def cylinder(w,h):
"""Generate DCEL for a triangulated cylinder of height h and circumference w"""
tops = []
bottoms = []
D = dcel.DCEL()
# Create h separate rings of height 1
for i in range(h):
RD,t,b = ring(w)
tops.append(t)
bottoms.append(b)
D |= RD
# Glue the rings top-to-bottom
for i in range(h-1):
dcel.glue_boundary(D, bottoms[i], tops[i + 1])
return D,tops[0],bottoms[-1]
def embedded_cylinder(nw, nh, coord_gen):
"""Generate DCEL for a triangulated cylinder of height h and circumference w"""
tops = []
bottoms = []
D = dcel.DCEL()
# Create h separate rings of height 1
for i in range(nh):
RD, t, b = embedded_ring(nw, i, coord_gen=coord_gen)
tops.append(t)
bottoms.append(b)
D |= RD
# Glue the rings top-to-bottom
for i in range(nh - 1):
dcel.glue_boundary(D, bottoms[i], tops[i + 1])
return D, tops[0], bottoms[-1]
def ring(w):
"""Generate DCEL for a triangulated ring of height 1 and circumference w.
Looks like:.. --T----------------...
|\ |\ |\ |\ |\
\ | \ | \ | \ | \ | \
\| \| \| \| \| \
..--B-----------------...
Returns typle (D,T,B)
D -- DCEL of the ring
T -- a "top" half-edge
B -- a "bottom" half edge directly below T
"""
# We create the vertices first in a 2d array; later the indices
# will correspond to position in the ring as follows:
#
# 00---01---02---03---04---05
# |\ |\ |\ |\ |\ |
# | \ | \ | \ | \ | \ |
# | \ | \ | \ | \ | \ |
# | \| \| \| \| \|
# 10---11---12---13---14---15
V = [[dcel.Vertex() for i in range(w)],
[dcel.Vertex() for i in range(w)]]
E = set()
F = set()
# Top triangles
for i in range(w):
j = (i+1) % w
EF,f = dcel.vertex_chain_to_face([V[1][j], V[0][j], V[0][i]])
if i == 0:
for e in EF:
if e.src == V[0][1] and e.dst == V[0][0]:
etop = e
break
E.update(EF)
F.add(f)
# Bottom triangles
for i in range(w):
j = (i+1) % w
EF,f = dcel.vertex_chain_to_face([V[0][i], V[1][i], V[1][j]])
if i == 0:
for e in EF:
if e.src == V[1][0] and e.dst == V[1][1]:
ebot = e
break
E.update(EF)
F.add(f)
# TODO: inefficient to search blindly for twin pairs, when we know
# exactly which ones are present. Make this more efficient.
# (Since vertex_chain_to_face doesn't expose any details about the
# order of edges returned, it is probably best to just manually
# create all of half-edges and store in an array like V.
dcel.set_twins(E)
return dcel.DCEL(V[0] + V[1], E, F), etop, ebot
def drawTest_old(self):
""" a grab bag of tests"""
self.ctx.set_source_rgba(*COLOUR)
# p = [0.3,0.6]
# l = 0.9
# utils.drawCircle(self.ctx,p[0],p[1],0.005)
# line = utils.createLine(0,l,1,l,1000)
# for x,y in line:
# utils.drawCircle(self.ctx,x,y,0.002)
# par = makeParabola(p,l,np.linspace(0,1,1000))
# print(par)
# for x,y in par:
# utils.drawCircle(self.ctx,x,y,0.002)
#DCEL Test:
dc = dcel.DCEL()
v1 = dc.newVertex(0.2, 0.2)
v2 = dc.newVertex(0.4, 0.2)
v3 = dc.newVertex(0.5, 0.6)
e1 = dc.newEdge(v1, v2)
e2 = dc.newEdge(v2, v3)
e3 = dc.newEdge(v3, v1)
f1 = dc.newFace()
dc.linkEdgesTogether([e1, e2, e3])
dc.setFaceForEdgeLoop(f1, e1)
#utils.drawDCEL(self.ctx,dc)
#Draw an arc:
centre = np.array([[0.5, 0.5]])
r = 0.2
rads = pi / 2
self.ctx.set_line_width(0.002)
for xy in centre:
self.ctx.arc(*xy, r, 0, rads)
self.ctx.stroke()
#Draw the end points
p1 = centre + [r, 0]
p2 = utils.rotatePoint(p1, centre, rads)
utils.drawCircle(self.ctx, *centre[0], 0.006)
utils.drawCircle(self.ctx, *p1[0], 0.006)
utils.drawCircle(self.ctx, *p2[0], 0.006)
#draw a chord:
self.ctx.move_to(*p1[0])
self.ctx.line_to(*p2[0])
self.ctx.stroke()
#midpoint:
e = 1 #direction 1/-1 counter/clockwise
d = utils.get_distance(p1, p2)
m = utils.get_midpoint(p1, p2)
utils.drawCircle(self.ctx, *m[0], 0.006)
#normal:
n = utils.get_normal(p1, p2)
bisector = utils.get_bisector(p1, p2)
h = np.sqrt(pow(r, 2) - (pow(d, 2) / 4)) #height from centre
c = m + (e * h * bisector) #centre calculated
self.ctx.move_to(*m[0])
self.ctx.line_to(*c[0])
self.ctx.stroke()
#extend a line:
self.ctx.set_source_rgba(0.8, 0.6, 0.2, 1)
extend_point = p2
extend_distance = 5
extended_line = utils.extend_line(p1, p2, extend_distance)
self.ctx.move_to(*extend_point[0])
self.ctx.line_to(*extended_line[0])
self.ctx.stroke()
#clip the line
self.ctx.set_source_rgba(0.5, 0.1, 0.1, 1)
clippedLine = utils.bound_line_in_bbox(
np.row_stack((extend_point, extended_line)), [0.5, 0, 1, 1])
self.ctx.move_to(*clippedLine[0])
self.ctx.line_to(*clippedLine[1])
self.ctx.stroke()
#intersect two lines
l1 = utils.random_points(2)
l2 = utils.random_points(2)
#l1 = np.array([0.2,0.2,0.4,0.4])
#l2 = np.array([0.4,0.2,0.2,0.4])
self.ctx.move_to(l1[0], l1[1])
self.ctx.line_to(l1[2], l1[3])
self.ctx.stroke()
self.ctx.move_to(l2[0], l2[1])
self.ctx.line_to(l2[2], l2[3])
self.ctx.stroke()
intersect = utils.intersect(l1, l2)
print(intersect)
if intersect is not None:
utils.drawCircle(self.ctx, *intersect, 0.005)