Код: Выделить всё

bzr branch lp:gcodetools

Код: Выделить всё

alignl {
   left lbrace alignl stack{
      x = x_1+t_1 n_x1#y = y_1+t_1 n_y1
   } right none
} newline newline 

alignl {
   left lbrace alignl stack{
      x = x_2+t_2 n_x2#   
      y = y_2+t_2 n_y2#
      x_2 = a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x#
      y_2 = a_y t_{3}^3 + b_y t_{3}^2 + c_y t_{3} + d_y#
      n_x2 = -(3a_y t_{3}^2 + 2b_y t_3 +c_y)#
      n_y2 = 3a_x t_{3}^2 + 2b_x t_3 +c_x
   } right none
}newline newline 

alignl {
   (x_1 - x)^2 + (y_1 - y)^2 = (a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - x)^2+(a_y t_{3}^3 + b_y t_{3}^2 + c_y t_3 + d_y - y)^2
} newline  newline 

alignl {
   t_3 in [0;1] 
}newline  newline 

alignl {
   left lbrace alignl stack{
      x_1+ n_x1 t_1 = a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - t_2(3a_y t_{3}^2 + 2b_y t_3 +c_y)#
      y_1+t_1 n_y1 = a_y t_{3}^3 + b_y t_{3}^2 + c_y t_{3} + d_y + t_2 (3a_x t_{3}^2 + 2b_x t_3 +c_x)#
       (x_1 - x_1+ n_x1 t_1)^2 + (y_1 - y_1+t_1 n_y1)^2 = (a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - x_1+ n_x1 t_1)^2+(a_y t_{3}^3 + b_y t_{3}^2 + c_y t_3 + d_y - y_1+t_1 n_y1)^2
   } right none
}newline newline 
alignl {
   t_3 in [0;1] 
}newline  newline 

Код: Выделить всё

   left lbrace alignl stack{
      x = x_1+t_1 n_x1#y = y_1+t_1 n_y1
   } right none
newline newline 

   left lbrace alignl stack{
      x = x_2+t_2 n_x2#   
      y = y_2+t_2 n_y2#
      x_2 = a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x#
      y_2 = a_y t_{3}^3 + b_y t_{3}^2 + c_y t_{3} + d_y#
      n_x2 = -(3a_y t_{3}^2 + 2b_y t_3 +c_y)#
      n_y2 = 3a_x t_{3}^2 + 2b_x t_3 +c_x
   } right none
newline newline 


   (x_1 - x)^2 + (y_1 - y)^2 = (a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - x)^2+(a_y t_{3}^3 + b_y t_{3}^2 + c_y t_3 + d_y - y)^2
newline  newline 


   t_3 in [0;1] 
newline  newline 


   left lbrace alignl stack{
      x_1+ n_x1 t_1 = a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - t_2(3a_y t_{3}^2 + 2b_y t_3 +c_y)#
      y_1+t_1 n_y1 = a_y t_{3}^3 + b_y t_{3}^2 + c_y t_{3} + d_y + t_2 (3a_x t_{3}^2 + 2b_x t_3 +c_x)#
       (x_1 - x_1- n_x1 t_1)^2 + (y_1 - y_1-t_1 n_y1)^2 = (a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - x_1- n_x1 t_1)^2+(a_y t_{3}^3 + b_y t_{3}^2 + c_y t_3 + d_y - y_1-t_1 n_y1)^2
   } right none
newline newline 


   t_3 in [0;1] 
newline  newline 



   left lbrace alignl stack{
      x_1+ n_x1 t_1 - (a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x) + t_2(3a_y t_{3}^2 + 2b_y t_3 +c_y) = 0#
      y_1+ n_y1 t_1 - (a_y t_{3}^3 + b_y t_{3}^2 + c_y t_{3} + d_y) - t_2 (3a_x t_{3}^2 + 2b_x t_3 +c_x) = 0#
       (n_x1 t_1)^2 + (n_y1 t_1)^2 - (a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - x_1- n_x1 t_1)^2 - (a_y t_{3}^3 + b_y t_{3}^2 + c_y t_3 + d_y - y_1 - t_1 n_y1)^2 = 0
   } right none
newline newline 
   
   left [ matrix{
n_x1 #
3a_y t_{3}^2 + 2b_y t_3 +c_y #
-(3a_x t_{3}^2 + 2b_x t_3 +c_x) + t_2(6a_y t_3 + 2b_y) ##

n_y1 #
-(3a_x t_{3}^2 + 2b_x t_3 +c_x) #
-(3a_y t_{3}^2 + 2b_y t_3 +c_y) - t_2(6a_x t_3 + 2b_x) ##

2(n_x1^2+n_y1^2) t_1 + 2n_x1 (a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - x_1- n_x1 t_1) +2n_y1(a_y t_{3}^3 + b_y t_{3}^2 + c_y t_3 + d_y - y_1-t_1 n_y1)  #0 #

-2(3a_x t_{3}^2 + 2b_x t_3 +c_x)(a_x t_{3}^3 + b_x t_{3}^2 + c_x t_{3} + d_x - x_1- n_x1 t_1) - 2(3a_y t_{3}^2 + 2b_y t_3 +c_y) (a_y t_{3}^3 + b_y t_{3}^2 + c_y t_3 + d_y - y_1-t_1 n_y1)
 
}right ]
   
newline newline 

Введем обознаяения fx'(t3), fy'(t3), fx(t3), fy(t3)
newline newline 



left [ matrix{
n_x1 #
fy'(t_3) #
-fx'(t_3) + t_2(6a_y t_3 + 2b_y) ##

n_y1 #
-fx'(t_3) #
-fy'(t_3) - t_2(6a_x t_3 + 2b_x) ##

2(n_x1^2+n_y1^2) t_1 + 2n_x1 (fx(t_3) - x_1- n_x1 t_1) +2n_y1(fy(t_3) - y_1-t_1 n_y1)  #0 #

