#define pulse2(a,b,fuzz,x) (smoothstep((a)-(fuzz),(a),(x)) - \
               smoothstep((b)-(fuzz),(b),(x)))
  
#define boxstep2(a,b,x)    clamp(((x) - (a))/((b) - (a)), 0, 1)
  
#define repeat2(x,freq)    (mod((x) * (freq), 1.0))
  
#define odd2(x)            (mod((x), 2) == 1)
#define even2(x)           (mod((x), 2) == 0)
  
#define whichtile2(x,freq) (floor((x) * (freq)))
  
/* rotate2d()
 *
 * 2D rotation of point (x,y) about origin (ox,oy) by an angle rad.
 * The resulting point is (rx, ry).
 *
 */
#define rotate2d2(x,y,rad,ox,oy,rx,ry) \
  rx = ((x) - (ox)) * cos(rad) - ((y) - (oy)) * sin(rad) + (ox); \
  ry = ((x) - (ox)) * sin(rad) + ((y) - (oy)) * cos(rad) + (oy)
  
/* topolar2d()
 * 
 * 2D cartesian -> polar coordinates
 * converts the point (x,y) to radius 'r' and angle 'theta' (in radians).
 * theta will be in the range [-PI,PI].
 *
 */
#define topolar2d2(x, y, r, theta) \
  r = sqrt((x) * (x) + (y) * (y)); \
  theta = atan(y, x) 
  
/* boolean ops (from Perlin85)
 *
 */
#define intersection2(a,b) ((a) * (b))
#define union2(a,b)        ((a) + (b) - (a) * (b))
#define difference2(a,b)   ((a) - (a) * (b))
#define complement2(a)     (1 - (a))
  
  
/* blend() and lerp() are equivalent. blend() is used as a substitute for
 * mix because it allows non-scalar 3rd arguments.
 *
 */
#define blend2(a,b,x) ((a) * (1 - (x)) + (b) * (x))
#define lerp2(a,b,x)  ((a) * (1 - (x)) + (b) * (x))
  
/* signed noise
 *
 */
#define snoise2(x)    (noise(x) * 2 - 1)
#define snoise22(x,y) (noise(x,y) * 2 - 1)
  
/* uniformly distributed noise
 *
 */
#define udn2(x,lo,hi) (smoothstep(.25, .75, noise(x)) * ((hi) - (lo)) + (lo))
#define udn22(x,y,lo,hi) (smoothstep(.25, .75, noise(x,y)) * ((hi)-(lo))+(lo))
  
/* sample rate metrics (from Apodaca92)
 *
 */
#define MINFILTERWIDTH2  1e-7
#define MINDERIV2        0.0003    /* sqrt(MINFILTERWIDTH) */
  
#define filterwidth2(x) (max(abs(Du(x) * (du)) + (Dv(x) * (dv)),MINFILTERWIDTH))
#define filterwidth_point2(p) (max(sqrt(area(p)), MINFILTERWIDTH))
  
  
  
  
/* CIRCLE!!! */
  
#define circle(r, fuzz, ss, tt) \
1-smoothstep(r-fuzz, r+fuzz, sqrt((ss-0.5)*(ss-0.5)+(tt-0.5)*(tt-0.5)))