def paint_polygon(polygon: tr.Triangle, draw: ImageDraw, texture: Image, z_buffer ):
"""
Colorize inner part of triangle with specified color
"""
first , second , third = polygon.first.projection() , polygon.second.projection() , polygon.third.projection()
x0 = int(min(first.x, second.x, third.x))
x1 = int(max(first.x, second.x, third.x))
y0 = int(min(first.y, second.y, third.y))
y1 = int(max(first.y, second.y, third.y))
for x in range( x0 , x1 + 1 ) :
for y in range( y0 , y1 + 1 ) :
barycentric = polygon.getBaricenterCordinates(gr.Point(x, y))
is_inside_triangle = all( i >= 0 for i in barycentric )
if is_inside_triangle :
# получаем координаты пикселя, соответствующего отрисовываемому в данный момент, из файла текстур
# получаем цвет пикселя из файла текстур по вычисленным координатам
z = polygon.tmp_Z(barycentric)
get_pixel = get_texture_point(polygon, barycentric)
color = (texture.getpixel(get_pixel))
pixels = texture.load()
intensity = (polygon.normalFirst.first +polygon.normalFirst.second + polygon.normalFirst.third) *barycentric[0]+\
(polygon.normalSecond.first +polygon.normalSecond.second + polygon.normalSecond.third) *barycentric[1]+\
(polygon.normalThird.first +polygon.normalThird.second + polygon.normalThird.third) *barycentric[2]
color = (int(color[0]*intensity),int(color[1]*intensity),int(color[2]*intensity))
draw_pixel(tr.Point(x, y, z), z_buffer, draw,get_pixel,intensity ,pixels,color)
def __init__(self, master):
self.dim = 500
#init vars
self.got_edge = 0
#self.move_line = 0
#self.move_oval = 0
self.anistack = deque()
self.moveanistack = deque()
# create paining area
self.canv = Canvas(root, width=self.dim, height=self.dim)
self.canv.bind("<Button-1>", self.clicked)
self.canv.bind("<B1-Motion>", self.moved)
self.canv.bind("<ButtonRelease-1>", self.released)
self.canv.pack()
self.tri = Triangle([50, 70], [300, 300], [400, 100])
self.tri.id = self.canv.create_polygon(self.tri.coo, fill='yellow')
frame = Frame(master)
frame.pack()
self.button = Button(frame, text="QUIT", fg="red", command=frame.quit)
self.button.pack(side=LEFT)
self.hi_there = Button(frame, text="Reset", command=self.reset)
self.hi_there.pack(side=LEFT)
def main():
"""
Asks user for an input file
Converts the series of height data values into triangles
Writes triangles to file in stl format
:return: None
"""
# Ask user for file path and return data:
in_path, data, meta_data = file_path_and_data()
# Get useful meta data:
cell_size = meta_data["cellsize"]
offset = (meta_data["xllcorner"], meta_data["yllcorner"])
# Set up output file:
out_path = os.path.splitext(in_path)[0] + ".stl"
setup_out_file(out_path)
# Loop through data and write to file:
# Each data point and its three right and lower neighbours
# generate two surface triangles
print("Writing STL surface...")
for j0, row in enumerate(data[:-1]):
for i0, z0 in enumerate(row[:-1]):
# Triangle 1
i = [i0, i0 + 1, i0]
j = [j0, j0 + 1, j0 + 1]
vx, vy, vz = calc_vertices(i, j, data, cell_size, offset)
write_to_file(out_path, Triangle(vx, vy, vz))
# Triangle 2
i = [i0, i0 + 1, i0 + 1]
j = [j0, j0, j0 + 1]
vx, vy, vz = calc_vertices(i, j, data, cell_size, offset)
write_to_file(out_path, Triangle(vx, vy, vz))
end_out_file(out_path)
print("Done.")
