201 lines
6.5 KiB
Python
201 lines
6.5 KiB
Python
|
import math
|
||
|
|
from kivy.graphics import Color,Line,Rectangle
|
||
|
|
from kivy.uix.widget import Widget
|
||
|
|
|
||
|
|
from point import Point
|
||
|
|
|
||
|
|
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):
|
||
|
|
# fill
|
||
|
|
#if not self.selected:
|
||
|
|
# Color(*(self.color))
|
||
|
|
#else:
|
||
|
|
# Color(1,0,0)
|
||
|
|
Color(*(self.color))
|
||
|
|
Rectangle(pos=(self.pos.x-self.size*1.5,self.pos.y-self.size*0.5),size=(3*self.size,self.size))
|
||
|
|
Rectangle(pos=(self.pos.x-self.size*0.5,self.pos.y-self.size*1.5),size=(self.size,3*self.size))
|
||
|
|
|
||
|
|
# stroke
|
||
|
|
Color(1,1,1)
|
||
|
|
Line(points=(
|
||
|
|
*(self.pos.x-self.size*0.5,self.pos.y-self.size*0.5),
|
||
|
|
*(self.pos.x-self.size*0.5,self.pos.y-self.size*1.5),
|
||
|
|
*(self.pos.x+self.size*0.5,self.pos.y-self.size*1.5),
|
||
|
|
*(self.pos.x+self.size*0.5,self.pos.y-self.size*0.5),
|
||
|
|
*(self.pos.x+self.size*1.5,self.pos.y-self.size*0.5),
|
||
|
|
*(self.pos.x+self.size*1.5,self.pos.y+self.size*0.5),
|
||
|
|
*(self.pos.x+self.size*0.5,self.pos.y+self.size*0.5),
|
||
|
|
*(self.pos.x+self.size*0.5,self.pos.y+self.size*1.5),
|
||
|
|
*(self.pos.x-self.size*0.5,self.pos.y+self.size*1.5),
|
||
|
|
*(self.pos.x-self.size*0.5,self.pos.y+self.size*0.5),
|
||
|
|
*(self.pos.x-self.size*1.5,self.pos.y+self.size*0.5),
|
||
|
|
*(self.pos.x-self.size*1.5,self.pos.y-self.size*0.5),
|
||
|
|
*(self.pos.x-self.size*0.5,self.pos.y-self.size*0.5),
|
||
|
|
))
|
||
|
|
|
||
|
|
# check whether a cross at pos interacts with cross
|
||
|
|
def check_interaction(self,pos):
|
||
|
|
return ((pos-self.pos)/self.size).int()**2>=5
|
||
|
|
|
||
|
|
# 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)/self.size,v/self.size)*self.size+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)
|
||
|
|
|
||
|
|
|
||
|
|
# 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)
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
# cross painter
|
||
|
|
class Cross_painter(Widget):
|
||
|
|
|
||
|
|
def __init__(self,**kwargs):
|
||
|
|
|
||
|
|
# list of crosses
|
||
|
|
self.crosses=[]
|
||
|
|
|
||
|
|
# selected cross
|
||
|
|
self.selected=None
|
||
|
|
|
||
|
|
# init Widget
|
||
|
|
super(Cross_painter,self).__init__(**kwargs)
|
||
|
|
|
||
|
|
|
||
|
|
# draw all crosses
|
||
|
|
def draw(self):
|
||
|
|
with self.canvas:
|
||
|
|
for cross in self.crosses:
|
||
|
|
cross.draw()
|
||
|
|
|
||
|
|
|
||
|
|
# respond to mouse down
|
||
|
|
def on_touch_down(self,touch):
|
||
|
|
# create new cross
|
||
|
|
if touch.button=="right":
|
||
|
|
if self.check_add(Point(touch.x,touch.y)):
|
||
|
|
new=Cross(touch.x,touch.y)
|
||
|
|
with self.canvas:
|
||
|
|
new.draw()
|
||
|
|
# add to list
|
||
|
|
self.crosses.append(new)
|
||
|
|
|
||
|
|
# select cross
|
||
|
|
if touch.button=="left":
|
||
|
|
# unselect
|
||
|
|
if self.selected!=None:
|
||
|
|
self.selected.selected=False
|
||
|
|
|
||
|
|
# find cross under touch
|
||
|
|
self.selected=self.find_cross(Point(touch.x,touch.y))
|
||
|
|
# select
|
||
|
|
if self.selected!=None:
|
||
|
|
self.selected.selected=True
|
||
|
|
|
||
|
|
|
||
|
|
# respond to drag
|
||
|
|
def on_touch_move(self,touch):
|
||
|
|
# only move on left click
|
||
|
|
if touch.button=="left" and self.selected!=None:
|
||
|
|
self.selected.pos=self.check_move(Point(touch.x,touch.y),self.selected)
|
||
|
|
# redraw
|
||
|
|
self.canvas.clear()
|
||
|
|
self.draw()
|
||
|
|
|
||
|
|
|
||
|
|
# find the cross at position pos
|
||
|
|
def find_cross(self,pos):
|
||
|
|
for cross in self.crosses:
|
||
|
|
if cross_distx(pos,cross.pos)<=cross.size/2 or cross_disty(pos,cross.pos)<=cross.size/2:
|
||
|
|
return cross
|
||
|
|
# none found
|
||
|
|
return None
|
||
|
|
|
||
|
|
# check that a cross can move to new position
|
||
|
|
def check_move(self,newpos,cross):
|
||
|
|
for other in self.crosses:
|
||
|
|
# do not compare a cross to itself
|
||
|
|
if other!=cross:
|
||
|
|
# move would make cross overlap with other
|
||
|
|
if other.check_interaction(newpos)==False:
|
||
|
|
# stick to the cross
|
||
|
|
return other.move_on_line_to_stick(cross.pos,newpos-cross.pos)
|
||
|
|
return newpos
|
||
|
|
|
||
|
|
# check that a cross can be added at position
|
||
|
|
def check_add(self,pos):
|
||
|
|
for cross in self.crosses:
|
||
|
|
if cross.check_interaction(pos)==False:
|
||
|
|
return False
|
||
|
|
return True
|
||
|
|
|
||
|
|
|