def RemoveEdgesWithKnife(doc, Ax, Ay, Bx, By):
"""
For a graph document in a 2D embedding in the plane
with doc["V"], doc["E"] and doc["pts"] defined,
remove edges of doc["E"] such that for edge
e in doc["E"] and u,v = e, form
Cx,Cy = doc["pts"][u][:2]
Dx,Dy = doc["pts"][v][:2]
and do
flag,X,Y = line_intersection.SegmentIntersect(Ax,Ay,Bx,By,Cx,Cy,Dx,Dy)
and if flag, then remove e. The knife is given
by line segment AB with A = [Ax,Ay] and B = [Bx,By].
"""
doc1 = deepcopy(doc)
ES = []
for e in doc["E"]:
u, v = e
Cx, Cy = doc["pts"][u][:2]
Dx, Dy = doc["pts"][v][:2]
flag, X, Y = line_intersection.SegmentIntersect(
Ax, Ay, Bx, By, Cx, Cy, Dx, Dy)
if not flag:
ES.append(e)
doc1["E"] = ES
return doc1
def Intersect(line1, line2):
A, B = line1
C, D = line2
flag, x, y = li.SegmentIntersect(A[0], A[1], B[0], B[1], C[0], C[1], D[0],
D[1])
E = [x, y]
return flag, E
def MassSpectrometer(I, show=True):
# W,H used in calculation of measurement
W = 600
H = 600
if show:
gr = racg.Graphics(w=W, h=H)
E0 = 0
B0 = 2 # light amplitude
lam = 5 # light wavelength
black = [0, 0, 0]
blue = [0, 0, 255]
pt_last = [0, 300]
direction = 1 # direction y-axis or -(y-axis)
#print "Press 'e' to exit"
tmax = 55 # time units maximum
Z = 0
while I.t <= tmax:
# make direction change periodically
direction = 1
#gr.Clear()
r = I.x
# Screen transformation of r -> [x,y,z]
xmin = -10
xmax = 10
ymin = -10
ymax = 10
x = mapto.MapTo(xmin, 0, xmax, W, r[0])
y = mapto.MapTo(ymin, 0, ymax, H, r[1])
z = 0
# Projective Transformation of [x,y,z] -> [x2,y2]
pt = [x - W / 2, y]
#gr.Point(pt,color=black)
#print pt,r
if show:
gr.Line(pt, pt_last, color=blue)
sW = 0.5
P = [W * sW, 0]
Q = [W * sW, H]
if show:
gr.Line(P, Q, color=black)
flag, X, Y = li.SegmentIntersect(
pt[0],
pt[1],
pt_last[0],
pt_last[1], # segment 1
P[0],
P[1],
Q[0],
Q[1])
s = "Y = %.2f" % (Y)
if show:
gr.Text(s, X + 10, Y, black)
pt_last = pt
if show:
if fmod(I.t, 0.1) < 0.001:
ch = gr.Show("result", 5)
if ch == ord('e'):
break
E, B = EMfield(I.t, lam, E0, B0)
F = LorenzForce(I.q, I.v, E, B)
I.Update(F)
if flag:
Z = Y
if show:
m0 = finv(Z) * I.q
s = "mass m = %.3f" % (m0)
gr.Text(s, X + 10, Y - 25, black)
if show:
gr.Show("result", -1)
break
if show:
gr.Close()
return Z
def SliceWithKnife(doc, Ax, Ay, Bx, By, alpha=0.15, beta=0.15):
"""
New points added at lerp t = alpha and t = beta
with default alpha = 0.25 and beta = 0.25 if knife
AB slices an edge.
For a graph document doc in a 2D embedding in the plane,
with doc["V"],doc["E"],doc["pts"] defined, slice
the edges of doc with knife. The knife is given
by line segment AB with A = [Ax,Ay] and B = [Bx,By].
doc1 = deepcopy(doc)
For e in doc1["E"] and u,v = e,
Cx,Cy = doc1["pts"][u][:2]
Dx,Dy = doc1["pts"][v][:2]
flag,X,Y = line_intersection.SegmentIntersect(Ax,Ay,Bx,By,Cx,Cy,Dx,Dy)
then if flag, then break line segments into separated
two segments and
orient CD such that C is on interior of plane n*(x-mid) < 0
# add Utility package folder with sys.path.insert(0, <utility_path>)
AB = list(array([Ax,Ay]) - array([Bx,By]))
epsilon = generalized_cross_product.Epsilon(2) # do once to get Cross
normal = epsilon_levicivita_TMP.Cross([AB])
n = normal/vectors.norm(normal)
mid = vectors.lerp([Cx,Cy],[Dx,Dy],0.5)
xm = list(array(x) - array(mid))
interior = vectors.dotprod(n,xm)
if not interior:
#swap Cx,Cy with Dx,Dy if not interior
tx = Cx
ty = Cy
Cx = Dx
Cy = Dy
Dx = tx
Dy = ty
pt_1 = vectors.lerp([Cx,Cy,0],[Dx,Dy,0], alpha=0.25)
pt_2 = vectors.lerp([Cx,Cy,0],[Dx,Dy,0], beta=0.75)
doc1,u2 = graph.SplitVertex(doc1,u)
doc1["pts"].append(pt_1) # assign pt_1 to u2
doc1,v2 = graph.SplitVertex(doc1,v)
doc1["pts"].append(pt_2) # assign pt_2 to v2
and returns:
doc1 = SliceWithKnife(doc, Ax, Ay, Bx, By)
"""
doc1 = deepcopy(doc)
ES = []
VS = []
for e in doc1["E"]:
u, v = e
Cx, Cy = doc1["pts"][u][:2]
Dx, Dy = doc1["pts"][v][:2]
flag, X, Y = line_intersection.SegmentIntersect(
Ax, Ay, Bx, By, Cx, Cy, Dx, Dy)
if flag:
AB = list(array([Ax, Ay]) - array([Bx, By]))
normal = generalized_cross_product.cross2(array(AB))
n = normal / vectors.norm(normal) + [0]
mid = vectors.lerp([Cx, Cy, 0], [Dx, Dy, 0], 0.5)
# use x = [Cx,Cy] to check if on interior side
xm = list(array([Cx, Cy, 0]) - array(mid))
interior = vectors.dotprod(n, xm)
if not interior:
#swap Cx,Cy with Dx,Dy if not interior
tx = Cx
ty = Cy
Cx = Dx
Cy = Dy
Dx = tx
Dy = ty
pt_1 = vectors.lerp([X, Y, 0], [Cx, Cy, 0], alpha)
pt_2 = vectors.lerp([X, Y, 0], [Dx, Dy, 0], beta)
doc1, u2 = graph.SplitVertex(doc1, u)
doc1["pts"].append(pt_1) # assign pt_1 to u2
doc1, v2 = graph.SplitVertex(doc1, v)
doc1["pts"].append(pt_2) # assign pt_2 to v2
ES.append([u, u2])
ES.append([v2, v])
VS.append(u2)
VS.append(v2)
else:
ES.append(e)
doc1["E"] = ES
doc1["V"] = doc["V"] + VS
for k in range(len(doc1["pts"])):
doc1["pts"][k] = map(int, map(round, doc1["pts"][k]))
return doc1