class TestTriangle(unittest.TestCase):
def setUp(self):
self.triangle = Triangle(2, 3, 4)
def testInvariants(self):
self.assertAlmostEqual(
math.pi,
self.triangle.alfa() + self.triangle.beta() +
self.triangle.gamma())
self.assertAlmostEqual(
self.triangle.a / math.sin(self.triangle.alfa()),
self.triangle.b / math.sin(self.triangle.beta()))
self.assertAlmostEqual(
self.triangle.c / math.sin(self.triangle.gamma()),
self.triangle.b / math.sin(self.triangle.beta()))
def testCircumference(self):
self.assertAlmostEqual(9, self.triangle.circumference())
def testScale(self):
self.triangle.scale(10)
self.assertAlmostEqual(20, self.triangle.a)
self.assertAlmostEqual(30, self.triangle.b)
self.assertAlmostEqual(40, self.triangle.c)
self.testInvariants()
def make_triangles(self):
polyline = []
triangles = []
for p in self.points_list:
polyline.append(p.get_coord())
this_polygon = None
for i in range(5):
try:
this_polygon = poly2tri.Triangulator(polyline)
break
except:
pass
if not this_polygon:
return None
for triangle in this_polygon.polygons:
point_a = Point()
point_a.set_coord(triangle[0].x, triangle[0].y)
point_b = Point()
point_b.set_coord(triangle[1].x, triangle[1].y)
point_c = Point()
point_c.set_coord(triangle[2].x, triangle[2].y)
this_triangle = Triangle()
this_triangle.set_point_by_points(point_a,
point_b,
point_c)
triangles.append(this_triangle)
return triangles
def polygon_triangulation(self):
"""returns a list of triangles that describe the current polygon"""
self.close_polygon()
poly_line = []
triangles = []
for point in self.polygon_points:
poly_line.append(point.get_point())
this_polygon = None
for i in range(5):
try:
this_polygon = poly2tri.Triangulator(poly_line)
break
except:
pass
if not this_polygon:
return None
for triangle in this_polygon.polygons:
point_a = Point()
point_a.set_point(triangle[0].x, triangle[0].y)
point_b = Point()
point_b.set_point(triangle[1].x, triangle[1].y)
point_c = Point()
point_c.set_point(triangle[2].x, triangle[2].y)
this_triangle = Triangle()
this_triangle.set_points_by_point(point_a, point_b, point_c)
triangles.append(this_triangle)
return triangles
def testTriangleThirdNode(self):
n1 = Node((0,0),1)
n2 = Node((1,1),2)
n3 = Node((0,1),3)
t = Triangle(n1, n2, n3)
self.assertEqual(n1, t.getThirdNode(n2,n3))
self.assertEqual(n2, t.getThirdNode(n1,n3))
self.assertEqual(n3, t.getThirdNode(n1,n2))
def test_normal_Triangle(self):
t = Triangle(Point(0, 1, 0), Point(-1, 0, 0), Point(1, 0, 0))
n1 = t.local_normal_at(Point(0, 0.5, 0))
n2 = t.local_normal_at(Point(-0.5, 0.75, 0))
n3 = t.local_normal_at(Point(0.5, 0.25, 0))
self.assertEqual(n1, t.normal)
self.assertEqual(n2, t.normal)
self.assertEqual(n3, t.normal)
def test_triangle_bounding_box(self):
p1 = Point(-3, 7, 2)
p2 = Point(6, 2, -4)
p3 = Point(2, -1, -1)
shape = Triangle(p1, p2, p3)
box = shape.bounds_of()
self.assertEqual(box.min, Point(-3, -1, -4))
self.assertEqual(box.max, Point(6, 7, 2))
def add_point(self, p):
# получаем новые образованные рёбра и треугольники в виде очереди
flip_list = self.make_triangles(p)
# флипаем некоторые рёбра, добавляем их соседей в очередь
while flip_list:
t1, e = flip_list.popleft()
if t1 is None:
continue
t2 = t1.get_neigh(e)
if t2 is None:
continue
p1, p2 = e
p3 = t1.get_opposite(e)
p4 = t2.get_opposite(e)
# получаем окружность по трём точкам
circle = Circle.get_circle(p1, p2, p3)
# если четвертая точка в окружности, то делаем флип
if Circle.is_in_circle(circle, p4):
id1 = t1.id
id2 = t2.id
e13 = (p1, p3)
e14 = (p1, p4)
e23 = (p2, p3)
e24 = (p2, p4)
e34 = (p3, p4)
t13 = t1.get_neigh(e13)
t23 = t1.get_neigh(e23)
t14 = t2.get_neigh(e14)
t24 = t2.get_neigh(e24)
t1_new = Triangle([[e13, t13],
[e14, t14],
[e34, None]],
id1)
t2_new = Triangle([[e23, t23],
[e24, t24],
[e34, t1_new]],
id2)
t1_new.set_neigh(e34, t2_new)
# заменяем старые треугольники на новые
self.triangles_list[id1] = t1_new
self.triangles_list[id2] = t2_new
if t13 is not None:
t13.set_neigh(e13, t1_new)
if t14 is not None:
t14.set_neigh(e14, t1_new)
if t23 is not None:
t23.set_neigh(e23, t2_new)
if t24 is not None:
t24.set_neigh(e24, t2_new)
# добавляем новые потенциально опасные ребра в виде пар [треугольник, проблемное ребро]
flip_list.append([t14, e14])
flip_list.append([t24, e24])
flip_list.append([t13, e13])
flip_list.append([t23, e23])
def calcAffordances(self, lines):
# Calculate affordances by intersecting agains one triangle per affordance
# make initial triangle
o = Point(0,0,0)
