"""
Signed distance drawing functions using numpy.
"""
import math
import numpy as np
from numpy import linalg as npla
def vector2_dot(a,b):
return a[...,0]*b[...,0]+a[...,1]*b[...,1]
def vector2_dot2(a):
return a[...,0]*a[...,0]+a[...,1]*a[...,1]
def vector2_cross(a,b):
return a[...,0]*b[...,1]-a[...,1]*b[...,0]
def circle_faded( wh, center, fade_dists ):
"""
returns drawn circle in [h,w,1] output range [0..1.0] float32
wh = [w,h] resolution
center = [x,y] center of circle
fade_dists = [fade_start, fade_end] fade values
"""
w,h = wh
pts = np.empty( (h,w,2), dtype=np.float32 )
pts[...,0] = np.arange(w)[:,None]
pts[...,1] = np.arange(h)[None,:]
pts = pts.reshape ( (h*w, -1) )
pts_dists = np.abs ( npla.norm(pts-center, axis=-1) )
if fade_dists[1] == 0:
fade_dists[1] = 1
pts_dists = ( pts_dists - fade_dists[0] ) / fade_dists[1]
pts_dists = np.clip( 1-pts_dists, 0, 1)
return pts_dists.reshape ( (h,w,1) ).astype(np.float32)
def bezier( wh, A, B, C ):
"""
returns drawn bezier in [h,w,1] output range float32,
every pixel contains signed distance to bezier line
wh [w,h] resolution
A,B,C points [x,y]
"""
width,height = wh
A = np.float32(A)
B = np.float32(B)
C = np.float32(C)
pos = np.empty( (height,width,2), dtype=np.float32 )
pos[...,0] = np.arange(width)[:,None]
pos[...,1] = np.arange(height)[None,:]
a = B-A
b = A - 2.0*B + C
c = a * 2.0
d = A - pos
b_dot = vector2_dot(b,b)
if b_dot == 0.0:
return np.zeros( (height,width), dtype=np.float32 )
kk = 1.0 / b_dot
kx = kk * vector2_dot(a,b)
ky = kk * (2.0*vector2_dot(a,a)+vector2_dot(d,b))/3.0;
kz = kk * vector2_dot(d,a);
res = 0.0;
sgn = 0.0;
p = ky - kx*kx;
p3 = p*p*p;
q = kx*(2.0*kx*kx - 3.0*ky) + kz;
h = q*q + 4.0*p3;
hp_sel = h >= 0.0
hp_p = h[hp_sel]
hp_p = np.sqrt(hp_p)
hp_x = ( np.stack( (hp_p,-hp_p), -1) -q[hp_sel,None] ) / 2.0
hp_uv = np.sign(hp_x) * np.power( np.abs(hp_x), [1.0/3.0, 1.0/3.0] )
hp_t = np.clip( hp_uv[...,0] + hp_uv[...,1] - kx, 0.0, 1.0 )
hp_t = hp_t[...,None]
hp_q = d[hp_sel]+(c+b*hp_t)*hp_t
hp_res = vector2_dot2(hp_q)
hp_sgn = vector2_cross(c+2.0*b*hp_t,hp_q)
hl_sel = h < 0.0
hl_q = q[hl_sel]
hl_p = p[hl_sel]
hl_z = np.sqrt(-hl_p)
hl_v = np.arccos( hl_q / (hl_p*hl_z*2.0)) / 3.0
hl_m = np.cos(hl_v)
hl_n = np.sin(hl_v)*1.732050808;
hl_t = np.clip( np.stack( (hl_m+hl_m,-hl_n-hl_m,hl_n-hl_m), -1)*hl_z[...,None]-kx, 0.0, 1.0 );
hl_d = d[hl_sel]
hl_qx = hl_d+(c+b*hl_t[...,0:1])*hl_t[...,0:1]
hl_dx = vector2_dot2(hl_qx)
hl_sx = vector2_cross(c+2.0*b*hl_t[...,0:1], hl_qx)
hl_qy = hl_d+(c+b*hl_t[...,1:2])*hl_t[...,1:2]
hl_dy = vector2_dot2(hl_qy)
hl_sy = vector2_cross(c+2.0*b*hl_t[...,1:2],hl_qy);
hl_dx_l_dy = hl_dx<hl_dy
hl_dx_ge_dy = hl_dx>=hl_dy
hl_res = np.empty_like(hl_dx)
hl_res[hl_dx_l_dy] = hl_dx[hl_dx_l_dy]
hl_res[hl_dx_ge_dy] = hl_dy[hl_dx_ge_dy]
hl_sgn = np.empty_like(hl_sx)
hl_sgn[hl_dx_l_dy] = hl_sx[hl_dx_l_dy]
hl_sgn[hl_dx_ge_dy] = hl_sy[hl_dx_ge_dy]
res = np.empty( (height, width), np.float32 )
res[hp_sel] = hp_res
res[hl_sel] = hl_res
sgn = np.empty( (height, width), np.float32 )
sgn[hp_sel] = hp_sgn
sgn[hl_sel] = hl_sgn
sgn = np.sign(sgn)
res = np.sqrt(res)*sgn
return res[...,None]
def random_faded(wh):
"""
apply one of them:
random_circle_faded
random_bezier_split_faded
"""
rnd = np.random.randint(2)
if rnd == 0:
return random_circle_faded(wh)
elif rnd == 1:
return random_bezier_split_faded(wh)
def random_circle_faded ( wh, rnd_state=None ):
if rnd_state is None:
rnd_state = np.random
w,h = wh
wh_max = max(w,h)
fade_start = rnd_state.randint(wh_max)
fade_end = fade_start + rnd_state.randint(wh_max- fade_start)
return circle_faded (wh, [ rnd_state.randint(h), rnd_state.randint(w) ],
[fade_start, fade_end] )
def random_bezier_split_faded( wh ):
width, height = wh
degA = np.random.randint(360)
degB = np.random.randint(360)
degC = np.random.randint(360)
deg_2_rad = math.pi / 180.0
center = np.float32([width / 2.0, height / 2.0])
radius = max(width, height)
A = center + radius*np.float32([ math.sin( degA * deg_2_rad), math.cos( degA * deg_2_rad) ] )
B = center + np.random.randint(radius)*np.float32([ math.sin( degB * deg_2_rad), math.cos( degB * deg_2_rad) ] )
C = center + radius*np.float32([ math.sin( degC * deg_2_rad), math.cos( degC * deg_2_rad) ] )
x = bezier( (width,height), A, B, C )
x = x / (1+np.random.randint(radius)) + 0.5
x = np.clip(x, 0, 1)
return x
