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piliko_tcents.py
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piliko_tcents.py
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from piliko_asymp import *
from piliko import *
############################### triangle centers
############## orthocenters
def blue_orthocenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
terma = eval_asympoly( 'x1*x2*y2', t )
termb = eval_asympoly( 'y1*y2*y2', t )
termc = eval_asympoly( 'x1*y2', t )
termd = eval_asympoly( 'x1*y1*y2', t )
terme = eval_asympoly( 'x1*x1*x2', t )
termf = eval_asympoly( 'x1*y2', t )
x = Fraction( terma + termb, termc )
y = Fraction( termd + terme, termf )
return point(x,y)
def red_orthocenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
terma = eval_asympoly( 'x1*x2*y2', t )
termb = eval_asympoly( 'y1*y2*y2', t )
termc = eval_asympoly( 'x1*y2', t )
termd = eval_asympoly( 'x1*y1*y2', t )
terme = eval_asympoly( 'x1*x1*x2', t )
termf = eval_asympoly( 'x1*y2', t )
x = Fraction( terma - termb, termc )
y = Fraction( termd - terme, termf )
return point(x,y)
def green_orthocenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
terma = eval_asympoly( 'x1*x1*y2', t )
termb = eval_asympoly( 'x1*x2*y1', t )
termc = eval_asympoly( 'x1*y2', t )
termd = eval_asympoly( 'x1*y2*y2', t )
terme = eval_asympoly( 'x1*y1*y2', t )
termf = eval_asympoly( 'x1*y2', t )
x = Fraction( terma + termb, termc )
y = Fraction( termd - terme, termf )
return point(x,y)
def blue_orthocenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
blue_orthocenter_from_triangle( t )
def red_orthocenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
red_orthocenter_from_triangle( t )
def green_orthocenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
green_orthocenter_from_triangle( t )
def blue_orthocenter( *args ):
if checktype(triangle, args[0]):
return blue_orthocenter_from_triangle( args[0] )
if checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return blue_orthocenter_from_points( p1, p2, p3 )
def red_orthocenter( *args ):
if checktype(triangle, args[0]):
return red_orthocenter_from_triangle( args[0] )
if checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return red_orthocenter_from_points( p1, p2, p3 )
def green_orthocenter( *args ):
if checktype(triangle, args[0]):
return green_orthocenter_from_triangle( args[0] )
if checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return green_orthocenter_from_points( p1, p2, p3 )
orthocenter=blue_orthocenter
def blue_centroid( t ):
x = avg(t.p0.x,t.p1.x,t.p2.x)
y = avg(t.p0.y,t.p1.y,t.p2.y)
return point(x,y)
def red_centroid( t ):
return blue_centroid(t)
def green_centroid( t ):
return blue_centroid(t)
centroid=blue_centroid
############ circumcenters
def blue_circumcenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
terma = eval_asympoly( 'x1*x1*y2', t )
termb = eval_asympoly( 'y1*y1*y2', t )
termc = eval_asympoly( 'x1*y2', t )
termd = eval_asympoly( 'x1*y2*y2', t )
terme = eval_asympoly( 'x1*x2*x2', t )
termf = eval_asympoly( 'x1*y2', t )
x = Fraction( terma + termb, 2 * termc )
y = Fraction( termd + terme, 2 * termf )
return point(x,y)
def red_circumcenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
terma = eval_asympoly( 'x1*x1*y2', t )
termb = eval_asympoly( 'y1*y1*y2', t )
termc = eval_asympoly( 'x1*y2', t )
termd = eval_asympoly( 'x1*y2*y2', t )
terme = eval_asympoly( 'x1*x2*x2', t )
termf = eval_asympoly( 'x1*y2', t )
x = Fraction( terma - termb, 2 * termc )
y = Fraction( termd - terme, 2 * termf )
return point(x,y)
def green_circumcenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
terma = eval_asympoly( 'x1*x2*y2', t )
termb = 0
termc = eval_asympoly( 'x1*y2', t )
termd = eval_asympoly( 'x1*y1*y2', t )
terme = 0
termf = eval_asympoly( 'x1*y2', t )
x = Fraction( terma + termb, termc )
y = Fraction( termd - terme, termf )
return point(x,y)
def blue_circumcenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
blue_circumcenter_from_triangle( t )
def red_circumcenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
red_circumcenter_from_triangle( t )
def green_circumcenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
green_circumcenter_from_triangle( t )
def blue_circumcenter( *args ):
if checktype(triangle, args[0]):
return blue_circumcenter_from_triangle( args[0] )
if checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return blue_circumcenter_from_points( p1, p2, p3 )
def red_circumcenter( *args ):
if checktype(triangle, args[0]):
return red_circumcenter_from_triangle( args[0] )
if checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return red_circumcenter_from_points( p1, p2, p3 )
def green_circumcenter( *args ):
if checktype(triangle, args[0]):
return green_circumcenter_from_triangle( args[0] )
if checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return green_circumcenter_from_points( p1, p2, p3 )
circumcenter=blue_circumcenter
######################## nine point centers
def blue_ninepointcenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
p1 = red_circumcenter_from_triangle( t )
p2 = green_circumcenter_from_triangle( t )
return midpoint_from_points( p1, p2 )
def red_ninepointcenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
p1 = blue_circumcenter_from_triangle( t )
p2 = green_circumcenter_from_triangle( t )
return midpoint_from_points( p1, p2 )
def green_ninepointcenter_from_triangle( t ):
if not checktype(triangle,t): raise Exception('need triangle')
p1 = blue_circumcenter_from_triangle( t )
p2 = red_circumcenter_from_triangle( t )
return midpoint_from_points( p1, p2 )
def blue_ninepointcenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
return blue_ninepointcenter_from_triangle( t )
def red_ninepointcenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
return red_ninepointcenter_from_triangle( t )
def green_ninepointcenter_from_points( p1, p2, p3 ):
t = triangle( p1, p2, p3 )
return green_ninepointcenter_from_triangle( t )
def blue_ninepointcenter( *args ):
if checktype(triangle, args[0]):
return blue_ninepointcenter_from_triangle( args[0] )
elif checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return blue_ninepointcenter_from_points( p1, p2, p3 )
else: raise Exception('unknown input type')
def red_ninepointcenter( *args ):
if checktype(triangle, args[0]):
return red_ninepointcenter_from_triangle( args[0] )
elif checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return red_ninepointcenter_from_points( p1, p2, p3 )
else: raise Exception('unknown input type')
def green_ninepointcenter( *args ):
if checktype(triangle, args[0]):
return green_ninepointcenter_from_triangle( args[0] )
elif checktype(point, args[0]) and checktype(point, args[1]):
if checktype(point, args[2]):
p1,p2,p3=args[0],args[1],args[2]
return green_ninepointcenter_from_points( p1, p2, p3 )
else: raise Exception('unknown input type')
ninepointcenter=blue_ninepointcenter