# The triangle is a bit behind
oBehind = Point(-.2,0,0)
v1 = Point(cos(self.aperture/2)*self.lenght, sin(self.aperture/2)*self.lenght,0)
v2 = Point(cos(self.aperture/2)*self.lenght, -sin(self.aperture/2)*self.lenght,0)
t = Triangle([o,v1,v2])
# for each angle: transform the triangle and intersect it with all lines
lBase = Line(o, Point(1,0,0));
affordances = []
markers = []
i = 0
for angle in self.possibleAngles:
# reference transformation
lTransform = Line(o, Point(cos(angle), sin(angle), 0))
mov = Movement(lBase, lTransform)
tMoved = t.moved(mov);
canMove = True
j = 0
while j < len(lines) and canMove:
l = lines[j]
p1 = l.p1
p2 = l.p2
canMove = canMove and not tMoved.containedOrIntersect(Point(p1.x,p1.y,p1.z), Point(p2.x,p2.y,p2.z))
if not canMove:
print "cant move to", angle
print tMoved.vertices
print p1
print p2
j += 1
affordances.append(canMove)
# if canMove:
# color = 'b'
# else:
# color = 'r'
# geomPoints = [geometry_msgs.msg.Point(p.r[0],p.r[1],p.r[2]) for p in tMoved.vertices]
# geomPoints.append(geomPoints[0])
# markers.append(self.getLineStrip(geomPoints, i, rospy.Time.now(), color))
# i += 1
# for l in lines:
## print "line", a
# markers.append(self.getLineStrip([l.p1,l.p2], i, rospy.Time.now(), 'g'))
# i = i + 1
#
# mArray = MarkerArray()
# mArray.markers = markers
# self.pubMarker.publish(mArray)
# print "lines", lines
return affordances
def flip_edges(self, min_sabr=0.05):
new_internal_edges = list()
while len(self.internal_edges) != 0:
edge = self.internal_edges.pop()
o_edge = opposite_edge(edge)
if o_edge is not None:
edge_len_squared = distance_squared(edge[0], edge[1])
o_edge_len_squared = distance_squared(o_edge[0], o_edge[1])
# sabr = "squared altitude-base ratio"
current_too_skinny = min_sabr > min(
o_edge[0].dist_squared_from_line(edge[0], edge[1]) /
edge_len_squared,
o_edge[1].dist_squared_from_line(edge[0], edge[1]) /
edge_len_squared)
new_too_skinny = min_sabr > min(
edge[0].dist_squared_from_line(o_edge[0], o_edge[1]) /
o_edge_len_squared,
edge[1].dist_squared_from_line(o_edge[0], o_edge[1]) /
o_edge_len_squared)
current_tri1 = [o_edge[0], edge[0], edge[1]]
current_tri2 = [o_edge[1], edge[0], edge[1]]
new_tri1 = [edge[0], o_edge[0], o_edge[1]]
new_tri2 = [edge[1], o_edge[0], o_edge[1]]
if new_too_skinny == current_too_skinny: # we won't check var_improves if (F, T) or (T, F)
current_var1 = self.variance(pixels_in_tri(current_tri1))
current_var2 = self.variance(pixels_in_tri(current_tri2))
new_var1 = self.variance(pixels_in_tri(new_tri1))
new_var2 = self.variance(pixels_in_tri(new_tri2))
var_improves = None not in (current_var1, current_var2, new_var1, new_var2) and \
new_var1 + new_var2 < current_var1 + current_var1
# the edge will be flipped if a bordering triangle is currently too skinny (and flipping will fix that)
# or if the variance would be better in the other direction
if (current_too_skinny and not new_too_skinny) or \
(current_too_skinny and var_improves) or \
(not new_too_skinny and var_improves):
# flip the edge
self.tris.remove(Triangle(current_tri1))
self.tris.remove(Triangle(current_tri2))
self.tris.add(Triangle(new_tri1))
self.tris.add(Triangle(new_tri2))
remove_edge(edge[0], edge[1])
self.add_edge(o_edge[0], o_edge[1], auto_add_to_ie=False)
new_internal_edges.append(o_edge)
else:
new_internal_edges.append(edge)
else:
new_internal_edges.append(edge)
self.internal_edges = new_internal_edges
def _generate_back(self):
a = self._l_t + Point3D(z=self._step_count * self._step_height)
b = a + Point3D(self._width)
self.triangles.append(Triangle(a, b, self._r_t))
self.triangles.append(Triangle(a, self._l_t, self._r_t))
self.edges.append(Edge(a, self._l_t))
self.edges.append(Edge(b, self._r_t))
def main(): sh = Shape() print sh t = Triangle(5, 10) print t.area() print "%s Static Method" % t.static_area(10, 20) s = Square(20) print s.area() print s.perimeter()
def main(args):
side1 = int(args[1])
side2 = int(args[2])
side3 = int(args[3])
height = int(args[4])
print("the three sides and height of triangle area %d %d %d and %d" %
(side1, side2, side3, height))
t1 = Triangle(side1, side2, side3, height)
print("Perimeter: ", t1.perimeter())
print("Area: ", t1.area())
def make_triangles(self, p):
# ищем треугольник для вставки внутрь него точки
for index in range(len(self.triangles_list)):
if self.triangles_list[index].is_point_in(p):
insert_index = index
break
else:
print("Точка должна лежать по крайней мере в одном из треугольников.")
