21 |
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22 |
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Lu, Lv - local (u,v) coordinates |
23 |
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24 |
< |
For brdf functions, the following are also available: |
24 |
> |
For *func & *data materials, the following are also available: |
25 |
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26 |
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NxP, NyP, NzP - perturbed surface normal |
27 |
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RdotP - perturbed ray dot product |
41 |
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42 |
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sin(x), cos(x), tan(x), |
43 |
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asin(x), acos(x), |
44 |
< |
atan(x), atan2(y,x) - standard trig functions |
44 |
> |
atan(x), atan2(y,x) - standard trig functions (radians) |
45 |
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46 |
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floor(x), ceil(x) - g.l.b. & l.u.b. |
47 |
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51 |
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52 |
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rand(x) - pseudo-random function (0 to 1) |
53 |
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54 |
– |
hermite(p0,p1,r0,r1,t) - 1-dimensional hermite polynomial |
55 |
– |
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54 |
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noise3(x,y,z), noise3x(x,y,z), |
55 |
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noise3y(x,y,z), noise3z(x,y,z) - noise function with gradient (-1 to 1) |
56 |
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121 |
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fade(near_val,far_val,dist) : far_val + |
122 |
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if (16-dist, (near_val-far_val)/(1+dist*dist), 0); |
123 |
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124 |
+ |
hermite(p0,p1,r0,r1,t) : p0 * ((2*t-3)*t*t+1) + |
125 |
+ |
p1 * (-2*t+3)*t*t + |
126 |
+ |
r0 * (((t-2)*t+1)*t) + |
127 |
+ |
r1 * ((t-1)*t*t); |
128 |
+ |
|
129 |
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bezier(p1, p2, p3, p4, t) : p1 * (1+t*(-3+t*(3-t))) + |
130 |
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p2 * 3*t*(1+t*(-2+t)) + |
131 |
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p3 * 3*t*t*(1-t) + |
150 |
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151 |
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{ Normal distribution from uniform range (0,1) } |
152 |
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153 |
< |
un2`P(t) : t - (2.515517+t*(.802853+t*.010328))/ |
153 |
> |
un2`P.(t) : t - (2.515517+t*(.802853+t*.010328))/ |
154 |
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(1+t*(1.432788+t*(.189269+t*.001308))) ; |
155 |
< |
un1`P(p) : un2`P(sqrt(-2*log(p))) ; |
155 |
> |
un1`P.(p) : un2`P.(sqrt(-2*log(p))) ; |
156 |
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157 |
< |
unif2norm(p) : if( .5-p, -un1`P(p), un1`P(1-p) ) ; |
157 |
> |
unif2norm(p) : if( .5-p, -un1`P.(p), un1`P.(1-p) ) ; |
158 |
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159 |
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nrand(x) = unif2norm(rand(x)); |
160 |
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161 |
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{ Local (u,v) coordinates for planar surfaces } |
162 |
< |
crosslen`P = Nx*Nx + Ny*Ny; |
162 |
> |
crosslen`P. = Nx*Nx + Ny*Ny; |
163 |
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{ U is distance from projected Z-axis } |
164 |
< |
U = if( crosslen`P - FTINY, |
165 |
< |
(Py*Nx - Px*Ny)/crosslen`P, |
164 |
> |
U = if( crosslen`P. - FTINY, |
165 |
> |
(Py*Nx - Px*Ny)/crosslen`P., |
166 |
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Px); |
167 |
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{ V is defined so that N = U x V } |
168 |
< |
V = if( crosslen`P - FTINY, |
169 |
< |
Pz - Nz*(Px*Nx + Py*Ny)/crosslen`P, |
168 |
> |
V = if( crosslen`P. - FTINY, |
169 |
> |
Pz - Nz*(Px*Nx + Py*Ny)/crosslen`P., |
170 |
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Py); |
171 |
+ |
|
172 |
+ |
{ Local hemisphere direction for *func & *data types } |
173 |
+ |
{ last 3 real args = unnormalized up-vector } |
174 |
+ |
Vux`P. = arg(AC-1)*NzP - arg(AC)*NyP; |
175 |
+ |
Vuy`P. = arg(AC)*NxP - arg(AC-2)*NzP; |
176 |
+ |
Vuz`P. = arg(AC-2)*NyP - arg(AC-1)*NxP; |
177 |
+ |
vnorm`P. = 1/sqrt(Vux`P.*Vux`P. + Vuy`P.*Vuy`P. + Vuz`P.*Vuz`P.); |
178 |
+ |
Vnx`P. = Vux`P.*vnorm`P.; |
179 |
+ |
Vny`P. = Vuy`P.*vnorm`P.; |
180 |
+ |
Vnz`P. = Vuz`P.*vnorm`P.; |
181 |
+ |
Unx`P. = NyP*Vnz`P. - NzP*Vny`P.; |
182 |
+ |
Uny`P. = NzP*Vnx`P. - NxP*Vnz`P.; |
183 |
+ |
Unz`P. = NxP*Vny`P. - NyP*Vnx`P.; |
184 |
+ |
{ Transform vectors, normalized (dx,dy,dz) away from surf } |
185 |
+ |
Ldx(dx,dy,dz) = dx*Unx`P. + dy*Uny`P. + dz*Unz`P.; |
186 |
+ |
Ldy(dx,dy,dz) = dx*Vnx`P. + dy*Vny`P. + dz*Vnz`P.; |
187 |
+ |
Ldz(dx,dy,dz) = dx*NxP + dy*NyP + dz*NzP; |
188 |
+ |
{ Incident vector transformed to our coords } |
189 |
+ |
Idx = Ldx(-Dx,-Dy,-Dz); |
190 |
+ |
Idy = Ldy(-Dx,-Dy,-Dz); |
191 |
+ |
Idz = RdotP; |