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UtilsFunc.py
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UtilsFunc.py
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import taichi as ti
import taichi_glsl as ts
import math
from taichi_glsl.vector import normalize
########################### Important !!!! ###############################
#struct description
#material : type_f aleboTex_f color_v3 param_v5 10
# 0 disney metallic_f roughness_f
# 1 glass ior extinction
# 2 light
# 10 spectral
#shape : type_f pos_v3 param_v6 10
# 1 sphere radius
# 2 quad v1 v2
# 3 spot r1 r2 scale normal
# 4 dir radius X X normal
#
#vertex : pos_v3 normal_v3 tex_v3 9
#primitive : type(0:tri 1:shape) vertexIndex(shape_index) matIndex 3
# 32bit | 32bit | 32bit | 32bit | 32bit |96bit |96bit
#bvh_node : is_leaf axis |left_node right_node parent_node prim_index min_v3 max_v3 11
# 1bit 2bit
# 32bit |32bit |32bit |96bit |96bit
#compact_node : is_leaf axis |prim_index offset min_v3 max_v3 9
# 1bit 2bit
########################### Important !!!! ###############################
AXIS_X = 0
AXIS_Y = 1
AXIS_Z = 2
EPS = 0.00001
M_PIf = 3.1415956
INF_VALUE = 1000000.0
k_B = 1.38064852e-23
h = 6.62607015e-34
c = 299792458.0
xyz_to_srgb = ti.Matrix([[3.240479, -1.537150, -0.498535],[-0.969256, 1.875991, 0.041556],[0.055648, -0.204043, 1.057311]])
srgb_to_xyz = ti.Matrix([[0.412453, 0.357580, 0.180423 ],[0.212671, 0.715160, 0.072169],[0.019334, 0.119193, 0.950227]])
########################### color function ###############################
#http://brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html
@ti.func
def calc_matr_rgb_to_xyz(xy_r, xy_g, xy_b,XYZ_W):
x_rgb = ti.Vector([xy_r.x, xy_g.x, xy_b.x])
y_rgb = ti.Vector([xy_r.y, xy_g.y, xy_b.y])
X_rgb = x_rgb / y_rgb
Y_rgb = ti.Vector([1.0, 1.0, 1.0])
Z_rgb = (ti.Vector([1.0, 1.0, 1.0]) - x_rgb - y_rgb ) / y_rgb
S_rgb = ti.Matrix.rows([X_rgb,Y_rgb,Z_rgb]).inverse() @ XYZ_W[0]
return ti.Matrix.rows([S_rgb * X_rgb,S_rgb * Y_rgb,S_rgb * Z_rgb])
#https://en.wikipedia.org/wiki/Planck%27s_law#The_law
def Planck(Lambda, temperature):
lambda_m = Lambda * 1.0e-9 #nm->m
#First radiation constant 2 h c²
c_1L = 2.0 * h*c*c
#Second radiation constant h c / k_B
c_2 = h*c/k_B
numer = c_1L
denom = pow(lambda_m,5.0) * (math.exp( c_2 / (lambda_m*temperature) ) - 1.0)
value = numer / denom
return value * 1.0e-9
@ti.func
def srgb_to_lrgb(srgb):
ret = ti.Vector([0.0, 0.0, 0.0])
for i in ti.static(range(3)):
if srgb[i] < 0.04045:
ret[i] = srgb[i] / 12.92
else:
ret[i] = pow((srgb[i] + 0.055) / 1.055, 2.4)
return ret
@ti.func
def lrgb_to_srgb(lrgb):
ret = ti.Vector([0.0, 0.0, 0.0])
for i in ti.static(range(3)):
if lrgb[i] < 0.0031308:
ret[i] = lrgb[i] * 12.92
else:
ret[i] = 1.055 * pow(lrgb[i], 1.0 / 2.4) - 0.055
return ts.clamp(ret, 0.0, 1.0)
@ti.func
def xyz_to_Yxy(xyz):
ret = ti.Vector([0.0, 0.0, 0.0])
coff = xyz[0] + xyz[1]+ xyz[2]
if coff > 0.0:
coff = 1.0 / coff
