| 1 |
#ifndef lint |
| 2 |
static const char RCSid[] = "$Id$"; |
| 3 |
#endif |
| 4 |
/* |
| 5 |
* Disk2Square.c |
| 6 |
* |
| 7 |
* Code by Peter Shirley and Kenneth Chiu |
| 8 |
* |
| 9 |
* Associated paper in ~/Documents/Others/Shirley+Chiu_JGT-97.pdf |
| 10 |
* |
| 11 |
* Modified interface slightly (G. Ward) |
| 12 |
*/ |
| 13 |
|
| 14 |
#include <math.h> |
| 15 |
|
| 16 |
/* |
| 17 |
This transforms points on [0,1]^2 to points on unit disk centered at |
| 18 |
origin. Each "pie-slice" quadrant of square is handled as a seperate |
| 19 |
case. The bad floating point cases are all handled appropriately. |
| 20 |
The regions for (a,b) are: |
| 21 |
|
| 22 |
phi = pi/2 |
| 23 |
-----*----- |
| 24 |
|\ /| |
| 25 |
| \ 2 / | |
| 26 |
| \ / | |
| 27 |
phi=pi* 3 * 1 *phi = 0 |
| 28 |
| / \ | |
| 29 |
| / 4 \ | |
| 30 |
|/ \| |
| 31 |
-----*----- |
| 32 |
phi = 3pi/2 |
| 33 |
|
| 34 |
change log: |
| 35 |
26 feb 2004. bug fix in computation of phi (now this matches the paper, |
| 36 |
which is correct). thanks to Atilim Cetin for catching this. |
| 37 |
*/ |
| 38 |
|
| 39 |
|
| 40 |
/* Map a [0,1]^2 square to a unit radius disk */ |
| 41 |
void |
| 42 |
SDsquare2disk(double ds[2], double seedx, double seedy) |
| 43 |
{ |
| 44 |
|
| 45 |
double phi, r; |
| 46 |
double a = 2.*seedx - 1; /* (a,b) is now on [-1,1]^2 */ |
| 47 |
double b = 2.*seedy - 1; |
| 48 |
|
| 49 |
if (a > -b) { /* region 1 or 2 */ |
| 50 |
if (a > b) { /* region 1, also |a| > |b| */ |
| 51 |
r = a; |
| 52 |
phi = (M_PI/4.) * (b/a); |
| 53 |
} |
| 54 |
else { /* region 2, also |b| > |a| */ |
| 55 |
r = b; |
| 56 |
phi = (M_PI/4.) * (2. - (a/b)); |
| 57 |
} |
| 58 |
} |
| 59 |
else { /* region 3 or 4 */ |
| 60 |
if (a < b) { /* region 3, also |a| >= |b|, a != 0 */ |
| 61 |
r = -a; |
| 62 |
phi = (M_PI/4.) * (4. + (b/a)); |
| 63 |
} |
| 64 |
else { /* region 4, |b| >= |a|, but a==0 and b==0 could occur. */ |
| 65 |
r = -b; |
| 66 |
if (b != 0.) |
| 67 |
phi = (M_PI/4.) * (6. - (a/b)); |
| 68 |
else |
| 69 |
phi = 0.; |
| 70 |
} |
| 71 |
} |
| 72 |
|
| 73 |
ds[0] = r * cos(phi); |
| 74 |
ds[1] = r * sin(phi); |
| 75 |
|
| 76 |
} |
| 77 |
|
| 78 |
/* Map point on unit disk to a unit square in [0,1]^2 range */ |
| 79 |
void |
| 80 |
SDdisk2square(double sq[2], double diskx, double disky) |
| 81 |
{ |
| 82 |
double r = sqrt( diskx*diskx + disky*disky ); |
| 83 |
double phi = atan2( disky, diskx ); |
| 84 |
double a, b; |
| 85 |
|
| 86 |
if (phi < -M_PI/4) phi += 2*M_PI; /* in range [-pi/4,7pi/4] */ |
| 87 |
if ( phi < M_PI/4) { /* region 1 */ |
| 88 |
a = r; |
| 89 |
b = phi * a / (M_PI/4); |
| 90 |
} |
| 91 |
else if ( phi < 3*M_PI/4 ) { /* region 2 */ |
| 92 |
b = r; |
| 93 |
a = -(phi - M_PI/2) * b / (M_PI/4); |
| 94 |
} |
| 95 |
else if ( phi < 5*M_PI/4 ) { /* region 3 */ |
| 96 |
a = -r; |
| 97 |
b = (phi - M_PI) * a / (M_PI/4); |
| 98 |
} |
| 99 |
else { /* region 4 */ |
| 100 |
b = -r; |
| 101 |
a = -(phi - 3*M_PI/2) * b / (M_PI/4); |
| 102 |
} |
| 103 |
|
| 104 |
sq[0] = (a + 1) * 0.5; |
| 105 |
sq[1] = (b + 1) * 0.5; |
| 106 |
} |