return None
# треугольник, в который вставляем точку
insert_triangle = self.triangles_list[insert_index]
# создаём 3 новых треугольника
p1, p2, p3 = insert_triangle.points()
e1 = (p1, p2)
e2 = (p2, p3)
e3 = (p1, p3)
e4 = (p1, p)
e5 = (p2, p)
e6 = (p3, p)
t1 = insert_triangle.get_neigh(e1)
t2 = insert_triangle.get_neigh(e2)
t3 = insert_triangle.get_neigh(e3)
new_t1 = Triangle([[e1, t1],
[e4, None],
[e5, None]],
insert_index)
new_t2 = Triangle([[e2, t2],
[e5, new_t1],
[e6, None]],
len(self.triangles_list))
new_t3 = Triangle([[e3, t3],
[e4, new_t1],
[e6, new_t2]],
len(self.triangles_list) + 1)
new_t1.set_neigh(e5, new_t2)
new_t1.set_neigh(e4, new_t3)
new_t2.set_neigh(e6, new_t3)
# обновляем соседей треугольника, в который вставили точку
if t1 is not None:
t1.set_neigh(e1, new_t1)
if t2 is not None:
t2.set_neigh(e2, new_t2)
if t3 is not None:
t3.set_neigh(e3, new_t3)
# заменяем старый треугольник и добавляем новые
self.triangles_list[insert_index] = new_t1
self.triangles_list.append(new_t2)
self.triangles_list.append(new_t3)
# рёбра для возможного flip - пары [треугольник, проблемное ребро]
return deque([[new_t1, e1], [new_t2, e2], [new_t3, e3]])
def _generate_base(self):
self._l_t = self._base_point
self._r_t = self._l_t + Point3D(self._width)
self._r_b = self._r_t + Point3D(y=self._step_count * self._step_length)
self._l_b = self._r_b + Point3D(x=-self._width)
self.triangles.append(Triangle(self._l_t, self._r_t, self._r_b))
self.triangles.append(Triangle(self._l_t, self._l_b, self._r_b))
self.edges.append(Edge(self._l_t, self._r_t))
self.edges.append(Edge(self._r_t, self._r_b))
self.edges.append(Edge(self._r_b, self._l_b))
self.edges.append(Edge(self._l_b, self._l_t))
def test_one_cell_mesh():
t = Triangle()
points = [(0., 0.), (1., 0.), (0., 1.)]
