| 37 |
|
|
| 38 |
|
select(N, a1, a2, ..) - return aN |
| 39 |
|
|
| 40 |
+ |
min(a1, a2, ..) - return minimum argument |
| 41 |
+ |
max(a1, a2, ..) - return maximum argument |
| 42 |
+ |
|
| 43 |
|
sqrt(x) - square root function |
| 44 |
|
|
| 45 |
|
sin(x), cos(x), tan(x), |
| 96 |
|
abs(x) : if( x, x, -x ); |
| 97 |
|
sgn(x) : if( x, 1, if(-x, -1, 0) ); |
| 98 |
|
sq(x) : x*x; |
| 96 |
– |
max(a,b) : if( a-b, a, b ); |
| 97 |
– |
min(a,b) : if( a-b, b, a ); |
| 99 |
|
inside(a,x,b) : and(x-a,b-x); |
| 100 |
|
frac(x) : x - floor(x); |
| 101 |
|
mod(n,d) : n - floor(n/d)*d; |
| 151 |
|
|
| 152 |
|
{ Normal distribution from uniform range (0,1) } |
| 153 |
|
|
| 154 |
< |
un2`P(t) : t - (2.515517+t*(.802853+t*.010328))/ |
| 154 |
> |
un2`P.(t) : t - (2.515517+t*(.802853+t*.010328))/ |
| 155 |
|
(1+t*(1.432788+t*(.189269+t*.001308))) ; |
| 156 |
< |
un1`P(p) : un2`P(sqrt(-2*log(p))) ; |
| 156 |
> |
un1`P.(p) : un2`P.(sqrt(-2*log(p))) ; |
| 157 |
|
|
| 158 |
< |
unif2norm(p) : if( .5-p, -un1`P(p), un1`P(1-p) ) ; |
| 158 |
> |
unif2norm(p) : if( .5-p, -un1`P.(p), un1`P.(1-p) ) ; |
| 159 |
|
|
| 160 |
|
nrand(x) = unif2norm(rand(x)); |
| 161 |
|
|
| 162 |
|
{ Local (u,v) coordinates for planar surfaces } |
| 163 |
< |
crosslen`P = Nx*Nx + Ny*Ny; |
| 163 |
> |
crosslen`P. = Nx*Nx + Ny*Ny; |
| 164 |
|
{ U is distance from projected Z-axis } |
| 165 |
< |
U = if( crosslen`P - FTINY, |
| 166 |
< |
(Py*Nx - Px*Ny)/crosslen`P, |
| 165 |
> |
U = if( crosslen`P. - FTINY, |
| 166 |
> |
(Py*Nx - Px*Ny)/crosslen`P., |
| 167 |
|
Px); |
| 168 |
|
{ V is defined so that N = U x V } |
| 169 |
< |
V = if( crosslen`P - FTINY, |
| 170 |
< |
Pz - Nz*(Px*Nx + Py*Ny)/crosslen`P, |
| 169 |
> |
V = if( crosslen`P. - FTINY, |
| 170 |
> |
Pz - Nz*(Px*Nx + Py*Ny)/crosslen`P., |
| 171 |
|
Py); |
| 172 |
+ |
|
| 173 |
+ |
{ Local hemisphere direction for *func & *data types } |
| 174 |
+ |
{ last 3 real args = unnormalized up-vector } |
| 175 |
+ |
Vux`P. = arg(AC-1)*NzP - arg(AC)*NyP; |
| 176 |
+ |
Vuy`P. = arg(AC)*NxP - arg(AC-2)*NzP; |
| 177 |
+ |
Vuz`P. = arg(AC-2)*NyP - arg(AC-1)*NxP; |
| 178 |
+ |
vnorm`P. = 1/sqrt(Vux`P.*Vux`P. + Vuy`P.*Vuy`P. + Vuz`P.*Vuz`P.); |
| 179 |
+ |
Vnx`P. = Vux`P.*vnorm`P.; |
| 180 |
+ |
Vny`P. = Vuy`P.*vnorm`P.; |
| 181 |
+ |
Vnz`P. = Vuz`P.*vnorm`P.; |
| 182 |
+ |
Unx`P. = NyP*Vnz`P. - NzP*Vny`P.; |
| 183 |
+ |
Uny`P. = NzP*Vnx`P. - NxP*Vnz`P.; |
| 184 |
+ |
Unz`P. = NxP*Vny`P. - NyP*Vnx`P.; |
| 185 |
+ |
{ Transform vectors, normalized (dx,dy,dz) away from surf } |
| 186 |
+ |
Ldx(dx,dy,dz) = dx*Unx`P. + dy*Uny`P. + dz*Unz`P.; |
| 187 |
+ |
Ldy(dx,dy,dz) = dx*Vnx`P. + dy*Vny`P. + dz*Vnz`P.; |
| 188 |
+ |
Ldz(dx,dy,dz) = dx*NxP + dy*NyP + dz*NzP; |
| 189 |
+ |
{ Incident vector transformed to our coords } |
| 190 |
+ |
Idx = Ldx(-Dx,-Dy,-Dz); |
| 191 |
+ |
Idy = Ldy(-Dx,-Dy,-Dz); |
| 192 |
+ |
Idz = RdotP; |