-2fx'(t_3)(fx(t_3) - x_1- n_x1 t_1) - 2fy'(t_3)(fy(t_3) - y_1-t_1 n_y1)
 
}right ]

Код: Выделить всё

def find_cutter_center((x1,y1),(nx1,ny1), sp1,sp2):
					bez = (sp1[1][:],sp1[2][:],sp2[0][:],sp2[1][:])
					ax,ay,bx,by,cx,cy,dx,dy=bezmisc.bezierparameterize(bez)
					d,t3 = get_distance_from_point_to_csp((x1,y1),sp1,sp2)
					t = numpy.matrix([[d/math.sqrt(nx1**2+ny1**2)],[1./2],[t3]])
					fx,fy = bezmisc.bezierpointatt(bez,t3)
					i = 0
					ta = []
					while i==0 or abs(F.sum())>straight_distance_tolerance and i<10:
						ta += [t]
						print_()
						print_()
						print_()
						print_()
						print_(t)
						print_()						
						t1,t2,t3 = t.transpose().getA()[0]
						fx,fy = bezmisc.bezierpointatt(bez,t3)
						f1x,f1y = bezmisc.bezierslopeatt(bez,t3)
						i+=1
						F = numpy.matrix(
							[
								x1+nx1*t1-fx+t2*f1y,
								y1+ny1*t1-fy-t2*f1x,
								(nx1**2+ny1**2)*(t1**2) - (fx-x1-nx1*t1)**2 -(fy-y1-ny1*t1)**2
							])
						print_(F)
						print_(F.sum())
						F1 = numpy.matrix(
									[
										[
											nx1,			f1y,		-f1x+t2*(6*ay*t3+2*by)
										],
										[
											ny1,			-f1x,		-f1y-t2*(6*ax*t3+2*bx)
										],
										[
											2*(nx1**2+ny1**2)*t1+2*nx1*(fx-x1-nx1*t1) +2*ny1*(fy-y1-ny1*t1),
															0,
																		-2*f1x*(fx-x1-nx1*t1) -2*f1y*(fy-y1-ny1*t1)
										]
									]
								)
						print_()								
						print_(F1)						
						if numpy.linalg.det(F1)	!=0:
							print_()						
							print_(numpy.linalg.inv(F1))
							t = t - numpy.linalg.inv(F1)*(F.transpose())
						else: break	
					return t

Код: Выделить всё

def get_distance_from_point_to_csp(p,sp1,sp2, tolerance = 0.01 ): 
	n, i = 10, 0
	d, dl = [None,(0,0)],[0,(0,0)]
	while i<2 or (abs(d[0]-dl[0])>tolerance and i<4):
		i += 1
		dl = d[:]	
		for j in range(n+1):
			t = float(j)/n
			cp = csp_at_t(sp1,sp2,t) 
			d = min( [(P(cp)-P(p)).mag(),t], d) if d[0]!=None else [(P(cp)-P(p)).mag(),t]
		n=n*2
	return d

Код: Выделить всё

					m += [ [ti**3,3*(1-ti)*(ti**2),3*((1-ti)**2)*ti, (1-ti)**3] ]
					xi += [ [x1+nx*r,y1+ny*r] ]
				m = numpy.array(m)
				xi = numpy.array(xi)
				sp1,sp2 = [[0.,0.],[0.,0.],[0.,0.]], [[0.,0.],[0.,0.],[0.,0.]]
				a,b,c,d = numpy.linalg.solve(m, xi).tolist()

Код: Выделить всё

   left lbrace alignl stack{
      x = B_ix+t_1 n_x1#y = B_iy+t_1 n_y1#
      (x-B_ix)^2 + (y-B_iy)^2 = (x-T_ix)^2 + (y-T_iy)^2
   } right none
newline newline 
Пусть, (x_1,y_1)=(B_ix,B_iy), (x_2,y_2)=(T_ix,T_iy)newline newline

   left lbrace alignl stack{
      x = x_1+t_1 n_x1#y = y_1+t_1 n_y1#
      (x-x_1)^2 + (y-y_1)^2 = (x-x_2)^2 + (y-y_2)^2
   } right none
newline newline 

 left lbrace alignl stack{
      x = x_1+t_1 n_x1#y = y_1+t_1 n_y1#
      (x_1+t_1 n_x1-x_1)^2 + (y_1+t_1 n_y1-y_1)^2 = (x_1+t_1 n_x1-x_2)^2 + (y_1+t_1 n_y1-y_2)^2
   } right none
   
newline newline 

 left lbrace alignl stack{
      x = x_1+t_1 n_x1#y = y_1+t_1 n_y1#
      n_x1^2 t_1^2 +n_y1^2 t_1^2 = n_x1^2 t_1^2 +x_1^2+x_2^2+2x_1 n_x1 t_1 -2x_2 n_x1  t_1 -2x_2 x_1 +n_y1^2 t_1^2 +y_1^2 + y_2^2 + 2y_1 n_y1 t_1 -2 y_2 n_y1 t_1 -2y_1 y_2
     
   } right none
   newline newline 

 left lbrace alignl stack{
      x = x_1+t_1 n_x1#y = y_1+t_1 n_y1#

     (2x_1 n_x1- 2x_2 n_x1 + 2y_1 n_y1 -2 y_2 n_y1)t_1 = 2x_1 x_2 + 2y_1 y_2 - x_1^2 -x_2^2 -y_1^2 - y_2^2
   } right none