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greg |
2.6 |
{ RCSid $Id: disk2square.cal,v 2.5 2019/08/13 18:29:23 greg Exp $ }
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greg |
2.1 |
{
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Convert between unit square and disk, using Shirley-Chiu mapping
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5/20/2011 G. Ward
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Inputs:
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in_disk_x Input unit disk Cartesian coordiantes
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in_disk_y center at (0,0)
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or:
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in_square_x Input unit square [0,1]^2
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in_square_y
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Corresponding outputs:
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out_square_x Output unit square [0,1]^2
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out_square_y
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or:
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out_disk_x Output unit disk Cartesian coordinates
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out_disk_y center at (0,0)
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}
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{ Compute disk position from square coordinates }
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in_square_a = 2*in_square_x - 1;
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in_square_b = 2*in_square_y - 1;
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in_square_rgn = if(in_square_a + in_square_b,
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if(in_square_a - in_square_b, 1, 2),
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if(in_square_b - in_square_a, 3, 4));
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out_disk_r = select(in_square_rgn, in_square_a, in_square_b,
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-in_square_a, -in_square_b);
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out_disk_phi = PI/4 * select(in_square_rgn,
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in_square_b/in_square_a,
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2 - in_square_a/in_square_b,
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4 + in_square_b/in_square_a,
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if(in_square_b*in_square_b,
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6 - in_square_a/in_square_b,
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0));
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out_disk_x = out_disk_r*cos(out_disk_phi);
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out_disk_y = out_disk_r*sin(out_disk_phi);
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{ Compute square position from disk coordinates }
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norm_radians(p) : if(-p - PI/4, p + 2*PI, p);
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in_disk_r = sqrt(in_disk_x*in_disk_x + in_disk_y*in_disk_y);
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in_disk_phi = norm_radians(atan2(in_disk_y, in_disk_x));
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in_disk_rgn = floor((in_disk_phi + PI/4)/(PI/2)) + 1;
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out_square_a = select(in_disk_rgn,
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in_disk_r,
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(PI/2 - in_disk_phi)*in_disk_r/(PI/4),
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-in_disk_r,
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greg |
2.5 |
(in_disk_phi - 3*PI/2)*in_disk_r/(PI/4),
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in_disk_r);
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greg |
2.1 |
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out_square_b = select(in_disk_rgn,
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in_disk_phi*in_disk_r/(PI/4),
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in_disk_r,
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(PI - in_disk_phi)*in_disk_r/(PI/4),
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greg |
2.5 |
-in_disk_r, -in_disk_r);
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greg |
2.1 |
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out_square_x = (out_square_a + 1)/2;
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out_square_y = (out_square_b + 1)/2;
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{
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The following forumulas compute Shirley-Chiu bin "scbin" based on:
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greg |
2.4 |
RHS - right-handed system (-1 for left-handed coords)
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greg |
2.1 |
Dx,Dy,Dz - Incident direction (normalized, towards surface front)
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greg |
2.3 |
rNx,rNy,rNz - Surface normal (normalized, away from surface)
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greg |
2.1 |
Ux,Uy,Uz - Up direction vector (does not need to be normalized)
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The SCdim variable assigns the square side dimension for bins, which are
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ordered with the "up" direction changing fastest.
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}
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greg |
2.4 |
RHS = 1;
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greg |
2.1 |
{ Compute oriented axis values }
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greg |
2.3 |
inc_dz = -Dx*rNx-Dy*rNy-Dz*rNz;
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greg |
2.4 |
inc_rx = -RHS*(Dx*(Uy*rNz-Uz*rNy) + Dy*(Uz*rNx-Ux*rNz) + Dz*(Ux*rNy-Uy*rNx));
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greg |
2.6 |
inc_ry = Dx*Ux+Dy*Uy+Dz*Uz + inc_dz*(rNx*Ux+rNy*Uy+rNz*Uz);
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greg |
2.1 |
inc_den2 = inc_rx*inc_rx + inc_ry*inc_ry;
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greg |
2.3 |
inc_radf = if(inc_den2-1e-7, sqrt((1 - inc_dz*inc_dz)/inc_den2), 0);
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greg |
2.1 |
{ Pass to formulas in first section }
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in_disk_x = inc_rx*inc_radf;
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greg |
2.6 |
in_disk_y = -inc_ry*inc_radf;
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greg |
2.1 |
{ Compute final bin (-1 if behind surface) }
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greg |
2.2 |
scbin = if(inc_dz,
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greg |
2.1 |
floor(out_square_x*SCdim)*SCdim + floor(out_square_y*SCdim),
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-1);
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