Reflections | Documentation | La Vigile
Note that whichever of omega Subscript normal i or omega Subscript normal o has a larger value for cosine theta i. We can set sine alpha using the appropriate sine value computed at the beginning of the method. The tangent can then be computed using the identity tangent theta equals sine theta slash cosine theta. Reflection models based on microfacets that exhibit perfect specular reflection and transmission have been effective at modeling light scattering from a variety of glossy materials, including metals, plastic, and frosted glass.
The code here includes implementations of two widely used microfacet models.
MicrofacetDistribution defines the interface provided by microfacet implementations as well as some common functionality for them. In pbrt , microfacet distribution functions are defined in the same BSDF coordinate system as BxDF s; as such, a perfectly smooth surface could be described by a delta distribution that was non-zero only when omega Subscript normal h was equal to the surface normal: upper D left-parenthesis omega Subscript normal h Baseline right-parenthesis equals delta left-parenthesis omega Subscript normal h Baseline minus left-parenthesis 0 comma 0 comma 1 right-parenthesis right-parenthesis.
Microfacet distribution functions must be normalized to ensure that they are physically plausible. Intuitively, if we consider incident rays on the microsurface along the normal direction bold n Subscript , then each ray must intersect the microfacet surface exactly once.
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The method MicrofacetDistribution::D corresponds to the function upper D left-parenthesis omega Subscript normal h Baseline right-parenthesis ; implementations return the differential area of microfacets oriented with the given normal vector omega Subscript. A widely used microfacet distribution function based on a Gaussian distribution of microfacet slopes is due to Beckmann and Spizzichino ; our implementation is in the BeckmannDistribution class.
For example, given a alpha Subscript x for microfacets oriented perpendicular to the x axis and alpha Subscript y for the y axis, then alpha values for intermediate orientations can be interpolated by constructing an ellipse through these values. Note that the original isotropic variant of the Beckmann—Spizzichino model falls out when alpha Subscript x Baseline equals alpha Subscript y. The alphax and alphay member variables are set in the BeckmannDistribution constructor, which is straightforward and therefore not included here. The only additional implementation detail is that infinite values of tangent squared theta must be handled specially.
This case is actually valid—it happens at perfectly grazing directions.
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Therefore, zero is explicitly returned for this case, as that is the value that upper D left-parenthesis omega Subscript normal h Baseline right-parenthesis converges to as tangent theta Subscript normal h goes to infinity. Another useful microfacet distribution function is due to Trowbridge and Reitz In comparison to the Beckmann—Spizzichino model, Trowbridge—Reitz has higher tails—it falls off to zero more slowly for directions far from the surface normal.
This characteristic matches the properties of many real-world surfaces well. The RoughnessToAlpha method, not included here, performs a mapping from such roughness values to alpha values.
Note that 0 less-than-or-equal-to upper G 1 left-parenthesis omega Subscript Baseline comma omega Subscript normal h Baseline right-parenthesis less-than-or-equal-to 1. In the usual case where the probability a microfacet is visible is independent of its orientation omega Subscript normal h , we can write this function as upper G 1 left-parenthesis omega Subscript Baseline right-parenthesis.
The area of visible microfacets seen from this direction must also be equal to normal d upper A Subscript Baseline cosine theta , which leads to a normalization constraint for upper G 1 :. In other words, the projected area of visible microfacets for a given direction omega Subscript must be equal to left-parenthesis omega Subscript Baseline dot bold n Subscript Baseline right-parenthesis equals cosine theta times the differential area of the macrosurface normal d upper A Subscript. Because the microfacets form a heightfield, every backfacing microfacet shadows a forward-facing microfacet of equal projected area in the direction omega.
We can thus alternatively write the masking-shadowing function as the ratio of visible microfacet area to total forward-facing microfacet area:. Shadowing-masking functions are traditionally expressed in terms of an auxiliary function normal upper Lamda left-parenthesis omega Subscript Baseline right-parenthesis , which measures invisible masked microfacet area per visible microfacet area. The Lambda method computes this function. Its implementation is specific to each microfacet distribution. Some algebra lets us express upper G 1 left-parenthesis omega Subscript Baseline right-parenthesis in terms of normal upper Lamda left-parenthesis omega Subscript Baseline right-parenthesis :.
For many microfacet models, a closed-form expression can be found. Under the assumption of no correlation of the heights of nearby points, normal upper Lamda left-parenthesis omega Subscript Baseline right-parenthesis for the isotropic Beckmann—Spizzichino distribution is.
Masking-shadowing functions for anisotropic distributions are most easily computed by taking their corresponding isotropic function and stretching the underlying microsurface according to the alpha Subscript x and alpha Subscript y values. Under the uncorrelated height assumption, the form of normal upper Lamda left-parenthesis omega Subscript Baseline right-parenthesis for the Trowbridge—Reitz distribution is quite simple:.
Note that the function is close to one over much of the domain but falls to zero at grazing angles. Note also that increasing surface roughness i. One last useful function related to the geometric properties of a microfacet distribution is upper G left-parenthesis omega Subscript normal o Baseline comma omega Subscript normal i Baseline right-parenthesis , which gives the fraction of microfacets in a differential area that are visible from both directions omega Subscript normal o and omega Subscript normal i.
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Defining upper G requires some additional assumptions. Very nice!
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I'm no good at drawing cloth, and for this reason, I'm very easily impressed by other peoples' drawing of clothing. However, this giratina gijinka's regal robes hit about a mile high above most of the clothes I see gijinkas wear. You can easily feel you could reach out and touch the royal velvet and regal silk the giratina man wears, which you impressively created by hand.
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Anyway, please let me know when and if you decide to do this. Antarel Professional Digital Artist. Thank you for leaving this comment. First of all, I'm really sorry but I am not taking in any artwork requests at the moment. Also, I'd really prefer if you'd correspond via note if it's not feedback on the artwork you wish to talk about.
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Still though, this is a very original and well-done gijinka. My favorite thing about this picture is the texture of his robes.
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