def draw_debug_derivatives( self ) : v = 11.5 glColor3f(1,0,0) glBegin(GL_LINES) p = csurf.bspline_surf ( 0 , v , self.array_pts ) dv= csurf.bspline_surf_prime_v( 0 , v , self.array_pts ) du= csurf.bspline_surf_prime_u( 0 , v , self.array_pts ) glVertex3f( p[0] , p[1] , p[2] ) glVertex3f(*(p+dv) ) glVertex3f( p[0] , p[1] , p[2] ) glVertex3f(*(p+du) ) glVertex3f( p[0] , p[1] , p[2] ) for i in np.linspace(float(self.size[0])/64,self.size[0],64,False) : p = csurf.bspline_surf ( i , v , self.array_pts ) dv= csurf.bspline_surf_prime_v( i , v , self.array_pts ) du= csurf.bspline_surf_prime_u( i , v , self.array_pts ) glVertex3f( p[0] , p[1] , p[2] ) glVertex3f( p[0] , p[1] , p[2] ) glVertex3f(*(p+dv) ) glVertex3f( p[0] , p[1] , p[2] ) glVertex3f(*(p+du) ) glVertex3f( p[0] , p[1] , p[2] ) p = csurf.bspline_surf ( self.size[0] , v , self.array_pts ) dv= csurf.bspline_surf_prime_v( self.size[0] , v , self.array_pts ) du= csurf.bspline_surf_prime_u( self.size[0] , v , self.array_pts ) glVertex3f( p[0] , p[1] , p[2] ) glVertex3f(*(p+dv) ) glVertex3f( p[0] , p[1] , p[2] ) glVertex3f(*(p+du) ) glVertex3f( p[0] , p[1] , p[2] ) glEnd() glColor3f(1,1,1,0)
def draw_debug_derivatives(self):
v = 11.5
glColor3f(1, 0, 0)
glBegin(GL_LINES)
p = csurf.bspline_surf(0, v, self.array_pts)
dv = csurf.bspline_surf_prime_v(0, v, self.array_pts)
du = csurf.bspline_surf_prime_u(0, v, self.array_pts)
glVertex3f(p[0], p[1], p[2])
glVertex3f(*(p + dv))
glVertex3f(p[0], p[1], p[2])
glVertex3f(*(p + du))
glVertex3f(p[0], p[1], p[2])
for i in np.linspace(
float(self.size[0]) / 64, self.size[0], 64, False):
p = csurf.bspline_surf(i, v, self.array_pts)
dv = csurf.bspline_surf_prime_v(i, v, self.array_pts)
du = csurf.bspline_surf_prime_u(i, v, self.array_pts)
glVertex3f(p[0], p[1], p[2])
glVertex3f(p[0], p[1], p[2])
glVertex3f(*(p + dv))
glVertex3f(p[0], p[1], p[2])
glVertex3f(*(p + du))
glVertex3f(p[0], p[1], p[2])
p = csurf.bspline_surf(self.size[0], v, self.array_pts)
dv = csurf.bspline_surf_prime_v(self.size[0], v, self.array_pts)
du = csurf.bspline_surf_prime_u(self.size[0], v, self.array_pts)
glVertex3f(p[0], p[1], p[2])
glVertex3f(*(p + dv))
glVertex3f(p[0], p[1], p[2])
glVertex3f(*(p + du))
glVertex3f(p[0], p[1], p[2])
glEnd()
glColor3f(1, 1, 1, 0)
def find_trimming(self, r):
u, v, head_pts = self.get_curve_data(self.head)
u, v, hand_pts = self.get_curve_data(self.hand)
head_trm = self.trm_uv_head
hand_trm = self.trm_uv_hand
bi = min(head_trm.minimal_v_id, head_trm.maximal_v_id)
ei = max(head_trm.minimal_v_id, head_trm.maximal_v_id)
nv = 32
di = (ei - bi) / float(nv)
path = []
head_derv = []
hand_derv = []
fi = float(bi)
while fi <= ei:
i = int(fi)
p = csurf.bspline_surf(head_trm.l[i][0], head_trm.l[i][1],
head_pts)
du = csurf.bspline_surf_prime_u(hand_trm.l[i][0], hand_trm.l[i][1],
hand_pts)
dv = csurf.bspline_surf_prime_v(hand_trm.l[i][0], hand_trm.l[i][1],
hand_pts)
hand_n = np.cross(du, dv)
hand_n = hand_n / np.linalg.norm(hand_n)
hand_derv.append((du, dv))
du = csurf.bspline_surf_prime_u(head_trm.l[i][0], head_trm.l[i][1],
head_pts)
dv = csurf.bspline_surf_prime_v(head_trm.l[i][0], head_trm.l[i][1],
head_pts)
head_n = np.cross(du, dv)
head_n = head_n / np.linalg.norm(head_n)
head_derv.append((du, dv))
n = head_n + hand_n
n = n / np.linalg.norm(n)
ln = m.sqrt(2) * r / m.sqrt(1 + np.dot(head_n, hand_n)) * 1.08
path.append(p + n * ln)
fi += di
return path, head_derv, hand_derv
def gen_line_u(self, pts, path, r, v, bu, eu, nu):
sys.stdout.write('.')
