upd xlib.image.sd

xlib/image/sd/__init__.py

@@ -0,0 +1,4 @@
+from .calc import dist_to_edges
+from .draw import (bezier, circle_faded, random_bezier_split_faded,
+                   random_circle_faded, random_circle_faded_multi,
+                   random_faded)

xlib/image/sd/calc.py

@@ -0,0 +1,25 @@
+import numpy as np
+import numpy.linalg as npla
+
+def dist_to_edges(pts, pt, is_closed=False):
+    """
+    returns array of dist from pt to edge and projection pt to edges
+    """
+    if is_closed:
+        a = pts
+        b = np.concatenate( (pts[1:,:], pts[0:1,:]), axis=0 )
+    else:
+        a = pts[:-1,:]
+        b = pts[1:,:]
+
+    pa = pt-a
+    ba = b-a
+    
+    div = np.einsum('ij,ij->i', ba, ba)
+    div[div==0]=1
+    h = np.clip( np.einsum('ij,ij->i', pa, ba) / div, 0, 1 )
+    
+    x = npla.norm ( pa - ba*h[...,None], axis=1 )
+    
+    return x, a+ba*h[...,None]
+    

xlib/image/sd/draw.py

@@ -0,0 +1,216 @@
+"""
+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_circle_faded_multi( wh, complexity=1, rnd_state=None):
+    mask = random_circle_faded( wh, rnd_state=rnd_state )
+    while True:
+        complexity -= 1
+        if complexity == 0:
+            break
+
+        opacity = random_circle_faded( wh, rnd_state=rnd_state )
+        add_mask = random_circle_faded( wh, rnd_state=rnd_state )
+
+        mask *= opacity
+        mask += add_mask*(1-opacity)
+
+        mask *= random_circle_faded( wh, rnd_state=rnd_state )
+    return mask
+
+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