markers = [1, 1, 1]
t.set_points(points, markers=markers)
segments = [(0, 1), (1, 2), (2, 0)]
t.set_segments(segments)
t.triangulate(area=0.5)
cells = t.get_triangles()
assert len(cells) == 1
def get_triangles(self, vert):
# bottom triangles
d = self.density
triangles = []
# bottom arc 1-x, top arc 1+d+1 - 1 + 2d
# bottom triangles
for i in range(d - 2):
triangles.append(Triangle(vert[0], vert[i + 1], vert[i + 2]))
triangles.append(Triangle(
vert[0], vert[d], vert[1])) # we can safely assume vert[1] exists
# top triangles
for i in range(d - 2):
triangles.append(
Triangle(vert[d + 1], vert[i + d + 2], vert[i + d + 3]))
triangles.append(Triangle(vert[d + 1], vert[2 * d + 1], vert[d + 2]))
# side triangles
for i in range(d - 1):
triangles.append(
Triangle(vert[i + 1], vert[i + 2], vert[i + d + 2]))
triangles.append(
Triangle(vert[i + 2], vert[i + d + 2], vert[i + d + 3]))
triangles.append(Triangle(vert[d], vert[1], vert[2 * d + 1]))
triangles.append(Triangle(vert[1], vert[2 * d + 1], vert[d + 2]))
return triangles
def __init__(self):
self.__drawing_top = 0
self.__drawing_bottom = 0
self.__border_rect = Rectangle()
self.__radius = 0
self.__center = (0, 0)
self.__theta = 0
self.__triangle = Triangle()
self.__triangle.edge_color = PALE_GRAY
self.__triangle.node_radius = GRID_UNIT / 2
self.__triangle.nodes_color = (PALE_RED, PALE_BLUE, PALE_GREEN
) # 緑と青が逆なのが工夫
self.__triangle.center_color = PALE_GRAY
def main():
""""""
stage_color = clutter.Color(0, 0, 0, 255)
actor_color = clutter.Color(255, 255, 255, 153)
# Get the stage and set its size and color
stage = clutter.Stage()
stage.set_size(200, 200)
stage.set_color(stage_color)
# Add our custom actor to the stage
actor = Triangle(actor_color)
actor.set_size(100, 100)
actor.set_position(20, 20)
stage.add(actor)
actor.show()
# Show the stage
stage.show()
stage.connect('destroy', clutter.main_quit)
#actor.set_color('Red')
# Start the main loop, so we can respond to events
clutter.main()
return 0
def _generate_step(self, step_number):
a = self._l_b + Point3D(y=-(step_number * self._step_length))
b = a + Point3D(z=self._step_height * (step_number + 1))
c = b + Point3D(y=-self._step_length)
d = a + Point3D(y=-self._step_length)
f = b + Point3D(z=-self._step_height)
a1 = a + Point3D(x=self._width)
b1 = b + Point3D(x=self._width)
c1 = c + Point3D(x=self._width)
d1 = d + Point3D(x=self._width)
f1 = f + Point3D(x=self._width)
self.triangles.append(Triangle(a, b, c))
self.triangles.append(Triangle(a, d, c))
self.triangles.append(Triangle(a1, b1, c1))
self.triangles.append(Triangle(a1, d1, c1))
self.triangles.append(Triangle(b, f, f1))
self.triangles.append(Triangle(f1, b1, b))
self.triangles.append(Triangle(c, b, b1))
self.triangles.append(Triangle(b1, c1, c))
self.edges.append(Edge(f, b))
self.edges.append(Edge(f1, b1))
self.edges.append(Edge(b, b1))
self.edges.append(Edge(c, c1))
self.edges.append(Edge(b, c))
self.edges.append(Edge(b1, c1))
def update(self, x, y):
Box.update(self, x, y)
pos = vec2(x, y)
self.a, self.b, self.c = a, b, c = self.get_vertices(x, y)
self.left_triangle = Triangle(a, b, pos, self.color, self.batch)
self.bottom_triangle = Triangle(b, c, pos, self.color, self.batch)
self.right_triangle = Triangle(c, a, pos, self.color, self.batch)
self.glow = self.batch.add_indexed(6, pyglet.gl.GL_TRIANGLES, None, [0, 1, 3, 1, 4, 3, 1, 2, 4, 2, 5, 4, 2, 0, 5, 0, 3, 5],
('v2f', (a.x-255, a.y+512 , b.x-255, b.y-255, c.x+512, c.y-255, a.x, a.y, b.x, b.y, c.x, c.y)),
('c4f', (self.color+(0.0,))*3+(self.color+(1.0,))*3)
)
self.leftattach = (b.x, y)
self.bottomattach = (x, b.y)
self.rightattach = (x+self.s1, y+self.s1)
def on_pre_render(self):
world_matrix = self.transform.get_matrix()
tris = []
if ((self.material != None) and (self.mesh)):
#distance culling
if (self.cull_by_distance):
direction_from_camera = self.transform.position - Application.scene.camera.transform.position
dist = direction_from_camera.magnitude()