sys.stdout.flush()
odu = None
cn = None # current normal
pn = None # previous normal
for iu in np.linspace(bu, eu, nu):
p = csurf.bspline_surf(iu, v, pts)
dv = csurf.bspline_surf_prime_v(iu, v, pts)
du = csurf.bspline_surf_prime_u(iu, v, pts)
n = np.cross(du, dv)
nlen = np.linalg.norm(n)
dlen = np.linalg.norm(du)
ndu = du / dlen
# paths count optimization
if odu != None and np.allclose(ndu, odu, atol=0.001):
continue
if dlen > 0.01:
n = n / nlen
if cn == None and pn != None: # C0 edge
cn = n
tn = (pn + cn)
tn = tn / np.linalg.norm(tn)
path.append(np.array(p + tn * r))
else: # normal is well defined
pn = cn
cn = n
path.append(np.array(p + cn * r))
else: # normal is undefined
cn = None
odu = ndu
def gen_bspline_point(self, u, v, r, pts):
p = csurf.bspline_surf(u, v, pts)
dv = csurf.bspline_surf_prime_v(u, v, pts)
du = csurf.bspline_surf_prime_u(u, v, pts)
n = np.cross(du, dv)
n = n / np.linalg.norm(n)
return p + n * r
def gen_line_u( self , pts , path , r , v , bu , eu , nu ) :
sys.stdout.write('.')
sys.stdout.flush()
odu = None
cn = None # current normal
pn = None # previous normal
for iu in np.linspace(bu,eu,nu) :
p = csurf.bspline_surf ( iu, v, pts )
dv= csurf.bspline_surf_prime_v( iu, v, pts )
du= csurf.bspline_surf_prime_u( iu, v, pts )
n = np.cross( du , dv )
nlen = np.linalg.norm( n )
dlen = np.linalg.norm( du )
ndu = du / dlen
# paths count optimization
if odu != None and np.allclose(ndu,odu,atol=0.001) :
continue
if dlen > 0.01 :
n = n / nlen
if cn == None and pn != None : # C0 edge
cn = n
tn = (pn+cn)
tn = tn / np.linalg.norm(tn)
path.append( np.array( p + tn*r ) )
else : # normal is well defined
pn = cn
cn = n
path.append( np.array( p + cn * r ) )
else : # normal is undefined
cn = None
odu = ndu
def gen_bspline_point( self , u , v , r , pts ) : p = csurf.bspline_surf ( u , v , pts ) dv= csurf.bspline_surf_prime_v( u , v , pts ) du= csurf.bspline_surf_prime_u( u , v , pts ) n = np.cross( du , dv ) n = n / np.linalg.norm( n ) return p + n * r
def find_trimming( self , r ) : u , v , head_pts = self.get_curve_data( self.head ) u , v , hand_pts = self.get_curve_data( self.hand ) head_trm = self.trm_uv_head hand_trm = self.trm_uv_hand bi = min( head_trm.minimal_v_id , head_trm.maximal_v_id ) ei = max( head_trm.minimal_v_id , head_trm.maximal_v_id ) nv = 32 di = (ei - bi) / float(nv) path = [] head_derv = [] hand_derv = [] fi = float(bi) while fi <= ei : i = int(fi) p = csurf.bspline_surf( head_trm.l[i][0] , head_trm.l[i][1] , head_pts ) du = csurf.bspline_surf_prime_u( hand_trm.l[i][0] , hand_trm.l[i][1] , hand_pts ) dv = csurf.bspline_surf_prime_v( hand_trm.l[i][0] , hand_trm.l[i][1] , hand_pts ) hand_n = np.cross( du , dv ) hand_n = hand_n / np.linalg.norm( hand_n ) hand_derv.append( (du,dv) ) du = csurf.bspline_surf_prime_u( head_trm.l[i][0] , head_trm.l[i][1] , head_pts ) dv = csurf.bspline_surf_prime_v( head_trm.l[i][0] , head_trm.l[i][1] , head_pts ) head_n = np.cross( du , dv ) head_n = head_n / np.linalg.norm( head_n ) head_derv.append( (du,dv) ) n = head_n + hand_n n = n / np.linalg.norm( n ) ln = m.sqrt(2) * r / m.sqrt( 1 + np.dot( head_n , hand_n ) ) * 1.08 path.append( p + n * ln ) fi += di return path , head_derv , hand_derv
def gen_line_u_with_trimming(self, v, bu, eu, nu, z0, pts, trm, dtrm,
path):
sys.stdout.write('.')
sys.stdout.flush()
odu = None
cn = None # current normal
pn = None # previous normal
for iu in np.linspace(bu, eu, nu):
p = csurf.bspline_surf(iu, v, pts)
dv = csurf.bspline_surf_prime_v(iu, v, pts)
du = csurf.bspline_surf_prime_u(iu, v, pts)
fi = 0
while fi < len(trm) and not self.check_pass(
p, trm[fi], dtrm[fi][1]):
fi += 1
ri = len(trm) - 1
while ri >= 0 and self.check_pass(p, trm[ri], dtrm[ri][1]):
ri -= 1
# if( fi<len(trm) and self.check_pass( p, trm[fi], dtrm[fi][0] )) \
# and( ri>=0 and not self.check_pass( p, trm[ri], dtrm[ri][0] )) :
if( fi<len(trm) and ri>=0 ) and \
((self.check_pass( p, trm[fi], dtrm[fi][0] )) or \
( self.check_pass( p, trm[ri], dtrm[ri][0] ))) :
continue
# if ri == -1 and fi == 0 : continue
# if not self.check_pass( p , np.array((0,0,z0)) , np.array((0,0,-1)) ) :
# continue
n = np.cross(du, dv)
nlen = np.linalg.norm(n)
dlen = np.linalg.norm(du)
ndu = du / dlen
# paths count optimization
if odu != None and np.allclose(ndu, odu, atol=0.001):
continue
if dlen > 0.01:
n = n / nlen
if cn == None and pn != None: # C0 edge
cn = n
tn = (pn + cn)
tn = tn / np.linalg.norm(tn)
path.append(np.array(p + tn * self.exac_r))
else: # normal is well defined
pn = cn
cn = n
path.append(np.array(p + cn * self.exac_r))
else: # normal is undefined
cn = None
odu = ndu
def gen_line_u_with_trimming( self , v , bu , eu , nu , z0 , pts , trm , dtrm , path ) :
sys.stdout.write('.')
