Adapt cross dynamics to square
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parent
152f70d402
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213
cross.py
213
cross.py
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import math
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import sys
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from kivy.graphics import Color,Line,Rectangle
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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,**kwargs):
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# set color
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if not self.selected:
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Color(*self.color)
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else:
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(r,g,b)=self.color
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# darken selected
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Color(r/2,g/2,b/2)
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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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4
point.py
4
point.py
@ -43,3 +43,7 @@ class Point:
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dist=(self-point)**2
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dist=(self-point)**2
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return closest
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return closest
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# L infinity norm
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def l_infinity(x):
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return max(abs(x.x),abs(x.y))
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128
polyomino.py
Normal file
128
polyomino.py
Normal file
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import math
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import sys
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from kivy.graphics import Color,Line,Rectangle
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from point import Point,l_infinity
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from tools import isint_nonzero,sgn,in_interval
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class Square():
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# size
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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,**kwargs):
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# set color
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if not self.selected:
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Color(*self.color)
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else:
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(r,g,b)=self.color
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# darken selected
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Color(r/2,g/2,b/2)
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Rectangle(pos=((self.pos.x-0.5)*self.size,(self.pos.y-0.5)*self.size),size=(self.size,self.size))
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# check whether a square at pos interacts with square
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def check_interaction(self,pos):
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return l_infinity(pos-self.pos)>=1
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# check whether a square at position pos is touching self
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def check_touch(self,pos):
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# allow for error
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if in_interval(l_infinity(pos-solf.pos),1-1e-11,1+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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# compute intersections with four lines making up square
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intersections=[\
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Point(self.pos.x+1/2,pos.y+v.y/v.x*(self.pos.x+1/2-pos.x)),\
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Point(self.pos.x-1/2,pos.y+v.y/v.x*(self.pos.x-1/2-pos.x)),\
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Point(pos.x+v.x/v.y*(self.pos.y+1/2-pos.y),self.pos.y+1/2),\
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Point(pos.x+v.x/v.y*(self.pos.y-1/2-pos.y),self.pos.y-1/2)\
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]
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# compute closest one, on square
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closest=None
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dist=math.inf
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for i in range(0,4):
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# check that it is on square
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if abs(intersections[i].x-self.pos.x)<=1/2+1e-11 and abs(intersections[i].y-self.pos.y)<=1/2+1e-11:
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if (intersections[i]-pos)**2<dist:
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closest=intersections[i]
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dist=(intersections[i]-pos)**2
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if closest==None:
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print("error: cannot move particle at (",pos.x,",",pos.y,") to the boundary of (",self.pos.x,",",self.pos.y,")",file=sys.stderr)
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exit(-1)
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return closest
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# move along edge of square
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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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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 rel<math.ceil(rel)-1e-11 and newrel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0:
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# stick to corner
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candidate.y=math.ceil(rel)+self.pos.y
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else:
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if rel>math.floor(rel)+1e-11 and newrel<math.floor(rel)-1e-11 and math.floor(rel)!=0:
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# stick to corner
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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):
|
||||||
|
# onlx move in x direction
|
||||||
|
candidate=Point(pos.x,newpos.x)
|
||||||
|
# do not move past corners
|
||||||
|
rel=pos.x-self.pos.x
|
||||||
|
newrel=newpos.x-self.pos.x
|
||||||
|
if newpos.x>pos.x:
|
||||||
|
if rel<math.ceil(rel)-1e-11 and newrel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0:
|
||||||
|
# stick to corner
|
||||||
|
candidate.x=math.ceil(rel)+self.pos.x
|
||||||
|
else:
|
||||||
|
if rel>math.floor(rel)+1e-11 and newrel<math.floor(rel)-1e-11 and math.floor(rel)!=0:
|
||||||
|
# stick to corner
|
||||||
|
candidate.x=math.floor(rel)+self.pos.x
|
||||||
|
return candidate
|
||||||
|
|
||||||
Loading…
Reference in New Issue
Block a user