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@Enigmatisms
Enigmatisms committed Aug 7, 2023
1 parent 0681c76 commit a2eb749
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83 changes: 43 additions & 40 deletions bxdf/brdf.py
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Original file line number Diff line number Diff line change
Expand Up @@ -16,7 +16,6 @@
import xml.etree.ElementTree as xet
from taichi.math import vec3, vec4, mat3

from bxdf.misc import *
from la.geo_optics import *
from la.cam_transform import *
from sampler.general_sampling import *
Expand Down Expand Up @@ -152,6 +151,7 @@ class BRDF:
"""
_type: int
is_delta: int # whether the BRDF is Dirac-delta-like
""" Note that thin-coat can be delta / non-delta at the same time (have specular + diffuse part)"""
k_d: vec3 # diffusive coefficient (albedo)
k_s: vec3 # specular coefficient
k_g: vec3 # glossiness coefficient
Expand Down Expand Up @@ -357,51 +357,56 @@ def sample_thin_coat(self, it: ti.template(), incid: vec3):

dot_normal = tm.dot(incid, it.n_s)
# We will not have total reflection for incident ray
refra_in, _v = snell_refraction(incid, it.n_s, dot_normal, 1.0, self.k_g[2])
in_ref_F = fresnel_equation(1., self.k_g[0], ti.abs(dot_normal), ti.abs(tm.dot(refra_in, it.n_s)))
refra_in, cos_r2 = snell_refraction(incid, it.n_s, dot_normal, 1.0, self.k_g[2])
in_ref_F = fresnel_equation(1., self.k_g[0], ti.abs(dot_normal), ti.sqrt(cos_r2))
""" There are two Fresnel term sampling:
- sample: direct reflection
- sample: total internal reflection in the coating layer - absorbed
"""
is_specular = False
if ti.random(float) > in_ref_F: # refracting into the thin layer
# Lambertian sampling
local_new_dir, pdf = cosine_hemisphere()
ray_out_d, _ = delocalize_rotate(it.n_s, local_new_dir)
dot_out = tm.dot(ray_out_d, it.n_s)
if not is_total_reflection(dot_out, self.k_g[0], 1.0): # total reflection - set spec to 0
if not is_total_reflection(dot_out, self.k_g[2], 1.0): # total reflection - set spec to 0
# sample the second Fresnel term: whether we will have a total reflection?
refra_out, _v = snell_refraction(ray_out_d, it.n_s, dot_out, self.k_g[2], 1.0)
out_ref_F = fresnel_equation(self.k_g[0], 1., ti.abs(dot_out), ti.abs(tm.dot(refra_out, it.n_s)))
if ti.random(float) > out_ref_F: # refraction out to the world
fresnel_value = (1. - in_ref_F) * (1. - out_ref_F)
pdf *= fresnel_value
ray_out_d = refra_out
# Oren-Nayar evaluation
spec = self.eval_oren_nayar(it, refra_in, ray_out_d)
spec *= fresnel_value
refra_out, cos_r2 = snell_refraction(ray_out_d, it.n_s, dot_out, self.k_g[2], 1.0)
out_ref_F = fresnel_equation(self.k_g[2], 1., ti.abs(dot_out), ti.sqrt(cos_r2))
pdf *= (1. - in_ref_F)
ray_out_d = refra_out
# Oren-Nayar evaluation
spec = self.eval_oren_nayar(it, refra_in, ray_out_d)
spec *= (1. - in_ref_F) * (1. - out_ref_F)
else: # reflection
spec = self.k_s
# sample specular, we should tag it
spec = self.k_s * in_ref_F
ray_out_d, _ = inci_reflect_dir(incid, it.n_s)
pdf = in_ref_F
return ray_out_d, spec, pdf
is_specular = True
return ray_out_d, spec, pdf, is_specular

