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root/radiance/ray/src/util/disk2square.cal
Revision: 2.5
Committed: Tue Aug 13 18:29:23 2019 UTC (3 years, 1 month ago) by greg
Branch: MAIN
CVS Tags: rad5R3, HEAD
Changes since 2.4: +4 -3 lines
Log Message:
Improved handling of edge cases

File Contents

# Content
1 { RCSid $Id: disk2square.cal,v 2.4 2015/03/27 18:58:06 greg Exp $ }
2 {
3 Convert between unit square and disk, using Shirley-Chiu mapping
4
5 5/20/2011 G. Ward
6
7 Inputs:
8 in_disk_x Input unit disk Cartesian coordiantes
9 in_disk_y center at (0,0)
10 or:
11 in_square_x Input unit square [0,1]^2
12 in_square_y
13
14 Corresponding outputs:
15 out_square_x Output unit square [0,1]^2
16 out_square_y
17 or:
18 out_disk_x Output unit disk Cartesian coordinates
19 out_disk_y center at (0,0)
20 }
21 { Compute disk position from square coordinates }
22 in_square_a = 2*in_square_x - 1;
23 in_square_b = 2*in_square_y - 1;
24
25 in_square_rgn = if(in_square_a + in_square_b,
26 if(in_square_a - in_square_b, 1, 2),
27 if(in_square_b - in_square_a, 3, 4));
28
29 out_disk_r = select(in_square_rgn, in_square_a, in_square_b,
30 -in_square_a, -in_square_b);
31
32 out_disk_phi = PI/4 * select(in_square_rgn,
33 in_square_b/in_square_a,
34 2 - in_square_a/in_square_b,
35 4 + in_square_b/in_square_a,
36 if(in_square_b*in_square_b,
37 6 - in_square_a/in_square_b,
38 0));
39
40 out_disk_x = out_disk_r*cos(out_disk_phi);
41 out_disk_y = out_disk_r*sin(out_disk_phi);
42
43 { Compute square position from disk coordinates }
44 norm_radians(p) : if(-p - PI/4, p + 2*PI, p);
45 in_disk_r = sqrt(in_disk_x*in_disk_x + in_disk_y*in_disk_y);
46 in_disk_phi = norm_radians(atan2(in_disk_y, in_disk_x));
47
48 in_disk_rgn = floor((in_disk_phi + PI/4)/(PI/2)) + 1;
49
50 out_square_a = select(in_disk_rgn,
51 in_disk_r,
52 (PI/2 - in_disk_phi)*in_disk_r/(PI/4),
53 -in_disk_r,
54 (in_disk_phi - 3*PI/2)*in_disk_r/(PI/4),
55 in_disk_r);
56
57 out_square_b = select(in_disk_rgn,
58 in_disk_phi*in_disk_r/(PI/4),
59 in_disk_r,
60 (PI - in_disk_phi)*in_disk_r/(PI/4),
61 -in_disk_r, -in_disk_r);
62
63 out_square_x = (out_square_a + 1)/2;
64 out_square_y = (out_square_b + 1)/2;
65 {
66 The following forumulas compute Shirley-Chiu bin "scbin" based on:
67
68 RHS - right-handed system (-1 for left-handed coords)
69 Dx,Dy,Dz - Incident direction (normalized, towards surface front)
70 rNx,rNy,rNz - Surface normal (normalized, away from surface)
71 Ux,Uy,Uz - Up direction vector (does not need to be normalized)
72
73 The SCdim variable assigns the square side dimension for bins, which are
74 ordered with the "up" direction changing fastest.
75 }
76 RHS = 1;
77 { Compute oriented axis values }
78 inc_dz = -Dx*rNx-Dy*rNy-Dz*rNz;
79 inc_rx = -RHS*(Dx*(Uy*rNz-Uz*rNy) + Dy*(Uz*rNx-Ux*rNz) + Dz*(Ux*rNy-Uy*rNx));
80 inc_ry = -Dx*Ux-Dy*Uy-Dz*Uz - inc_dz*(rNx*Ux+rNy*Uy+rNz*Uz);
81 inc_den2 = inc_rx*inc_rx + inc_ry*inc_ry;
82 inc_radf = if(inc_den2-1e-7, sqrt((1 - inc_dz*inc_dz)/inc_den2), 0);
83 { Pass to formulas in first section }
84 in_disk_x = inc_rx*inc_radf;
85 in_disk_y = inc_ry*inc_radf;
86 { Compute final bin (-1 if behind surface) }
87 scbin = if(inc_dz,
88 floor(out_square_x*SCdim)*SCdim + floor(out_square_y*SCdim),
89 -1);