def triangle(x0, y0, x1, y1, x2, y2):
# Find the angles of the points about the center
xm = (x0 + x1 + x2) / 3.
ym = (y0 + y1 + y2) / 3.
angles = [
math.atan2(y - ym, x - xm) for x, y in [(x0, y0), (x1, y1), (x2, y2)]
]
# Sort the angles so that the smallest one is first
if angles[1] < angles[0] and angles[1] < angles[2]:
angles = [angles[1], angles[2], angles[0]]
elif angles[2] < angles[0] and angles[2] < angles[1]:
angles = [angles[2], angles[0], angles[1]]
# Enforce that points must be in clockwise order by swapping if necessary
if angles[2] > angles[1]:
x0, y0, x1, y1 = x1, y1, x0, y0
def edge(x, y, dx, dy):
# dy*(X-x)-dx*(Y-y)
return '-*f%(dy)g-Xf%(x)g*f%(dx)g-Yf%(y)g' % locals()
e0 = edge(x0, y0, x1 - x0, y1 - y0)
e1 = edge(x1, y1, x2 - x1, y2 - y1)
e2 = edge(x2, y2, x0 - x2, y0 - y2)
# -min(e0, min(e1, e2))
s = MathTree('ni%(e0)si%(e1)s%(e2)s' % locals())
s.xmin, s.xmax = min(x0, x1, x2), max(x0, x1, x2)
s.ymin, s.ymax = min(y0, y1, y2), max(y0, y1, y2)
s.shape = True
return s
def triangle(x0, y0, x1, y1, x2, y2):
# Find the angles of the points about the center
xm = (x0 + x1 + x2) / 3.
ym = (y0 + y1 + y2) / 3.
angles = [math.atan2(y - ym, x - xm) for x, y in [(x0,y0), (x1,y1), (x2,y2)]]
# Sort the angles so that the smallest one is first
if angles[1] < angles[0] and angles[1] < angles[2]:
angles = [angles[1], angles[2], angles[0]]
elif angles[2] < angles[0] and angles[2] < angles[1]:
angles = [angles[2], angles[0], angles[1]]
# Enforce that points must be in clockwise order by swapping if necessary
if angles[2] > angles[1]:
x0, y0, x1, y1 = x1, y1, x0, y0
def edge(x, y, dx, dy):
# dy*(X-x)-dx*(Y-y)
return '-*f%(dy)g-Xf%(x)g*f%(dx)g-Yf%(y)g' % locals()
e0 = edge(x0, y0, x1-x0, y1-y0)
e1 = edge(x1, y1, x2-x1, y2-y1)
e2 = edge(x2, y2, x0-x2, y0-y2)
# -min(e0, min(e1, e2))
s = MathTree('ni%(e0)si%(e1)s%(e2)s' % locals())
s.xmin, s.xmax = min(x0, x1, x2), max(x0, x1, x2)
s.ymin, s.ymax = min(y0, y1, y2), max(y0, y1, y2)
s.shape = True
return s
def rectangle(x0, x1, y0, y1):
# max(max(x0 - X, X - x1), max(y0 - Y, Y - y1)
s = MathTree('aa-f%(x0)gX-Xf%(x1)ga-f%(y0)gY-Yf%(y1)g' % locals())
s.xmin, s.xmax = x0, x1
s.ymin, s.ymax = y0, y1
s.shape = True
return s
def rectangle(x0, x1, y0, y1):
# max(max(x0 - X, X - x1), max(y0 - Y, Y - y1)
s = MathTree('aa-f%(x0)gX-Xf%(x1)ga-f%(y0)gY-Yf%(y1)g' % locals())
s.xmin, s.xmax = x0, x1
s.ymin, s.ymax = y0, y1
s.shape = True
return s
def sphere(x0, y0, z0, r):
s = MathTree('-r++q%sq%sq%sf%g' % (('-Xf%g' % x0) if x0 else 'X',
('-Yf%g' % y0) if y0 else 'Y',
('-Zf%g' % z0) if z0 else 'Z',
r))
s.xmin, s.xmax = x0-r, x0+r
s.ymin, s.ymax = y0-r, y0+r
s.zmin, s.zmax = z0-r, z0+r
s.shape = True
return s
def circle(x0, y0, r):
# sqrt((X-x0)**2 + (Y-y0)**2) - r
r = abs(r)
s = MathTree('-r+q%sq%sf%g' % (('-Xf%g' % x0) if x0 else 'X',
('-Yf%g' % y0) if y0 else 'Y', r))
s.xmin, s.xmax = x0-r, x0+r
s.ymin, s.ymax = y0-r, y0+r
s.shape = True
return s
def circle(x0, y0, r):
# sqrt((X-x0)**2 + (Y-y0)**2) - r
r = abs(r)
s = MathTree('-r+q%sq%sf%g' % (('-Xf%g' % x0) if x0 else 'X',
('-Yf%g' % y0) if y0 else 'Y', r))
s.xmin, s.xmax = x0 - r, x0 + r
s.ymin, s.ymax = y0 - r, y0 + r
s.shape = True
return s
def triangle(x0, y0, x1, y1, x2, y2):
def edge(x, y, dx, dy):
# dy*(X-x)-dx*(Y-y)
return '-*f%(dy)g-Xf%(x)g*f%(dx)g-Yf%(y)g' % locals()
e0 = edge(x0, y0, x1 - x0, y1 - y0)
e1 = edge(x1, y1, x2 - x1, y2 - y1)
e2 = edge(x2, y2, x0 - x2, y0 - y2)
# -min(e0, min(e1, e2))
s = MathTree('ni%(e0)si%(e1)s%(e2)s' % locals())
s.xmin, s.xmax = min(x0, x1, x2), max(x0, x1, x2)
s.ymin, s.ymax = min(y0, y1, y2), max(y0, y1, y2)
s.shape = True
return s
def triangle(x0, y0, x1, y1, x2, y2):
def edge(x, y, dx, dy):
# dy*(X-x)-dx*(Y-y)
return '-*f%(dy)g-Xf%(x)g*f%(dx)g-Yf%(y)g' % locals()
e0 = edge(x0, y0, x1-x0, y1-y0)
e1 = edge(x1, y1, x2-x1, y2-y1)
e2 = edge(x2, y2, x0-x2, y0-y2)
# -min(e0, min(e1, e2))
s = MathTree('ni%(e0)si%(e1)s%(e2)s' % locals())
s.xmin, s.xmax = min(x0, x1, x2), max(x0, x1, x2)
s.ymin, s.ymax = min(y0, y1, y2), max(y0, y1, y2)
s.shape = True
return s