@ti.func
def eval_thin_coating(self, it:ti.template(), ray_in: vec3, ray_out: vec3):
# input Fresnel evaluation
ret_spec = ZERO_V3
reflect, _ = inci_reflect_dir(ray_in, it.n_s)
dot_in = tm.dot(ray_in, it.n_s)
# We will not have total reflection for incident ray
refra_in, _v = snell_refraction(ray_in, it.n_s, dot_in, 1.0, self.k_g[2])
in_ref_F = fresnel_equation(1., self.k_g[2], ti.abs(dot_in), ti.abs(tm.dot(refra_in, it.n_s)))

# output Fresnel evaluation
dot_out = tm.dot(ray_out, it.n_s)
refra_out, _v = snell_refraction(ray_out, it.n_s, dot_out, self.k_g[2], 1.0) # always valid
out_ref_F = fresnel_equation(self.k_g[2], 1.0, ti.abs(dot_out), ti.abs(tm.dot(refra_out, it.n_s)))
ret_spec = self.eval_oren_nayar(it, refra_in, refra_out) * ((1. - out_ref_F) * (1. - in_ref_F))
refra_in, cos_r2 = snell_refraction(ray_in, it.n_s, dot_in, 1.0, self.k_g[2])
in_ref_F = fresnel_equation(1., self.k_g[2], ti.abs(dot_in), ti.sqrt(cos_r2))
if ti.abs(tm.dot(ray_out, reflect)) > (1. - 1e-4):
ret_spec = self.k_s * in_ref_F
else:
# output Fresnel evaluation
dot_out = tm.dot(ray_out, it.n_s)
refra_out, cos_r2 = snell_refraction(ray_out, it.n_s, dot_out, 1.0, self.k_g[2]) # always valid
out_ref_F = fresnel_equation(1.0, self.k_g[2], ti.abs(dot_out), ti.sqrt(cos_r2))
ret_spec = self.eval_oren_nayar(it, refra_in, refra_out) * ((1. - out_ref_F) * (1. - in_ref_F))
return ret_spec

@ti.func
def thin_coat_fresnel(self, it: ti.template(), ray_in: vec3, ray_out: vec3) -> float:
def thin_coat_fresnel(self, it: ti.template(), ray_in: vec3) -> float:
""" Evaluating the Fresnel coating: mirror specular + Oren-Nayar diffuse
note that evaluation for mirror specular part is always 0
Expand All @@ -410,15 +415,10 @@ def thin_coat_fresnel(self, it: ti.template(), ray_in: vec3, ray_out: vec3) -> f
# input Fresnel evaluation
dot_in = tm.dot(ray_in, it.n_s)
# We will not have total reflection for incident ray
refra_in, _v = snell_refraction(ray_in, it.n_s, dot_in, 1.0, self.k_g[2])
in_ref_F = fresnel_equation(1., self.k_g[2], ti.abs(dot_in), ti.abs(tm.dot(refra_in, it.n_s)))

# output Fresnel evaluation
dot_out = tm.dot(ray_out, it.n_s)
refra_out, _v = snell_refraction(ray_out, it.n_s, dot_out, self.k_g[2], 1.0) # always valid
out_ref_F = fresnel_equation(self.k_g[2], 1.0, ti.abs(dot_out), ti.abs(tm.dot(refra_out, it.n_s)))

return (1. - out_ref_F) * (1. - in_ref_F)
ratio = 1.0 / self.k_g[2]
cos_r2 = 1. - ti.pow(ratio, 2) * (1. - ti.pow(dot_in, 2)) # refraction angle cosine
in_ref_F = fresnel_equation(1., self.k_g[2], ti.abs(dot_in), ti.sqrt(cos_r2))
return in_ref_F

