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Adapt cross dynamics to square

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Ian Jauslin 2021-11-24 17:18:27 -05:00
parent 152f70d402
commit a8359a98bf
4 changed files with 136 additions and 213 deletions
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213
cross.py
View File

@ -1,213 +0,0 @@
import math
import sys
from kivy.graphics import Color,Line,Rectangle
from point import Point
from tools import isint_nonzero,sgn
class Cross():
# size of central square
size=50
def __init__(self,x,y,**kwargs):
self.pos=Point(x,y)
self.color=kwargs.get("color",(0,0,1))
self.selected=False
# set position
def setpos(self,x,y):
self.pos.x=x
self.pos.y=y
def draw(self,**kwargs):
# set color
if not self.selected:
Color(*self.color)
else:
(r,g,b)=self.color
# darken selected
Color(r/2,g/2,b/2)
Rectangle(pos=((self.pos.x-1.5)*self.size,(self.pos.y-0.5)*self.size),size=(3*self.size,self.size))
Rectangle(pos=((self.pos.x-0.5)*self.size,(self.pos.y-1.5)*self.size),size=(self.size,3*self.size))
# stroke
Color(1,1,1)
Line(points=(
*((self.pos.x-0.5)*self.size,(self.pos.y-0.5)*self.size),
*((self.pos.x-0.5)*self.size,(self.pos.y-1.5)*self.size),
*((self.pos.x+0.5)*self.size,(self.pos.y-1.5)*self.size),
*((self.pos.x+0.5)*self.size,(self.pos.y-0.5)*self.size),
*((self.pos.x+1.5)*self.size,(self.pos.y-0.5)*self.size),
*((self.pos.x+1.5)*self.size,(self.pos.y+0.5)*self.size),
*((self.pos.x+0.5)*self.size,(self.pos.y+0.5)*self.size),
*((self.pos.x+0.5)*self.size,(self.pos.y+1.5)*self.size),
*((self.pos.x-0.5)*self.size,(self.pos.y+1.5)*self.size),
*((self.pos.x-0.5)*self.size,(self.pos.y+0.5)*self.size),
*((self.pos.x-1.5)*self.size,(self.pos.y+0.5)*self.size),
*((self.pos.x-1.5)*self.size,(self.pos.y-0.5)*self.size),
*((self.pos.x-0.5)*self.size,(self.pos.y-0.5)*self.size),
))
# check whether a cross at pos interacts with cross
def check_interaction(self,pos):
# allow for error
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
# check whether a cross at position pos is touching self
def check_touch(self,pos):
rel=pos-self.pos
for i in [-3,-2,-1,1,2,3]:
# allow for error
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:
return True
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:
return True
return False
# find position along a line that comes in contact with the line going through pos in direction v
def move_on_line_to_stick(self,pos,v):
# relative to cross
return self.move_on_line_to_stick_relative(pos-self.pos,v)+self.pos
def move_on_line_to_stick_relative(self,x,v):
# if x is in the right quadrant
if abs(x.y)<=x.x:
# find all stuck positions on lines
stuck=[]
# check intersections with vertical lines
if v.x!=0:
for i in range(1,4):
# candidate
y=Point(i,x.y+(i-x.x)*v.y/v.x)
# check that it is in the right range
if abs(y.y)<=4-i and abs(y.y)>=3-i:
stuck.append(y)
# check intersections with horizontal lines
if v.y!=0:
for i in [-3,-2,-1,1,2,3]:
# candidate
y=Point(x.x+(i-x.y)*v.x/v.y,i)
# check that it is in the right range
if y.x<=4-abs(i) and y.x>=3-abs(i):
stuck.append(y)
return x.closest(stuck)
# reflect other quadrants to the right one
# top quadrant
elif abs(x.x)<=x.y:
