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/* |
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* Disk2Square.c |
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* |
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* Code by Peter Shirley and Kenneth Chiu |
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* |
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* Associated paper in ~/Documents/Others/Shirley+Chiu_JGT-97.pdf |
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* |
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* Modified interface slightly (G. Ward) |
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*/ |
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|
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#include <math.h> |
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|
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/* |
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This transforms points on [0,1]^2 to points on unit disk centered at |
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origin. Each "pie-slice" quadrant of square is handled as a seperate |
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case. The bad floating point cases are all handled appropriately. |
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The regions for (a,b) are: |
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|
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phi = pi/2 |
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-----*----- |
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|\ /| |
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| \ 2 / | |
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| \ / | |
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phi=pi* 3 * 1 *phi = 0 |
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| / \ | |
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| / 4 \ | |
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|/ \| |
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-----*----- |
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phi = 3pi/2 |
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|
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change log: |
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26 feb 2004. bug fix in computation of phi (now this matches the paper, |
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which is correct). thanks to Atilim Cetin for catching this. |
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*/ |
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|
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|
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/* Map a [0,1]^2 square to a unit radius disk */ |
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void |
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SDsquare2disk(double ds[2], double seedx, double seedy) |
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{ |
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|
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double phi, r; |
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double a = 2.*seedx - 1; /* (a,b) is now on [-1,1]^2 */ |
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double b = 2.*seedy - 1; |
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|
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if (a > -b) { /* region 1 or 2 */ |
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if (a > b) { /* region 1, also |a| > |b| */ |
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r = a; |
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phi = (M_PI/4.) * (b/a); |
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} |
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else { /* region 2, also |b| > |a| */ |
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r = b; |
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phi = (M_PI/4.) * (2. - (a/b)); |
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} |
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} |
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else { /* region 3 or 4 */ |
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if (a < b) { /* region 3, also |a| >= |b|, a != 0 */ |
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r = -a; |
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phi = (M_PI/4.) * (4. + (b/a)); |
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} |
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else { /* region 4, |b| >= |a|, but a==0 and b==0 could occur. */ |
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r = -b; |
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if (b != 0.) |
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phi = (M_PI/4.) * (6. - (a/b)); |
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else |
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phi = 0.; |
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} |
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} |
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|
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ds[0] = r * cos(phi); |
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ds[1] = r * sin(phi); |
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|
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} |
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|
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/* Map point on unit disk to a unit square in [0,1]^2 range */ |
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void |
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SDdisk2square(double sq[2], double diskx, double disky) |
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{ |
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double r = sqrt( diskx*diskx + disky*disky ); |
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double phi = atan2( disky, diskx ); |
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double a, b; |
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|
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if (phi < -M_PI/4) phi += 2*M_PI; /* in range [-pi/4,7pi/4] */ |
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if ( phi < M_PI/4) { /* region 1 */ |
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a = r; |
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b = phi * a / (M_PI/4); |
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} |
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else if ( phi < 3*M_PI/4 ) { /* region 2 */ |
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b = r; |
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a = -(phi - M_PI/2) * b / (M_PI/4); |
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} |
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else if ( phi < 5*M_PI/4 ) { /* region 3 */ |
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a = -r; |
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b = (phi - M_PI) * a / (M_PI/4); |
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} |
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else { /* region 4 */ |
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b = -r; |
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a = -(phi - 3*M_PI/2) * b / (M_PI/4); |
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} |
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|
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sq[0] = (a + 1) * 0.5; |
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sq[1] = (b + 1) * 0.5; |
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} |