if (dist >= Application.scene.camera.culling_distance):
return
#display each side with a different color (DEBUG)
if (self.debug_mode == True):
colors = [(1, 0, 0), (0, 1, 0), (0, 0, 1), (.5, .5, 0),
(.5, 0, .5), (0, .5, .5)]
i = 0
#Apply transform matrix transformation to triangles
for triangle in self.mesh.tris:
tpoly = []
for v in triangle.vertices:
transformed = vector3.multiply_matrix(v, world_matrix)
tpoly.append(transformed)
t = Triangle(tpoly[0], tpoly[1], tpoly[2])
center = t.get_center()
#calculate lights
if (self.debug_mode == False):
light_intensity = .05
for light in Application.lights_buffer:
light_intensity += light.calculate_intensity(
center, t.normal)
if (light_intensity > 1):
light_intensity = 1
t.color = self.material.color * light_intensity
else:
j = colors[math.floor(i / 2)]
t.color = color(j[0], j[1], j[2], 1)
i += 1
tris.append(t)
#add triangle to buffer
Application.add_triangle_to_buffer(tris)
class AbstractorBox(Box):
def __init__(self, x, y):
self.topline = None
self.rightline = None
self.bottomline = None
self.color = (1.0, 0.4, 0.8)
Box.__init__(self, x, y)
def get_vertices(self, centerx, centery):
left = centerx-self.s2
right = centerx+self.s1
bottom = centery-self.s2
top = centery+self.s1
return vec2(right, bottom), vec2(right, top), vec2(left, top)
def update(self, x, y):
Box.update(self, x, y)
self.a, self.b, self.c = a, b, c = self.get_vertices(x, y)
pos = vec2(x, y)
self.leftattach = (b.x, y)
self.bottomattach = (x, b.y)
self.rightattach = (x+self.s1, y+self.s1)
self.right_triangle = Triangle(a, b, pos, self.color, self.batch)
self.top_triangle = Triangle(b, c, pos, self.color, self.batch)
self.bottom_triangle = Triangle(c, a, pos, self.color, self.batch)
self.glow = self.batch.add_indexed(6, pyglet.gl.GL_TRIANGLES, None, [0, 1, 3, 1, 4, 3, 1, 2, 4, 2, 5, 4, 2, 0, 5, 0, 3, 5],
('v2f', (a.x+255, a.y-512 , b.x+255, b.y+255, c.x-512, c.y+255, a.x, a.y, b.x, b.y, c.x, c.y)),
('c4f', (self.color+(0.0,))*3+(self.color+(1.0,))*3)
)
self.topattach = (x, a.y)
self.bottomattach = (x-self.s1, y-self.s1)
self.rightattach = (a.x, y)
def draw(self):
self.batch.draw()
def gethover(self, x, y):
hovered = False
if self.top_triangle.gethover(vec2(x, y)):
hovered = self, self.leftattach
if self.bottom_triangle.gethover(vec2(x, y)):
hovered = self, self.bottomattach
if self.right_triangle.gethover(vec2(x, y)):
hovered = self, self.rightattach
return hovered
def drag_end(self, x, y):
pass
def ReadBlend(self, fname):
"""imports an OBJ file, and populates tris and points
"""
print("filename",fname)
file = open(fname, "r")
currentLine = file.readline()
while (currentLine):
# parse out numbers from the string using Regex pattern language
# (from the re package)
numbers = re.findall(r'-?\d+(?:\.\d+)?', currentLine)
# find 'v' character and populate vertex information
if (currentLine[0] == "v" and currentLine[1] == " "):
# make a new vertex object out of it
self.newVertex = vertex(float(numbers[0]), float(numbers[1]), float(numbers[2]))
self.points.append(self.newVertex)
# find 'f' character and populate face information
elif (currentLine[0] == "f"):
self.newTriangle = Triangle(int(numbers[0])-1, int(numbers[3])-1, int(numbers[6])-1)
self.tris.append(self.newTriangle)
currentLine = file.readline()
for point in self.points:
point.printXYZ()
for tri in self.tris:
tri.printIV()
def read_file_into_mesh(file, to_pickle=False):
vertex_num = 0
vertices = {}
faces = []
vert_key = []
num_lines = len(open(file).readlines())
line_num = 0.0
print('Converting to work format...\n')
triangles = []
vectors = []
for line in open(file):
line_num += 1.0
split_line = line.split()
if split_line[0] == 'vertex':
vectors.append(
Vector(float(split_line[1]), float(split_line[2]),
float(split_line[3])))
elif split_line[0] == 'endloop':
triangles.append(Triangle(vectors[0], vectors[1], vectors[2]))
vectors = []
amtDone = line_num / num_lines
sys.stdout.write("\rProgress: [{0:50s}] {1:.1f}%".format(
'#' * int(amtDone * 50), amtDone * 100))