sys.stdout.flush()
odu = None
cn = None # current normal
pn = None # previous normal
for iu in np.linspace(bu,eu,nu) :
p = csurf.bspline_surf ( iu, v, pts )
dv= csurf.bspline_surf_prime_v( iu, v, pts )
du= csurf.bspline_surf_prime_u( iu, v, pts )
fi = 0
while fi<len(trm) and not self.check_pass( p , trm[fi] , dtrm[fi][1] ) :
fi+=1
ri = len(trm)-1
while ri>=0 and self.check_pass( p , trm[ri] , dtrm[ri][1] ) :
ri-=1
# if( fi<len(trm) and self.check_pass( p, trm[fi], dtrm[fi][0] )) \
# and( ri>=0 and not self.check_pass( p, trm[ri], dtrm[ri][0] )) :
if( fi<len(trm) and ri>=0 ) and \
((self.check_pass( p, trm[fi], dtrm[fi][0] )) or \
( self.check_pass( p, trm[ri], dtrm[ri][0] ))) :
continue
# if ri == -1 and fi == 0 : continue
# if not self.check_pass( p , np.array((0,0,z0)) , np.array((0,0,-1)) ) :
# continue
n = np.cross( du , dv )
nlen = np.linalg.norm( n )
dlen = np.linalg.norm( du )
ndu = du / dlen
# paths count optimization
if odu != None and np.allclose(ndu,odu,atol=0.001) :
continue
if dlen > 0.01 :
n = n / nlen
if cn == None and pn != None : # C0 edge
cn = n
tn = (pn+cn)
tn = tn / np.linalg.norm(tn)
path.append( np.array( p + tn*self.exac_r ) )
else : # normal is well defined
pn = cn
cn = n
path.append( np.array( p + cn * self.exac_r ) )
else : # normal is undefined
cn = None
odu = ndu
def gen_exact(self, z0, trm, tdhead, tdhand):
path_hand = []
path_head = []
#
# hand
#
u, v, hand_pts = self.get_curve_data(self.hand)
tn = np.cross(trm[-1] - trm[0], np.array((0, 0, 1)))
tp = trm[0]
bu = 3.0
eu = 7.0
nu = 64
nv = 128
dv = v / float(nv)
iv = 0.0
ev = iv
while iv <= v:
p = csurf.bspline_surf(eu, iv, hand_pts)
if self.check_pass(p, tp, tn):
self.gen_line_u_with_trimming(iv, bu, eu, nu, z0, hand_pts,
trm, tdhand, path_hand)
ev = iv
iv += dv
p = csurf.bspline_surf(eu, iv, hand_pts)
if self.check_pass(p, tp, tn):
self.gen_line_u_with_trimming(iv, eu, bu, nu, z0, hand_pts,
trm, tdhand, path_hand)
ev = iv
iv += dv
trmuv = self.trm_uv_hand.l
i = 1
for a in np.linspace(0, 1, 5):
for uv in trmuv if not i % 2 else reversed(trmuv):
if uv[0] > 3.0 and uv[0] < 7.0:
v = a * (uv[1] - 0.7) + (1 - a) * ev
p = csurf.bspline_surf(uv[0], v, hand_pts)
dv = csurf.bspline_surf_prime_v(uv[0], v, hand_pts)
du = csurf.bspline_surf_prime_u(uv[0], v, hand_pts)
n = np.cross(du, dv)
n = n / np.linalg.norm(n)
path_hand.append(np.array(p + n * self.exac_r))
i += 1
path_hand += trm
#
# head
#
u, v, head_pts = self.get_curve_data(self.head)
bu = 6.0
eu = 13.0
nu = 64
nv = 128
dv = v / float(nv)
iv = 0.0
while iv <= v:
self.gen_line_u_with_trimming(iv, bu, eu, nu, z0, head_pts, trm,
tdhead, path_head)
iv += dv
self.gen_line_u_with_trimming(iv, eu, bu, nu, z0, head_pts, trm,
tdhead, path_head)
iv += dv
print
path = path_hand
path.append(path_hand[-1] + np.array((0, 0, -1.2)))
path.append(path_head[1] + np.array((0, 0, -1.2)))
path += path_head
# move from center to bottom
for i in range(len(path)):
path[i][2] += self.exac_r
return np.array(path)
def gen_initial(self, r, l, z):