closest=self.move_on_line_to_stick_relative(Point(x.y,x.x),Point(v.y,v.x))
return Point(closest.y,closest.x)
# bottom quadrant
elif abs(x.x)<=-x.y:
closest=self.move_on_line_to_stick_relative(Point(-x.y,x.x),Point(-v.y,v.x))
return Point(closest.y,-closest.x)
# left quadrant
else:
closest=self.move_on_line_to_stick_relative(Point(-x.x,x.y),Point(-v.x,v.y))
return Point(-closest.x,closest.y)
# move along edge of cross
def move_along(self,newpos,pos):
rel=pos-self.pos
# check if the particle is stuck in the x direction
if isint_nonzero(rel.x):
# check y direction
if isint_nonzero(rel.y):
# in corner
# two types of corners: |x|_1=3 or |x|_1=4
if abs(rel.x)+abs(rel.y)<3.5:
if sgn(newpos.y-pos.y)==sgn(rel.y):
# stuck in x direction
return self.move_stuck_x(newpos,pos)
elif sgn(newpos.x-pos.x)==sgn(rel.x):
# stuck in y direction
return self.move_stuck_y(newpos,pos)
else:
if sgn(newpos.y-pos.y)==-sgn(rel.y):
# stuck in x direction
return self.move_stuck_x(newpos,pos)
elif sgn(newpos.x-pos.x)==-sgn(rel.x):
# stuck in y direction
return self.move_stuck_y(newpos,pos)
# stuck in both directions
return pos
else:
# stuck in x direction
return self.move_stuck_x(newpos,pos)
elif isint_nonzero(rel.y):
# stuck in y direction
return self.move_stuck_y(newpos,pos)
# this should never happen
else:
print("error: stuck particle has non-integer relative position: (",rel.x,",",rel.y,")",file=sys.stderr)
exit(-1)
# move when stuck in the x direction
def move_stuck_x(self,newpos,pos):
# only move in y direction
candidate=Point(pos.x,newpos.y)
# do not move past corners
rel=pos.y-self.pos.y
newrel=newpos.y-self.pos.y
if newpos.y>pos.y:
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):
# in open corner
if rel>math.ceil(rel)-1e-11:
candidate.y=math.ceil(rel)+1+self.pos.y
else:
candidate.y=math.ceil(rel)+self.pos.y
else:
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):
# in open corner
if rel<math.floor(rel)+1e-11:
candidate.y=math.floor(rel)-1+self.pos.y
else:
candidate.y=math.floor(rel)+self.pos.y
return candidate
# move when stuck in the y direction
def move_stuck_y(self,newpos,pos):
# only move in x direction
candidate=Point(newpos.x,pos.y)
# do not move past corners
rel=pos.x-self.pos.x
newrel=newpos.x-self.pos.x
if newpos.x>pos.x:
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):
# in open corner
if rel>math.ceil(rel)-1e-11:
candidate.x=math.ceil(rel)+1+self.pos.x
else:
candidate.x=math.ceil(rel)+self.pos.x
else:
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):
# in open corner
if rel<math.floor(rel)+1e-11:
candidate.x=math.floor(rel)-1+self.pos.x
else:
candidate.x=math.floor(rel)+self.pos.x
return candidate
# L_infinity distance rescalled by 3 in the x direction
def cross_distx(x,y):
return max(abs(x.x-y.x)/3,abs(x.y-y.y))
# L_infinity distance rescalled by 3 in the y direction
def cross_disty(x,y):
return max(abs(x.x-y.x),abs(x.y-y.y)/3)
# polar description of touching cross
def cross_polar(t):
# by symmetry, put angle in interval (-pi/4,pi/4), and take absolute value
tt=abs((t+math.pi/4)%(math.pi/2)-math.pi/4)
if tt<math.atan(1/3):
return 3/math.cos(tt)
elif tt<math.atan(1/2):
return 1/math.sin(tt)
else:
return 2/math.cos(tt)

