398 lines
15 KiB
Python
398 lines
15 KiB
Python
import math
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import sys
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from kivy.graphics import Color,Line,Rectangle
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from kivy.uix.widget import Widget
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from point import Point
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from tools import isint_nonzero,sgn
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class Cross():
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# size of central square
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size=50
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def __init__(self,x,y,**kwargs):
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self.pos=Point(x,y)
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self.color=kwargs.get("color",(0,0,1))
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self.selected=False
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# set position
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def setpos(self,x,y):
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self.pos.x=x
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self.pos.y=y
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def draw(self):
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Color(*(self.color))
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Rectangle(pos=((self.pos.x-1.5)*self.size,(self.pos.y-0.5)*self.size),size=(3*self.size,self.size))
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Rectangle(pos=((self.pos.x-0.5)*self.size,(self.pos.y-1.5)*self.size),size=(self.size,3*self.size))
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# stroke
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Color(1,1,1)
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Line(points=(
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*((self.pos.x-0.5)*self.size,(self.pos.y-0.5)*self.size),
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*((self.pos.x-0.5)*self.size,(self.pos.y-1.5)*self.size),
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*((self.pos.x+0.5)*self.size,(self.pos.y-1.5)*self.size),
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*((self.pos.x+0.5)*self.size,(self.pos.y-0.5)*self.size),
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*((self.pos.x+1.5)*self.size,(self.pos.y-0.5)*self.size),
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*((self.pos.x+1.5)*self.size,(self.pos.y+0.5)*self.size),
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*((self.pos.x+0.5)*self.size,(self.pos.y+0.5)*self.size),
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*((self.pos.x+0.5)*self.size,(self.pos.y+1.5)*self.size),
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*((self.pos.x-0.5)*self.size,(self.pos.y+1.5)*self.size),
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*((self.pos.x-0.5)*self.size,(self.pos.y+0.5)*self.size),
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*((self.pos.x-1.5)*self.size,(self.pos.y+0.5)*self.size),
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*((self.pos.x-1.5)*self.size,(self.pos.y-0.5)*self.size),
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*((self.pos.x-0.5)*self.size,(self.pos.y-0.5)*self.size),
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))
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# check whether a cross at pos interacts with cross
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def check_interaction(self,pos):
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# allow for error
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return int(pos.x-self.pos.x+sgn(pos.x-self.pos.x)*1e-11)**2+int(pos.y-self.pos.y+sgn(pos.y-self.pos.y)*1e-11)**2>=5
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# check whether a cross at position pos is touching self
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def check_touch(self,pos):
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rel=pos-self.pos
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for i in [-3,-2,-1,1,2,3]:
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# allow for error
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if abs(rel.x-i)<1e-11 and abs(rel.y)<=4-abs(i)+1e-11 and abs(rel.y)>=3-abs(i)-1e-11:
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return True
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if abs(rel.y-i)<1e-11 and abs(rel.x)<=4-abs(i)+1e-11 and abs(rel.x)>=3-abs(i)-1e-11:
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return True
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return False
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# find position along a line that comes in contact with the line going through pos in direction v
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def move_on_line_to_stick(self,pos,v):
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# relative to cross
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return self.move_on_line_to_stick_relative(pos-self.pos,v)+self.pos
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def move_on_line_to_stick_relative(self,x,v):
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# if x is in the right quadrant
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if abs(x.y)<=x.x:
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# find all stuck positions on lines
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stuck=[]
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# check intersections with vertical lines
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if v.x!=0:
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for i in range(1,4):
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# candidate
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y=Point(i,x.y+(i-x.x)*v.y/v.x)
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# check that it is in the right range
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if abs(y.y)<=4-i and abs(y.y)>=3-i:
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stuck.append(y)
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# check intersections with horizontal lines
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if v.y!=0:
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for i in [-3,-2,-1,1,2,3]:
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# candidate
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y=Point(x.x+(i-x.y)*v.x/v.y,i)
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# check that it is in the right range
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if y.x<=4-abs(i) and y.x>=3-abs(i):
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stuck.append(y)
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return x.closest(stuck)
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# reflect other quadrants to the right one
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# top quadrant
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elif abs(x.x)<=x.y:
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closest=self.move_on_line_to_stick_relative(Point(x.y,x.x),Point(v.y,v.x))
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return Point(closest.y,closest.x)
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# bottom quadrant
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elif abs(x.x)<=-x.y:
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closest=self.move_on_line_to_stick_relative(Point(-x.y,x.x),Point(-v.y,v.x))
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return Point(closest.y,-closest.x)
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# left quadrant
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else:
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closest=self.move_on_line_to_stick_relative(Point(-x.x,x.y),Point(-v.x,v.y))
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return Point(-closest.x,closest.y)
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# move along edge of cross
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def move_along(self,newpos,pos):
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rel=pos-self.pos
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# check if the particle is stuck in the x direction
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if isint_nonzero(rel.x):
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# check y direction
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if isint_nonzero(rel.y):
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# in corner
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# two types of corners: |x|_1=3 or |x|_1=4
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if abs(rel.x)+abs(rel.y)<3.5:
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if sgn(newpos.y-pos.y)==sgn(rel.y):
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# stuck in x direction
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return self.move_stuck_x(newpos,pos)
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elif sgn(newpos.x-pos.x)==sgn(rel.x):
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# stuck in y direction
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return self.move_stuck_y(newpos,pos)
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else:
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if sgn(newpos.y-pos.y)==-sgn(rel.y):
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# stuck in x direction
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return self.move_stuck_x(newpos,pos)