ret = ti.Vector([xyz[1], coff * xyz[0], coff * xyz[1]])
return ret
@ti.func
def Yxy_to_xyz(yxy):
ret = ti.Vector([0.0, 0.0, 0.0])
if yxy[2] > 0.0:
k = yxy[0] / yxy[2]
ret = ti.Vector([k*yxy[1], yxy[0], k *(1.0 -yxy[1]-yxy[2])])
return ret
#https://knarkowicz.wordpress.com/2016/01/06/aces-filmic-tone-mapping-curve/
@ti.func
def tone_ACES(x):
a = 2.51
b = 0.03
c = 2.43
d = 0.59
e = 0.14
return ts.clamp((x*(a*x+b))/(x*(c*x+d)+e),0.0, 1.0)
########################### tool function ###############################
@ti.func
def get_material_type(material, index):
return int(material[index][0])
@ti.func
def get_material_tex(material, index):
return int(material[index][1])
@ti.func
def get_material_color(material, index):
return ti.Vector([material[index][2], material[index][3], material[index][4] ])
@ti.func
def get_material_metallic(material, index):
return material[index][5]
@ti.func
def get_material_roughness(material, index):
return material[index][6]
@ti.func
def get_material_ior(material, index):
return material[index][5]
@ti.func
def get_material_extinction(material, index):
return material[index][6]
@ti.func
def get_vertex_pos(vertex, index):
return ti.Vector([vertex[index][0], vertex[index][1], vertex[index][2] ])
@ti.func
def get_vertex_normal(vertex, index):
return ti.Vector([vertex[index][3], vertex[index][4], vertex[index][5] ])
@ti.func
def get_vertex_uv(vertex, index):
return ti.Vector([vertex[index][6], vertex[index][7], vertex[index][8] ])
@ti.func
def set_vertex_normal(vertex, index, n):
vertex[index][3] = n[0]
vertex[index][4] = n[1]
vertex[index][5] = n[2]
@ti.func
def get_prim_type(primitive, index):
return primitive[index][0]
@ti.func
def get_prim_vindex(primitive, index):
return primitive[index][1]
@ti.func
def get_prim_mindex(primitive, index):
return primitive[index][2]
@ti.func
def get_shape_type(shape, index):
return int(shape[index][0])
@ti.func
def get_shape_pos(shape, index):
return ti.Vector([shape[index][1], shape[index][2], shape[index][3] ])
@ti.func
def get_shape_radius(shape, index):
return shape[index][4]
@ti.func
def get_shape_xita(shape, index):
return shape[index][4],shape[index][5]
@ti.func
def get_shape_scale(shape, index):
return shape[index][6]
@ti.func
def get_shape_v1(shape, index):
return ti.Vector([shape[index][4], shape[index][5], shape[index][6] ])
@ti.func
def get_shape_v2(shape, index):
return ti.Vector([shape[index][7], shape[index][8], shape[index][9] ])
@ti.func
def get_shape_normal(shape, index):
return ti.Vector([shape[index][7], shape[index][8], shape[index][9] ])
@ti.func
def get_hit_t( hit_info):
return hit_info[0]
@ti.func
def get_hit_prim( hit_info):
return int(hit_info[10])
@ti.func
def get_hit_pos( hit_info):
return ti.Vector([hit_info[1], hit_info[2], hit_info[3] ])
@ti.func
def get_hit_normal( hit_info):
return ti.Vector([hit_info[4], hit_info[5], hit_info[6] ])
@ti.func
def get_hit_uv( hit_info):
return ti.Vector([hit_info[7], hit_info[8], hit_info[9] ])