u, v, head_pts = self.get_curve_data(self.head)
bu, eu = 7.0, 12.0
bv, ev = 0, v
pmin = csurf.bspline_surf(bu, 0, head_pts)
pmax = csurf.bspline_surf(bu, v, head_pts)
if pmin[0] > pmax[0]:
pmin, pmax = pmax, pmin
bv, ev = ev, bv
bx, ex = BLOCK_X
by, ey = BLOCK_Y
path = []
x = bx
while x < ex:
if x >= pmin[0] - r: break
path.append(np.array((x, by, z)))
path.append(np.array((x, ey, z)))
x += r
if x >= pmin[0] - r: break
path.append(np.array((x, ey, z)))
path.append(np.array((x, by, z)))
x += r
p = csurf.bspline_surf(bu, bv, head_pts)
path[-2][0] = p[0] - self.init_r
path[-1][0] = p[0] - self.init_r
op = p = path[-1]
nu = 64
nv = 128
iv = (ev - bv) / float(nv)
v = bv
s = m.copysign(1, ev - bv)
while True:
while s * v <= s * ev and p != None and m.fabs(p[0] - op[0]) < l:
p = csurf.bspline_surf(eu, v, head_pts)
dv = csurf.bspline_surf_prime_v(eu, v, head_pts)
du = csurf.bspline_surf_prime_u(eu, v, head_pts)
n = np.cross(du, dv)
n = n / np.linalg.norm(n)
p = p + n * r
v += iv
op = p
if s * v > s * ev: break
if v < 12 and v > 5:
u1 = 8.0
u2 = 11.0
else:
u1 = bu
u2 = eu
tp = []
self.gen_line_u(head_pts, tp, r, v, u2, u1, nu)
tp.insert(0, np.array((tp[0][0], by, tp[0][2])))
tp.append(np.array((tp[-1][0], ey, tp[-1][2])))
path += tp
while s * v <= s * ev and p != None and m.fabs(p[0] - op[0]) < l:
p = csurf.bspline_surf(bu, v, head_pts)
dv = csurf.bspline_surf_prime_v(bu, v, head_pts)
du = csurf.bspline_surf_prime_u(bu, v, head_pts)
n = np.cross(du, dv)
n = n / np.linalg.norm(n)
p = p + n * r
v += iv
op = p
if s * v > s * ev: break
if v < 12 and v > 5:
u1 = 8.0
u2 = 11.0
else:
u1 = bu
u2 = eu
tp = []
self.gen_line_u(head_pts, tp, r, v, u1, u2, nu)
tp.insert(0, np.array((tp[0][0], ey, tp[0][2])))
tp.append(np.array((tp[-1][0], by, tp[-1][2])))
path += tp
x = path[-1][0] + r
while x < ex:
path.append(np.array((x, ey, z)))
path.append(np.array((x, by, z)))
x += r
path.append(np.array((x, by, z)))
path.append(np.array((x, ey, z)))
x += r
# move from center to bottom
for i in range(len(path)):
path[i][2] += self.init_r
return np.array(path)
def gen_exact( self , z0 , trm , tdhead , tdhand ) : path_hand = [] path_head = [] # # hand # u , v , hand_pts = self.get_curve_data( self.hand ) tn = np.cross( trm[-1] - trm[0] , np.array((0,0,1)) ) tp = trm[0] bu = 3.0 eu = 7.0 nu = 64 nv = 128 dv = v / float(nv) iv = 0.0 ev = iv while iv <= v : p = csurf.bspline_surf( eu , iv , hand_pts ) if self.check_pass( p , tp , tn ) : self.gen_line_u_with_trimming( iv , bu , eu , nu , z0 , hand_pts , trm , tdhand , path_hand ) ev = iv iv += dv p = csurf.bspline_surf( eu , iv , hand_pts ) if self.check_pass( p , tp , tn ) : self.gen_line_u_with_trimming( iv , eu , bu , nu , z0 , hand_pts , trm , tdhand , path_hand ) ev = iv iv += dv trmuv = self.trm_uv_hand.l i = 1 for a in np.linspace(0,1,5) : for uv in trmuv if not i%2 else reversed(trmuv) : if uv[0] > 3.0 and uv[0] < 7.0 : v = a*(uv[1] - 0.7) + (1-a)*ev p = csurf.bspline_surf ( uv[0] , v , hand_pts ) dv= csurf.bspline_surf_prime_v( uv[0] , v , hand_pts ) du= csurf.bspline_surf_prime_u( uv[0] , v , hand_pts ) n = np.cross( du , dv ) n = n / np.linalg.norm( n ) path_hand.append( np.array( p + n * self.exac_r ) ) i += 1 path_hand += trm # # head # u , v , head_pts = self.get_curve_data( self.head ) bu = 6.0 eu = 13.0 nu = 64 nv = 128 dv = v / float(nv) iv = 0.0 while iv <= v : self.gen_line_u_with_trimming( iv , bu , eu , nu , z0 , head_pts , trm , tdhead , path_head ) iv += dv self.gen_line_u_with_trimming( iv , eu , bu , nu , z0 , head_pts , trm , tdhead , path_head ) iv += dv print path = path_hand path.append( path_hand[-1] + np.array((0,0,-1.2)) ) path.append( path_head[ 1] + np.array((0,0,-1.2)) ) path += path_head # move from center to bottom for i in range(len(path)) : path[i][2] += self.exac_r return np.array( path )
def gen_initial( self , r , l , z ) : u , v , head_pts = self.get_curve_data( self.head ) bu , eu = 7.0 , 12.0 bv , ev = 0 , v pmin = csurf.bspline_surf( bu , 0 , head_pts ) pmax = csurf.bspline_surf( bu , v , head_pts ) if pmin[0] > pmax[0] : pmin , pmax = pmax , pmin bv , ev = ev , bv bx , ex = BLOCK_X by , ey = BLOCK_Y path = [] x = bx while x < ex : if x >= pmin[0] - r : break path.append( np.array((x,by,z)) ) path.append( np.array((x,ey,z)) ) x += r if x >= pmin[0] - r : break path.append( np.array((x,ey,z)) ) path.append( np.array((x,by,z)) ) x += r p = csurf.bspline_surf( bu , bv , head_pts ) path[-2][0] = p[0] - self.init_r path[-1][0] = p[0] - self.init_r op = p = path[-1] nu = 64 nv = 128 iv = (ev-bv) / float(nv) v = bv s = m.copysign( 1 , ev - bv ) while True : while s*v <= s*ev and p != None and m.fabs( p[0] - op[0] ) < l : p = csurf.bspline_surf( eu , v , head_pts ) dv= csurf.bspline_surf_prime_v( eu , v , head_pts ) du= csurf.bspline_surf_prime_u( eu , v , head_pts ) n = np.cross( du , dv ) n = n / np.linalg.norm( n ) p = p + n * r v += iv op = p if s*v > s*ev : break if v < 12 and v > 5 : u1 = 8.0 u2 = 11.0 else : u1 = bu u2 = eu tp = [] self.gen_line_u( head_pts , tp , r , v , u2 , u1 , nu ) tp.insert( 0 , np.array((tp[0][0],by,tp[0][2])) ) tp.append( np.array((tp[-1][0],ey,tp[-1][2])) ) path += tp while s*v <= s*ev and p != None and m.fabs( p[0] - op[0] ) < l : p = csurf.bspline_surf( bu , v , head_pts ) dv= csurf.bspline_surf_prime_v( bu , v , head_pts ) du= csurf.bspline_surf_prime_u( bu , v , head_pts ) n = np.cross( du , dv ) n = n / np.linalg.norm( n ) p = p + n * r v += iv op = p if s*v > s*ev : break if v < 12 and v > 5 : u1 = 8.0 u2 = 11.0 else : u1 = bu u2 = eu tp = [] self.gen_line_u( head_pts , tp , r , v , u1 , u2 , nu ) tp.insert( 0 , np.array((tp[0][0],ey,tp[0][2])) ) tp.append( np.array((tp[-1][0],by,tp[-1][2])) ) path += tp x = path[-1][0] + r while x < ex : path.append( np.array((x,ey,z)) ) path.append( np.array((x,by,z)) ) x += r path.append( np.array((x,by,z)) ) path.append( np.array((x,ey,z)) ) x += r # move from center to bottom for i in range(len(path)) : path[i][2] += self.init_r return np.array( path )