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elif sgn(newpos.x-pos.x)==-sgn(rel.x):
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# stuck in y direction
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return self.move_stuck_y(newpos,pos)
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# stuck in both directions
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return pos
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else:
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# stuck in x direction
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return self.move_stuck_x(newpos,pos)
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elif isint_nonzero(rel.y):
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# stuck in y direction
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return self.move_stuck_y(newpos,pos)
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# this should never happen
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else:
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print("error: stuck particle has non-integer relative position: (",rel.x,",",rel.y,")",file=sys.stderr)
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exit(-1)
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# move when stuck in the x direction
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def move_stuck_x(self,newpos,pos):
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# only move in y direction
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candidate=Point(pos.x,newpos.y)
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# do not move past corners
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rel=pos.y-self.pos.y
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newrel=newpos.y-self.pos.y
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if newpos.y>pos.y:
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if self.check_interaction(candidate)==False or (rel<math.ceil(rel)-1e-11 and newrel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0):
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# in open corner
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if rel>math.ceil(rel)-1e-11:
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candidate.y=math.ceil(rel)+1+self.pos.y
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else:
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candidate.y=math.ceil(rel)+self.pos.y
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else:
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if self.check_interaction(candidate)==False or (rel>math.floor(rel)+1e-11 and newrel<math.floor(rel)-1e-11 and math.floor(rel)!=0):
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# in open corner
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if rel<math.floor(rel)+1e-11:
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candidate.y=math.floor(rel)-1+self.pos.y
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else:
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candidate.y=math.floor(rel)+self.pos.y
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return candidate
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# move when stuck in the y direction
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def move_stuck_y(self,newpos,pos):
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# only move in x direction
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candidate=Point(newpos.x,pos.y)
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# do not move past corners
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rel=pos.x-self.pos.x
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newrel=newpos.x-self.pos.x
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if newpos.x>pos.x:
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if self.check_interaction(candidate)==False or (rel<math.ceil(rel)-1e-11 and newrel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0):
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# in open corner
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if rel>math.ceil(rel)-1e-11:
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candidate.x=math.ceil(rel)+1+self.pos.x
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else:
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candidate.x=math.ceil(rel)+self.pos.x
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else:
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if self.check_interaction(candidate)==False or (rel>math.floor(rel)+1e-11 and newrel<math.floor(rel)-1e-11 and math.floor(rel)!=0):
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# in open corner
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if rel<math.floor(rel)+1e-11:
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candidate.x=math.floor(rel)-1+self.pos.x
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else:
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candidate.x=math.floor(rel)+self.pos.x
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return candidate
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# L_infinity distance rescalled by 3 in the x direction
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def cross_distx(x,y):
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return max(abs(x.x-y.x)/3,abs(x.y-y.y))
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# L_infinity distance rescalled by 3 in the y direction
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def cross_disty(x,y):
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return max(abs(x.x-y.x),abs(x.y-y.y)/3)
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# polar description of touching cross
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def cross_polar(t):
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# by symmetry, put angle in interval (-pi/4,pi/4), and take absolute value
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tt=abs((t+math.pi/4)%(math.pi/2)-math.pi/4)
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if tt<math.atan(1/3):
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return 3/math.cos(tt)
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elif tt<math.atan(1/2):
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return 1/math.sin(tt)
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else:
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return 2/math.cos(tt)
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# cross painter
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class Cross_painter(Widget):
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def __init__(self,app,**kwargs):
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# list of crosses
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self.crosses=[]
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# selected cross
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self.selected=None
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# app is used to share information between widgets
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self.app=app
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# init Widget
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super(Cross_painter,self).__init__(**kwargs)
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def reset(self):
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self.crosses=[]
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self.selected=None
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self.canvas.clear()
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self.draw()
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# draw all crosses
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def draw(self):
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with self.canvas:
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for cross in self.crosses:
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cross.draw()
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# respond to mouse down
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def on_touch_down(self,touch):
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# only respond to touch in area
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if self.collide_point(*touch.pos):
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# create new cross
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if touch.button=="right":
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if self.check_interaction_any(Point(touch.x/Cross.size,touch.y/Cross.size),None):
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new=Cross(touch.x/Cross.size,touch.y/Cross.size)
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with self.canvas:
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new.draw()
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# add to list
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self.crosses.append(new)
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# select cross
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if touch.button=="left":
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# unselect
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if self.selected!=None:
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self.selected.selected=False
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# find cross under touch
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self.selected=self.find_cross(Point(touch.x/Cross.size,touch.y/Cross.size))
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# select
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if self.selected!=None:
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self.selected.selected=True
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# respond to drag
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def on_touch_move(self,touch):
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if self.collide_point(*touch.pos):
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# only move on left click
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if touch.button=="left" and self.selected!=None:
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self.selected.pos=self.check_move(Point(touch.x/Cross.size,touch.y/Cross.size),self.selected)
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# redraw
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self.canvas.clear()
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self.draw()
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# find the cross at position pos
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def find_cross(self,pos):
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for cross in self.crosses:
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if cross_distx(pos,cross.pos)<=0.5 or cross_disty(pos,cross.pos)<=0.5:
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return cross
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# none found
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return None
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# check whether a position intersects with any of the crosses
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def check_interaction_any(self,pos,exception):
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for other in self.crosses:
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if other!=exception:
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if other.check_interaction(pos)==False:
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return False
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return True
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# check that a cross can move to new position
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def check_move(self,newpos,cross):
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# whether newpos is acceptable
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accept_newpos=True
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for other in self.crosses:
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# do not compare a cross to itself
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if other!=cross:
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# move would make cross overlap with other
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if other.check_interaction(newpos)==False:
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accept_newpos=False
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# check if cross touches other
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if other.check_touch(cross.pos):
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# move along other while remaining stuck
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candidate=other.move_along(newpos,cross.pos)
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else:
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candidate=other.move_on_line_to_stick(cross.pos,newpos-cross.pos)
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if self.check_interaction_any(candidate,cross):
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return candidate
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if accept_newpos:
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return newpos
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else:
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# cannot move cross at all, try again
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return self.check_move(candidate,cross)
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# write configuration to file
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def write(self,file):
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ff=open(file,"w")
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for cross in self.crosses:
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ff.write("{:05.2f},{:05.2f};{:3.1f},{:3.1f},{:3.1f}\n".format(cross.pos.x,cross.pos.y,cross.color[0],cross.color[1],cross.color[2]))
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ff.close()
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# read configuration from file
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def read(self,file):
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self.reset()
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try:
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ff=open(file,"r")
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except:
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self.app.command_prompt.message="error: could not read file '"+file+"' (this should not happen and is probably a bug)"
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return
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# counter
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i=0
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try:
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lines=ff.readlines()
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except:
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self.app.command_prompt.message="error: could not read the contents of file '"+file+"'"
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return
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for line in lines:
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i+=1
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# remove newline
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line=line[:len(line)-1]
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# ignore comments
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if '#' in line:
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line=line[:line.find('#')]
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# ignore empty lines
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if len(line)==0:
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continue
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entries=line.split(";")
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# skip line if improperly formatted
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if len(entries)>2:
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print("warning: ignoring line "+str(i)+" in file '"+file+"': more than two ';' spearated entries in '"+line+"'",file=sys.stderr)
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continue
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# position
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pos_str=entries[0].split(",")
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# skip line if improperly formatted
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if len(pos_str)!=2:
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print("warning: ignoring line "+str(i)+" in file '"+file+"': position '"+entries[0]+"' does not have two components",file=sys.stderr)
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continue
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try:
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pos=Point(float(pos_str[0]),float(pos_str[1]))
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except:
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print("warning: ignoring line "+str(i)+" in file '"+file+"': position '"+entries[0]+"' cannot be read",file=sys.stderr)
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continue
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# color
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color=(0,0,1)
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if len(entries)==2:
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color_str=entries[1].split(",")
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# skip line if improperly formatted
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if len(color_str)!=3:
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print("warning: ignoring line "+str(i)+" in file '"+file+"': color '"+entries[1]+"' does not have three components",file=sys.stderr)
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continue
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try:
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color=(float(color_str[0]),float(color_str[1]),float(color_str[2]))
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except:
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print("warning: ignoring line "+str(i)+" in file '"+file+"': color '"+entries[1]+"' cannot be read",file=sys.stderr)
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continue
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if self.check_interaction_any(pos,None):
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# add to list
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self.crosses.append(Cross(pos.x,pos.y,color=color))
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else:
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print("warning: ignoring line "+str(i)+" in file '"+file+"': particle overlaps with existing particles",file=sys.stderr)
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ff.close()
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self.draw()
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