# 32bit | 32bit | 32bit | 32bit | 32bit |96bit |96bit
#bvh_node : is_leaf axis |left_node right_node parent_node prim_index min_v3 max_v3 11
# 1bit 2bit
@ti.func
def init_bvh_node(bvh_node, index):
bvh_node[index][0] = -1.0
bvh_node[index][1] = -1.0
bvh_node[index][2] = -1.0
bvh_node[index][3] = -1.0
bvh_node[index][4] = -1.0
bvh_node[index][5] = INF_VALUE
bvh_node[index][6] = INF_VALUE
bvh_node[index][7] = INF_VALUE
bvh_node[index][8] = -INF_VALUE
bvh_node[index][9] = -INF_VALUE
bvh_node[index][10] = -INF_VALUE
@ti.func
def set_node_type(bvh_node, index, type):
bvh_node[index][0] = float(int(bvh_node[index][0]) & (0xfffe | type))
@ti.func
def set_node_axis(bvh_node, index, axis):
axis = axis<<1
bvh_node[index][0] =float(int(bvh_node[index][0]) & (0xfff9 | type))
@ti.func
def set_node_prim_size(bvh_node, index, size):
bvh_node[index][0] =float(int(bvh_node[index][0]) & (0x0007 | size))
@ti.func
def set_node_left(bvh_node, index, left):
bvh_node[index][1] = float(left)
@ti.func
def set_node_right(bvh_node, index, right):
bvh_node[index][2] = float(right)
@ti.func
def set_node_parent(bvh_node, index, parent):
bvh_node[index][3] = float(parent)
@ti.func
def set_node_prim(bvh_node, index, prim):
bvh_node[index][4] = float(prim)
@ti.func
def set_node_min_max(bvh_node, index, minv,maxv):
bvh_node[index][5] = minv[0]
bvh_node[index][6] = minv[1]
bvh_node[index][7] = minv[2]
bvh_node[index][8] = maxv[0]
bvh_node[index][9] = maxv[1]
bvh_node[index][10] = maxv[2]
@ti.func
def get_node_type(bvh_node, index):
return int(bvh_node[index][0]) & 0x0001
@ti.func
def get_node_axis(bvh_node, index):
return int(bvh_node[index][0]) & 0x0006
@ti.func
def get_node_child(bvh_node, index):
return int(bvh_node[index][1]),int(bvh_node[index][2])
@ti.func
def get_node_parent(bvh_node, index):
return int(bvh_node[index][3])
@ti.func
def get_node_prim(bvh_node, index):
return int(bvh_node[index][4])
@ti.func
def get_node_min_max(bvh_node, index):
return ti.Vector([bvh_node[index][5], bvh_node[index][6], bvh_node[index][7] ]),ti.Vector([bvh_node[index][8], bvh_node[index][9], bvh_node[index][10] ])
@ti.func
def get_node_has_box(bvh_node, index):
return (bvh_node[index][5] <= bvh_node[index][8]) & (bvh_node[index][6] <= bvh_node[index][9]) & (bvh_node[index][7] <= bvh_node[index][10])
# 32bit |32bit |32bit |96bit |96bit
#compact_node : is_leaf axis |prim_index offset min_v3 max_v3 9
# 1bit 2bit
@ti.func
def get_compact_node_type(bvh_node, index):
return int(bvh_node[index][0]) & 0x0001
@ti.func
def get_compact_node_axis(bvh_node, index):
return int(bvh_node[index][0]) & 0x0006
@ti.func
def get_compact_node_prim_size(bvh_node, index):
return int(bvh_node[index][0]) & 0xfff8
@ti.func
def get_compact_node_prim(bvh_node, index):
return int(bvh_node[index][1])
@ti.func
def get_compact_node_offset(bvh_node, index):
return int(bvh_node[index][1])
@ti.func
def get_compact_node_min_max(bvh_node, index):