return triangles
def from_obj(file_path, mesh=None):
"""Load a mesh from an .obj file
Arguments:
file_path {string} -- the path to the file
Keyword Arguments:
mesh {Mesh} -- mesh to assign the polygons (default: {None})
Returns:
Mesh -- a mesh with the loaded polygons
"""
if (mesh == None):
mesh = Mesh(file_path)
vertices = []
file = open(file_path, 'r')
for line in file:
if (line[0] == 'v'):
elements = line.split()
p1 = float(elements[1])
p2 = float(elements[2])
p3 = float(elements[3])
vertices.append(vector3(p1, p2, p3))
if (line[0] == 'f'):
elements = line.split()
v1 = int(elements[1]) - 1
v2 = int(elements[2]) - 1
v3 = int(elements[3]) - 1
triangle = Triangle(vertices[v1], vertices[v2], vertices[v3])
mesh.tris.append(triangle)
return mesh
def __init__(self, size=trigon_rules.default_size):
self.size = size
n = size
field = []
for x in range(n):
line = []
for y in range(2 * (n + x) + 1):
line.append(Triangle(x + 1, y + 1, self.size))
field.append(line)
for x in range(n, 2 * n):
line = []
for y in range(4 * n - 1 - 2 * (x - n)):
line.append(Triangle(x + 1, y + 1, self.size))
field.append(tuple(line))
self.field = tuple(field)
def __init__(self, master):
self.dim = 500
#init vars
self.got_edge = 0
#self.move_line = 0
#self.move_oval = 0
self.anistack = deque()
self.moveanistack = deque()
# create paining area
self.canv = Canvas(root, width = self.dim, height = self.dim)
self.canv.bind("<Button-1>", self.clicked)
self.canv.bind("<B1-Motion>", self.moved)
self.canv.bind("<ButtonRelease-1>", self.released)
self.canv.pack()
self.tri = Triangle([50,70],[300,300],[400,100])
self.tri.id = self.canv.create_polygon(self.tri.coo,fill='yellow')
frame = Frame(master)
frame.pack()
self.button = Button(frame, text="QUIT", fg="red", command=frame.quit)
self.button.pack(side=LEFT)
self.hi_there = Button(frame, text="Reset", command=self.reset)
self.hi_there.pack(side=LEFT)
def fan_triangulation(vertices: Iterable[Point],
vertex_normals: Iterable[Point],
vertex_indices: Iterable[str]) -> Iterable:
from triangle import Triangle
triangles = []
vertex_1_info = vertex_indices[1].split('/')
for index in range(2, len(vertex_indices) - 1):
if len(vertex_1_info) == 1:
tri = Triangle(vertices[int(vertex_indices[1])],
vertices[int(vertex_indices[index])],
vertices[int(vertex_indices[index + 1])])
triangles.append(tri)
else:
vertex_2_info = vertex_indices[index].split('/')
vertex_3_info = vertex_indices[index + 1].split('/')
tri = SmoothTriangle(vertices[int(vertex_1_info[0])],
vertices[int(vertex_2_info[0])],
vertices[int(vertex_3_info[0])],
vertex_normals[int(vertex_1_info[2])],
vertex_normals[int(vertex_2_info[2])],
vertex_normals[int(vertex_3_info[2])])
triangles.append(tri)
return triangles
def createNewTriangles(self):
"""createNewTriangles calculates smaller triangles with new corners
"""
trisnew = []
for t in self.tris:
# calculate middle triangle
t2 = Triangle(t.ie[0], t.ie[1], t.ie[2])
# calculate triangles around the middle triangle
t0 = Triangle(t.ie[1], t.ie[0], t.iv[2])
t1 = Triangle(t.iv[0], t.ie[2], t.ie[1])
t3 = Triangle(t.ie[2], t.iv[1], t.ie[0])
trisnew.append(t0)
trisnew.append(t1)
trisnew.append(t2)
trisnew.append(t3)
self.tris = trisnew
class TestTriangle(unittest.TestCase):
def setUp(self):
self.triangle = Triangle(100, 30)
# Return dimension
def test_area(self):
self.assertEqual(1500, self.triangle.area())
def create_quad(origin, axis0, axis1, mesh):
if (mesh == None):
mesh = Mesh("UnknownQuad")
v1 = origin + axis0 + axis1
v2 = origin + axis0 - axis1
v3 = origin - axis0 - axis1
v4 = origin - axis0 + axis1
t1 = Triangle(v1, v2, v3)
t2 = Triangle(v1, v3, v4)
mesh.tris.append(t1)
mesh.tris.append(t2)
return mesh
def read_file_obj(file_obj):
first_line = file_obj.readline()
items = first_line.split()
x, y = [int(a) for a in items[:2]]
if len(items) == 3:
color_type = items[2]
else:
color_type = RGB
s = Sketch(Point(x, y), color_type)
for line in file_obj:
items = string_to_ints(line)
