[Bf-cycles] Oren-Nayar model revisited

Yasuhiro Fujii y-fujii at mimosa-pudica.net
Tue Feb 21 15:17:47 CET 2012

Hi all,

A few month ago, I implemented a Oren-Nayar model for cycles.  It has a little
wider range of roughness parameter, I noticed that it sometimes generates bad
results. For example, The dark rings are appeared on the spheres.
Essentially, it is caused a bad approximation of O-N model.

In the original paper, Oren and Nayar have proposed two approximate functions
(I call them full O-N and qualitative O-N, respectively). Qualitative O-N is
well known and widely used in CG community but full O-N is less used. I think
full O-N is too complex.

So I developed a tiny improvement of qualitative O-N.  It has the same
simplicity as qualitative O-N but yields very similar result as full O-N.

The detail are described at:

The implementation for cycles is very simple:

__device float3 bsdf_oren_nayar_get_intensity(const ShaderClosure *sc,
float3 n, float3 v, float3 l)
    float nl = max(dot(n, l), 0.0f);
    float nv = max(dot(n, v), 0.0f);
    float t = dot(l, v) - nl * nv;
    if (t > 0.0f)
        t /= max(nl, nv) + FLT_MIN;
    float is = nl * (sc->data0 + sc->data1 * t);
    return make_float3(is, is, is);

__device void bsdf_oren_nayar_setup(ShaderData *sd, ShaderClosure *sc,
float sigma)
    sd->flag |= SD_BSDF | SD_BSDF_HAS_EVAL;

    sigma = clamp(sigma, 0.0f, 1.0f);
    float div = 1.0f / (M_PI_F + ((3.0f * M_PI_F - 4.0f) / 6.0f) * sigma);

    sc->data0 =  1.0f * div;
    sc->data1 = sigma * div;

I've used this model in practice for 2, 3 month and no problems are
found at the moment.
I'd be happy if this improvement is reviewed.

-- Yasuhiro Fujii

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