William F Pokorny <ano### [at] anonymousorg> wrote:

> Question: I think the conserve_energy helps & turns the background dark
> because we cannot both reflect at >=1 and transmit at >=1. In other
> words, we don't see through the r=30 sphere to the plane with the
> granite pigment. Is this understanding correct?


To be precise, conserve_energy ensures that transmission is attenuated in
accordance with variable reflection, so that as effective reflection increases,
the effective transmission decreases accordingly. If transmission is set to 1
and reflection is set to 0 and 1 (min and max, respectively), then the effective
transmission plus effective reflection will be kept constant at 1. (Filter, too,
is subject to the same level of attenuation.)

In mathematical terms, given variable reflection with values REFL_MIN and
REFL_MAX, and transmit and filter set to TRANS and FILTER respectively, the
effective reflection, transmission and filter will be

    REFL_EFF   =   x   * (REFL_MAX - REFL_MIN) + REFL_MIN
    TRANS_EFF  = (1-x) * TRANS
    FILTER_EFF = (1-x) * FILTER

where x depends on the angle at which we are looking at the surface.


You could also say that using conserve_energy makes variable reflection blend
between reflection and transmission/fiter, rather than just varying the
reflection component.

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