# ============================================================================

Expand Down Expand Up @@ -536,14 +536,15 @@ def sample_new_rays(self, it:ti.template(), incid: vec3):
ret_dir = vec3([0, 1, 0])
ret_spec = vec3([1, 1, 1])
pdf = 1.0
is_specular = False
if self._type == BRDFTag.BLING_PHONG: # bling-phong glossy sampling
ret_dir, ret_spec, pdf = self.sample_blinn_phong(it, incid)
elif self._type == BRDFTag.LAMBERTIAN or self._type == BRDFTag.OREN_NAYAR: # Lambertian
ret_dir, ret_spec, pdf = self.sample_lambertian(it, it.n_s)
elif self._type == BRDFTag.SPECULAR: # Specular - specular has no cosine attenuation
ret_dir, ret_spec, pdf = self.sample_specular(it, incid, it.n_s)
elif self._type == BRDFTag.THIN_COAT:
ret_dir, ret_spec, pdf = self.sample_thin_coat(it, incid)
ret_dir, ret_spec, pdf, is_specular = self.sample_thin_coat(it, incid)
elif self._type == BRDFTag.MOD_PHONG: # Modified-Phong
ret_dir, ret_spec, pdf = self.sample_mod_phong(it, incid)
elif self._type == BRDFTag.FRESNEL_BLEND: # Fresnel-Blend
Expand All @@ -555,7 +556,7 @@ def sample_new_rays(self, it:ti.template(), incid: vec3):
# Prevent shading normal from light leaking or accidental shadowing
ret_dot = tm.dot(ret_dir, it.n_g)
ret_spec = ti.select(ret_dot > 0, ret_spec, 0.)
return ret_dir, ret_spec, pdf
return ret_dir, ret_spec, pdf, is_specular

@ti.func
def get_pdf(self, it: ti.template(), outdir: vec3, incid: vec3):
Expand All @@ -570,11 +571,8 @@ def get_pdf(self, it: ti.template(), outdir: vec3, incid: vec3):
if dot_outdir * dot_indir < 0.: # same hemisphere
if self._type == BRDFTag.BLING_PHONG:
pdf = dot_outdir * INV_PI # dot is cosine term
elif self._type == BRDFTag.LAMBERTIAN or self._type >= BRDFTag.OREN_NAYAR:
elif self._type == BRDFTag.LAMBERTIAN or self._type == BRDFTag.OREN_NAYAR:
pdf = dot_outdir * INV_PI
if self._type == BRDFTag.THIN_COAT:
# multiply two Fresnel terms
pdf *= self.thin_coat_fresnel(it, incid, outdir)
elif self._type == BRDFTag.MOD_PHONG:
glossiness = self.mean[2]
reflect_view, _ = inci_reflect_dir(incid, it.n_s)
Expand All @@ -583,6 +581,10 @@ def get_pdf(self, it: ti.template(), outdir: vec3, incid: vec3):
specular_pdf = 0.5 * (glossiness + 1.) * INV_PI * tm.pow(dot_ref_out, glossiness)
diffuse_color = ti.select(it.is_tex_invalid(), self.k_d, it.tex)
pdf = diffuse_color.max() * diffuse_pdf + self.k_s.max() * specular_pdf
elif self._type == BRDFTag.THIN_COAT:
reflect, _ = inci_reflect_dir(incid, it.n_s)
in_ref_F = self.thin_coat_fresnel(it, incid)
pdf = ti.select(ti.abs(tm.dot(outdir, reflect)) > (1. - 1e-3), in_ref_F, (1. - in_ref_F) * dot_outdir * INV_PI)
elif self._type == BRDFTag.FRESNEL_BLEND:
half_vec = (outdir - incid).normalized()
dot_half = tm.dot(half_vec, it.n_s)
Expand All @@ -595,4 +597,5 @@ def get_pdf(self, it: ti.template(), outdir: vec3, incid: vec3):
if self._type == BRDFTag.MICROFACET:
wh = (outdir - incid).normalized()
pdf = trow_reitz_pdf(-incid, wh, self.k_g, it.n_s) / (-4. * tm.dot(wh, incid))
return pdf
return pdf

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