return ti.Vector([bvh_node[index][2], bvh_node[index][3], bvh_node[index][4] ]),ti.Vector([bvh_node[index][5], bvh_node[index][6], bvh_node[index][7] ])
###################################################################
############algrithm##############
@ti.func
def mapToDisk(u1,u2):
phi = 0.0
r = 0.0
a = 2.0 *u1 - 1.0
b = 2.0 *u2 - 1.0
if (a > -b) :
if (a > b):
r = a
phi = (M_PIf / 4.0) * (b / a)
else :
r = b
phi = (M_PIf / 4.0) * (2.0 - a / b)
else:
if (a < b):
r = -a
phi = (M_PIf / 4.0) * (4.0 + b / a)
else:
r = -b
if b == 0.0:
phi = 0.0
else:
phi = (M_PIf / 4.0) * (6.0 - a / b)
#print(a,b,r,phi)
return r, phi
@ti.func
def CosineHemisphere_pdf(cosTheta):
return max(0.01, cosTheta/M_PIf)
@ti.func
def CosineSampleHemisphere( u1, u2):
r = ti.sqrt(u1)
phi = 2.0*M_PIf * u2
p = ti.Vector([0.0,0.0,0.0])
p.x = r * ti.cos(phi)
p.y = r * ti.sin(phi)
p.z = ti.sqrt(max(0.0, 1.0 - p.x*p.x - p.y*p.y))
return p.normalized()
@ti.func
def CosineSampleHemisphere_pdf( u1, u2):
r = ti.sqrt(u1)
phi = 2.0*M_PIf * u2
p = ti.Vector([0.0,0.0,0.0])
p.x = r * ti.cos(phi)
p.y = r * ti.sin(phi)
p.z = ti.sqrt(max(0.0, 1.0 - p.x*p.x - p.y*p.y))
p = p.normalized()
return p, CosineHemisphere_pdf(p.z)
@ti.func
def inverse_transform(dir, N):
Normal = N.normalized()
Binormal = ti.Vector([0.0, 0.0, 0.0])
if (abs(Normal.x) > abs(Normal.z)):
Binormal.x = -Normal.y
Binormal.y = Normal.x
Binormal.z = 0.0
else:
Binormal.x = 0.0
Binormal.y = -Normal.z
Binormal.z = Normal.y
Binormal = Binormal.normalized()
Tangent = Binormal.cross(Normal).normalized()
return dir.x*Tangent + dir.y*Binormal + dir.z*Normal
@ti.func
def sqr(x):
return x*x
@ti.func
def SchlickFresnel(u):
m = ts.clamp(1.0-u, 0.0, 1.0)
m2 = m*m
return m2*m2*m
@ti.func
def GTR1(NDotH, a):
ret =1.0/ M_PIf
if (a < 1.0):
a2 = a*a
t = 1.0 + (a2-1.0)*NDotH*NDotH
ret = (a2-1.0) / (M_PIf*ti.log(a2)*t)
return ret
@ti.func
def GTR2(NDotH, a):
a2 = a*a
t = 1.0 + (a2-1.0)*NDotH*NDotH
return a2 / (M_PIf * t*t)
@ti.func
def smithG_GGX(NDotv, alphaG):
a = alphaG*alphaG
b = NDotv*NDotv
return 1.0/(NDotv + ti.sqrt(a + b - a*b))
@ti.func
def refract(InRay, N, eta):
suc = -1.0
N_DOT_I = N.dot(InRay)
k = 1.0 - eta * eta * (1.0 - N_DOT_I * N_DOT_I)
R = ti.Vector([0.0,0.0,0.0])
if k > 0.0:
R = eta * InRay - (eta * N_DOT_I + ti.sqrt(k)) * N
suc = 1.0
return R,suc
@ti.func
def schlick(cosine, index_of_refraction):
r0 = (1.0 - index_of_refraction) / (1.0 + index_of_refraction)
r0 = r0 * r0
return r0 + (1.0 - r0) * pow((1.0 - cosine), 5.0)
@ti.func
def powerHeuristic( a, b):
t = a* a
return t / (b*b + t)
@ti.func
def offset_ray(p, n):
int_scale = 256.0
float_scale = 1.0 / 2048.0
origin = 1.0 / 256.0
ret = ti.Vector([0.0, 0.0, 0.0])
for k in ti.static(range(3)):
i_of = int(int_scale * n[k])
i_p = ti.bit_cast(p[k], ti.i32)
if p[k] < 0.0:
i_p = i_p - i_of
else:
i_p = i_p + i_of
f_p = ti.bit_cast(i_p, ti.f32)
if abs(p[k]) < origin:
ret[k] = p[k] + float_scale * n[k]
else:
ret[k] = f_p
return ret
