From 383cb5c4620e28b7d336d7770fafca527a9a0e3a Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian@jauslin.org>
Date: Tue, 27 Sep 2022 18:42:11 -0400
Subject: [PATCH] circular element (cannot interact with squares)

---
 src/element.py | 49 ++++++++++++++++++++++++++++++++++++++++++++++++-
 src/painter.py |  2 +-
 src/point.py   |  4 ++++
 3 files changed, 53 insertions(+), 2 deletions(-)

diff --git a/src/element.py b/src/element.py
index f356c5a..2c3bbd2 100644
--- a/src/element.py
+++ b/src/element.py
@@ -2,7 +2,7 @@
 import math
 import sys
 
-from point import Point,l_infinity
+from point import Point,l_infinity,l_2
 from tools import isint_nonzero,sgn,in_interval
 
 # parent class of all elements
@@ -39,6 +39,7 @@ class Element():
 
     # override in each subclass
     # move along edge of element
+    # delta is the impossible move that was asked for
     def move_along(self,delta,element):
         return element
 
@@ -47,6 +48,7 @@ class Element():
 class Element_square(Element):
 
     # check whether an element interacts with square
+    # TODO: this only works if element is a square!
     def check_interaction(self,element):
         # allow for error
         return l_infinity(element.pos-self.pos)<(self.size+element.size)/2-1e-11
@@ -56,6 +58,7 @@ class Element_square(Element):
         return l_infinity(self.pos-x)<=1/2
 
     # check whether an element is touching self
+    # TODO: this only works if element is a square!
     def check_touch(self,element):
         # allow for error
         if in_interval(l_infinity(element.pos-self.pos),(self.size+element.size)/2-1e-11,(self.size+element.size)/2+1e-11):
@@ -63,6 +66,7 @@ class Element_square(Element):
         return False
 
     # find position along a line that comes in contact with the line going through element.pos in direction v
+    # TODO: this only works if element is a square!
     def move_on_line_to_stick(self,element,v):
         # compute intersections with four lines making up square
         if v.x!=0:
@@ -106,6 +110,7 @@ class Element_square(Element):
         return closest-element.pos
 
     # move along edge of square
+    # TODO: this only works if element is a square!
     def move_along(self,delta,element):
         rel=element.pos-self.pos
         # check if the particle is stuck in the x direction
@@ -162,3 +167,45 @@ class Element_square(Element):
                 candidate.x=math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+self.pos.x-element.pos.x
         return candidate
 
+
+# circular elements
+# (size is the diameter)
+class Element_circle(Element):
+
+    # check whether an element interacts with square
+    # TODO: this only works if element is a circle!
+    def check_interaction(self,element):
+        # allow for error
+        return l_2(element.pos-self.pos)<(self.size+element.size)/2-1e-11
+
+    # whether x is in the support of the element
+    def in_support(self,x):
+        return l_2(self.pos-x)<=1/2
+
+    # check whether an element is touching self
+    # TODO: this only works if element is a circle!
+    def check_touch(self,element):
+        # allow for error
+        if in_interval(l_2(element.pos-self.pos),(self.size+element.size)/2-1e-11,(self.size+element.size)/2+1e-11):
+                return True
+        return False
+
+    # find position along a line that comes in contact with the line going through element.pos in direction v
+    # TODO: this only works if element is a circle!
+    def move_on_line_to_stick(self,element,v):
+        # relative position
+        x=element.pos-self.pos
+        # radius of collision circle
+        R=(element.size+self.size)/2
+
+        # smallest root of t^2 v^2+2x.v t+x^2-R^2
+        t=(-v.dot(x)+sqrt(v.dot(x)*v.dot(v)-v.dot(v)*(x.dot(x)-R*R)))/v.dot(v)
+
+        # return difference to pos
+        return t*v
+
+    # move along edge of circle
+    # TODO: this only works if element is a circle!
+    def move_along(self,delta,element):
+        x=element.pos-self.pos+delta
+        return x/l_2(x)*(element.size+self.size)/2+self.pos-element.pos
diff --git a/src/painter.py b/src/painter.py
index ee922ae..f2cc6a5 100644
--- a/src/painter.py
+++ b/src/painter.py
@@ -213,7 +213,7 @@ class Painter(Widget):
             touchx=self.coord_topos_x(touch.x)
             touchy=self.coord_topos_y(touch.y)
 
-            # create new cross
+            # create new particle
             if touch.button=="right":
                 new=Cross(touchx,touchy)
                 # snap to lattice
diff --git a/src/point.py b/src/point.py
index b67d4ed..91dca72 100644
--- a/src/point.py
+++ b/src/point.py
@@ -49,3 +49,7 @@ class Point:
 # L infinity norm
 def l_infinity(x):
     return max(abs(x.x),abs(x.y))
+
+# L 2 norm
+def l_2(x):
+    return sqrt(x.x*x.x+x.y*x.y)