Computer Graphics

Foundations

The quantities everything else is defined in terms of.

Colour is the family; a dashed line is the second member of it.

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G brdf BRDF radiance Radiance brdf->radiance defined as a ratio of radiance to irradiance reflection Reflection brdf->reflection bsdf BSDF bsdf->brdf covers the transmitted hemisphere as well energy-conservation Energy Conservation energy-conservation->bsdf the BSDF integrated over the sphere must not exceed 1 helmholtz-reciprocity Helmholtz Reciprocity helmholtz-reciprocity->bsdf swapping the directions must not change the value light-transport Light Transport radiance->light-transport reflection->light-transport refraction Refraction refraction->light-transport rendering-equation The Rendering Equation rendering-equation->light-transport rendering-equation->radiance the unknown it solves for is a radiance field scattering Scattering scattering->light-transport white-furnace-test White Furnace Test white-furnace-test->energy-conservation a lossless material must vanish into a uniform background

11 nodes

BRDF

Ratio of outgoing radiance to incoming irradiance for a pair of directions. The formalism that lets a material be specified independently of the tran… · 1965

The Rendering Equation

States outgoing radiance at a point as emission plus the integral of incoming radiance weighted by the BSDF. Unified the previously separate ray trac… · 1986

BSDF

A BRDF and a BTDF taken together, defined over the whole sphere rather than the upper hemisphere, so that one function describes both sides of a surf…

Energy Conservation

A surface may not reflect more energy than it receives. Violating it makes multi-bounce renders diverge into brightness rather than settle.

Helmholtz Reciprocity

A physically valid BSDF gives the same value when incoming and outgoing directions are swapped. Bidirectional algorithms depend on it: without it, a…

Light Transport

The problem of computing how radiance moves through a scene from emitters to the camera, accounting for every path it can take on the way.

Radiance

Power per unit projected area per unit solid angle. It is the quantity that is constant along a ray in a vacuum, which is why renderers transport it…

Reflection

Light leaving a surface on the same side it arrived from.

Refraction

Light crossing into a medium with a different index of refraction, bending by Snell's law and changing radiance by the squared IOR ratio.

Scattering

Light redirected inside a medium rather than at a surface boundary.

White Furnace Test

Render a material under uniform unit illumination with no absorption. A conserving, non-absorbing BSDF disappears against the background; anything vi…