% from sun, 20% from blue sky

	o falloff of illumination by point source on nearby surface  (optional)
		o of interest to lighting engineers (and painters?)
		o as distance increases:
			o light drops as cos(theta),
			o distance increases as cos(theta),
			o light drops as distance^2,
			o so light drops as cos^3(theta)
				-> Show derivation, from notebook

-------------------------------------------------------------------------------

			      *** Reflection I ***

Reflection from surfaces I - from geometrical optics:
	o Leonardo (p. 96)
		o reflection = "light" (body color) + "lustre" (highlight)
		o light is stationary; lustre moves with the eye
		o lustre of metals = color of metal; of glass = color of light
			(Leonardo was correct)

	o Pierre Bouguer (1760)
		o rough surfaces are composed of microfacets ("asperities")
		o if mostly randomly oriented, surface is "matte",
		  reflecting fairly uniformly in all directions
		o if most are aligned with surface, surface is "specular",
		  reflecting most strongly in mirror direction

	o Johann Lambert (1760)
		o ideal diffuse ("Lambertian") surface
		  reflects uniformly in all directions

			==> Demonstrate using photometer

	o Examples of diffuse surfaces
		o ideal diffuse:
			o luminous intensity falls off as cos(theta), but
			  luminance is constant for all angles

		o ideal scatterer:
			o luminous intensity is constant
			  luminance increases at grazing angles

-------------------------------------------------------------------------------