def right_triangle(x0, y0, h):
corner = MathTree.max(MathTree('-f%fX' % x0), MathTree('-f%fY' % y0))
corner.shape = True
shape = corner & MathTree('-X-f%f-Yf%f' % (x0 + h, y0))
shape.xmin = x0
shape.xmax = x0 + h
shape.ymin = y0
shape.ymax = y0 + h
return shape
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 blend(p0, p1, amount):
if not p0.shape or not p1.shape:
raise TypeError('Arguments must be math objects with shape=True')
joint = p0 + p1
# sqrt(abs(p0)) + sqrt(abs(p1)) - amount
fillet = MathTree('-+rb%srb%sf%g' % (p0.math, p1.math, amount), shape=True)
out = joint + fillet
out.bounds = [b for b in joint.bounds]
return out
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 right_triangle(x0, y0, h):
corner = MathTree.max(MathTree('-f%fX' % x0), MathTree('-f%fY' % y0))
corner.shape = True
return corner & MathTree('-X-f%f-Yf%f' % (x0 + h, y0))