4
point.py
View File

@ -43,3 +43,7 @@ class Point:
dist=(self-point)**2
return closest
# L infinity norm
def l_infinity(x):
return max(abs(x.x),abs(x.y))

128
polyomino.py Normal file
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@ -0,0 +1,128 @@
import math
import sys
from kivy.graphics import Color,Line,Rectangle
from point import Point,l_infinity
from tools import isint_nonzero,sgn,in_interval
class Square():
# size
size=50
def __init__(self,x,y,**kwargs):
self.pos=Point(x,y)
self.color=kwargs.get("color",(0,0,1))
self.selected=False
# set position
def setpos(self,x,y):
self.pos.x=x
self.pos.y=y
def draw(self,**kwargs):
# set color
if not self.selected:
Color(*self.color)
else:
(r,g,b)=self.color
# darken selected
Color(r/2,g/2,b/2)
Rectangle(pos=((self.pos.x-0.5)*self.size,(self.pos.y-0.5)*self.size),size=(self.size,self.size))
# check whether a square at pos interacts with square
def check_interaction(self,pos):
return l_infinity(pos-self.pos)>=1
# check whether a square at position pos is touching self
def check_touch(self,pos):
# allow for error
if in_interval(l_infinity(pos-solf.pos),1-1e-11,1+1e-11):
return True
return False
# find position along a line that comes in contact with the line going through pos in direction v
def move_on_line_to_stick(self,pos,v):
# compute intersections with four lines making up square
intersections=[\
Point(self.pos.x+1/2,pos.y+v.y/v.x*(self.pos.x+1/2-pos.x)),\
Point(self.pos.x-1/2,pos.y+v.y/v.x*(self.pos.x-1/2-pos.x)),\
Point(pos.x+v.x/v.y*(self.pos.y+1/2-pos.y),self.pos.y+1/2),\
Point(pos.x+v.x/v.y*(self.pos.y-1/2-pos.y),self.pos.y-1/2)\
]
# compute closest one, on square
closest=None
dist=math.inf
for i in range(0,4):
# check that it is on square
if abs(intersections[i].x-self.pos.x)<=1/2+1e-11 and abs(intersections[i].y-self.pos.y)<=1/2+1e-11:
if (intersections[i]-pos)**2<dist:
closest=intersections[i]
dist=(intersections[i]-pos)**2
if closest==None:
print("error: cannot move particle at (",pos.x,",",pos.y,") to the boundary of (",self.pos.x,",",self.pos.y,")",file=sys.stderr)
exit(-1)
return closest
# move along edge of square
def move_along(self,newpos,pos):
rel=pos-self.pos
# check if the particle is stuck in the x direction
if isint_nonzero(rel.x):
# check y direction
if isint_nonzero(rel.y):
# in corner
if sgn(newpos.y-pos.y)==-sgn(rel.y):
# stuck in x direction
return self.move_stuck_x(newpos,pos)
elif sgn(newpos.x-pos.x)==-sgn(rel.x):
# stuck in y direction
return self.move_stuck_y(newpos,pos)
# stuck in both directions
return pos
else:
# stuck in x direction
return self.move_stuck_x(newpos,pos)
elif isint_nonzero(rel.y):
# stuck in y direction
return self.move_stuck_y(newpos,pos)
# this should never happen
else:
print("error: stuck particle has non-integer relative position: (",rel.x,",",rel.y,")",file=sys.stderr)
exit(-1)
# move when stuck in the x direction
def move_stuck_x(self,newpos,pos):
# only move in y direction
candidate=Point(pos.x,newpos.y)
# do not move past corners
rel=pos.y-self.pos.y
newrel=newpos.y-self.pos.y
if newpos.y>pos.y:
if rel<math.ceil(rel)-1e-11 and newrel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0:
# stick to corner
candidate.y=math.ceil(rel)+self.pos.y
else:
if rel>math.floor(rel)+1e-11 and newrel<math.floor(rel)-1e-11 and math.floor(rel)!=0:
# stick to corner
candidate.y=math.floor(rel)+self.pos.y
return candidate
# move when stuck in the y direction
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

4
tools.py
View File

@ -9,3 +9,7 @@ def isint_nonzero(x):
if abs(x)<1e-11:
return False
return abs(round(x)-x)<1e-11
# check that a number is in an interval
def in_interval(x,a,b):
return x>=a and x<=b