# sometimes 3d model software will do normal smoothing,
# that will change the true geometry normal,so we use geometry normal as a ref
@ti.func
def faceforward(n, i, nref):
return ts.sign(i.dot(nref)) * n
@ti.func
def srgb_to_lrgb(srgb):
ret = ti.Vector([0.0, 0.0, 0.0])
for i in ti.static(range(3)):
if srgb[i] < 0.04045:
ret[i] = srgb[i] / 12.92
else:
ret[i] = pow((srgb[i] + 0.055) / 1.055, 2.4)
return ret
# https://refractiveindex.info/?shelf=glass&book=BK7&page=SCHOTT
@ti.func
def get_glass_ior(Lambda):
Lambda = Lambda/1000.0
Lambda2 = Lambda*Lambda
return ti.sqrt(1.0 + 1.03961212 * Lambda2/ (Lambda2 -0.00600069867 )+ 0.231792344 * Lambda2/ (Lambda2 -0.0200179144 ) + 1.01046945 * Lambda2/ (Lambda2 -103.560653))
@ti.func
def max_component( v):
return max(v.z, max(v[0], v.y) )
@ti.func
def min_component( v):
return min(v.z, min(v[0], v.y) )
@ti.func
def slabs(origin, direction, minv, maxv):
# most effcient algrithm for ray intersect aabb
# en vesrion: https://www.researchgate.net/publication/220494140_An_Efficient_and_Robust_Ray-Box_Intersection_Algorithm
# cn version: https://zhuanlan.zhihu.com/p/138259656
ret = 1
tmin = 0.0
tmax = INF_VALUE
for i in ti.static(range(3)):
if abs(direction[i]) < 0.000001:
if ( (origin[i] < minv[i]) | (origin[i] > maxv[i])):
ret = 0
else:
ood = 1.0 / direction[i]
t1 = (minv[i] - origin[i]) * ood
t2 = (maxv[i] - origin[i]) * ood
if(t1 > t2):
temp = t1
t1 = t2
t2 = temp
if(t1 > tmin):
tmin = t1
if(t2 < tmax):
tmax = t2
if(tmin > tmax) :
ret=0
return ret
'''
ret = 0
t0 = (minv - origin) / direction
t1 = (maxv - origin) / direction
tmin = min(t0,t1)
tmax = max(t0,t1)
if max_component(tmin) <= min_component(tmax):
ret = 1
return ret
'''
@ti.func
def expandBits( x):
'''
# nvidia blog : https://developer.nvidia.com/blog/thinking-parallel-part-iii-tree-construction-gpu/
v = ( (v * 0x00010001) & 0xFF0000FF)
v = ( (v * 0x00000101) & 0x0F00F00F)
v = ( (v * 0x00000011) & 0xC30C30C3)
v = ( (v * 0x00000005) & 0x49249249)
taichi can not handle it, so i change that to bit operate
'''
x = (x | (x << 16)) & 0x030000FF
x = (x | (x << 8)) & 0x0300F00F
x = (x | (x << 4)) & 0x030C30C3
x = (x | (x << 2)) & 0x09249249
return x
@ti.func
def common_upper_bits(lhs, rhs) :
x = lhs ^ rhs
ret = 32
while x > 0:
x = x>>1
ret -=1
#print(ret, lhs, rhs, x, find, ret)
#print(x)
return ret
@ti.func
def morton3D(x, y, z):
x = min(max(x * 1024.0, 0.0), 1023.0)
y = min(max(y * 1024.0, 0.0), 1023.0)
z = min(max(z * 1024.0, 0.0), 1023.0)
xx = expandBits(ti.cast(x, dtype = ti.i32))
yy = expandBits(ti.cast(y, dtype = ti.i32))
zz = expandBits(ti.cast(z, dtype = ti.i32))
#return zz | (yy << 1) | (xx<<2)
code = xx | (yy << 1) | (zz<<2)
if code == 0:
print(x,y,z)
return code
#https://knarkowicz.wordpress.com/2016/01/06/aces-filmic-tone-mapping-curve/
@ti.kernel
def tone_map(exposure:ti.f32, input:ti.template(), output:ti.template()):
for i,j in output:
output[i,j] = lrgb_to_srgb(tone_ACES(input[i,j]*exposure))