if color_type == RGB:
t = Triangle(items[:6], tuple(items[6:9]), items[9])
else:
t = Triangle(items[:6], items[6], items[7])
s.triangles.append(t)
return s
def bowyerWatson(points):
# https://en.wikipedia.org/wiki/Bowyer%E2%80%93Watson_algorithm
# print("Running bowyerWatson on %d points" % len(points))
triangulation = []
# must be large enough to completely contain all the points in pointList
P1 = Vec(-1e15, -1e15)
P2 = Vec(1e15, -1e15)
P3 = Vec(0, 1e15)
megaTriangle = Triangle(P1, P2, P3)
triangulation.append(megaTriangle)
# add all the points one at a time to the triangulation
for iP, P in enumerate(points):
badTriangles = []
# first find all the triangles that are no longer valid due to the insertion
for iT, T in enumerate(triangulation):
if distance(P, T.C) < T.R: # If point inside triangle circumcircle
badTriangles.append(T) # Triangle is bad
# find the boundary of the polygonal hole
polygon = []
for T in badTriangles:
for V in T.vertices: # for each edge in triangle
# if edge is not shared by any other triangles in badTriangles
if not any([_T.hasVertex(V)
for _T in badTriangles if T != _T]):
polygon.append(V)
for T in badTriangles:
triangulation.remove(T)
# re-triangulate the polygonal hole
for v1, v2 in polygon:
triangulation.append(Triangle(P, v1, v2))
# if triangle contains a vertex from original super-triangle
triangulation = [
T for T in triangulation if not T.sharesCornerWith(megaTriangle)
]
return triangulation
#######################################
def hit(self, ray_in, t_min, t_max): list_of_triangles = [] for face in self.faces: vertices = self.getFaceData(self.faces.index(face)) for triangle_no in range(0, len(vertices) - 2): list_of_triangles.append(Triangle(v = [vertices[0], vertices[triangle_no + 1], vertices[triangle_no + 2]], material = self.material)) hitable_list = Hitable_List(list_of_triangles) return hitable_list.hit(ray_in, t_min, t_max)
def __init__(self, inf = 65536, test = False):
self._initTriangle = Triangle(Point2D(-inf, -inf),
Point2D(inf, -inf),
Point2D(0, inf))
self.neighborhood = {self._initTriangle: {}}
self.lock = threading.RLock()
self.main_site = None
self.fail_site = None
self.fail_triangle = None
self.fail_witness = None
self.version = 0
self.check_triangulation = test
class TriangleTest(unittest.TestCase):
def setUp(self):
self.triangle = Triangle()
def test_get_side1(self):
self.assertEqual(
self.triangle.get_side1(),
self.triangle._Triangle__side1
)
def test_get_side2(self):
self.assertEqual(
self.triangle.get_side2(),
self.triangle._Triangle__side2
)
def test_get_side3(self):
self.assertEqual(
self.triangle.get_side3(),
self.triangle._Triangle__side3
)
def test_get_perimeter(self):
self.assertEqual(
self.triangle.get_perimeter(),
self.triangle._Triangle__side1 +
self.triangle._Triangle__side2 +
self.triangle._Triangle__side3
)
def test_get_area(self):
p = self.triangle.get_perimeter() / 2
area = math.sqrt(
p *
(p - self.triangle._Triangle__side1) *
(p - self.triangle._Triangle__side2) *
(p - self.triangle._Triangle__side3)
)
self.assertEqual(
self.triangle.get_area(),
area
)
def get_triangles_for_rectangle(self, min_x, max_x, min_y, max_y):
"""
Args:
min_x: int
max_x: int
min_y: int
max_y: int
Returns: List(tri_image.triangle.Triangle) of length 2
"""
if self.color_type == RGB:
c = (0, 0, 0)
else:
c = 0
t1 = Triangle([min_x, min_y, min_x, max_y, max_x, max_y], c, 255)
t1.set_color(self.source_image, self.color_type)
t2 = Triangle([min_x, min_y, max_x, min_y, max_x, max_y], c, 255)
t2.set_color(self.source_image, self.color_type)
return [t1, t2]
class ApplicatorBox(Box):
def __init__(self, x, y):
self.leftline = None
self.rightline = None
self.bottomline = None
self.color = (0.4, 1.0, 0.8)
Box.__init__(self, x, y)
def get_vertices(self, centerx, centery):
left = centerx-self.s1
right = centerx+self.s2
bottom = centery-self.s1
top = centery+self.s2
return vec2(left, top), vec2(left, bottom), vec2(right, bottom)
def update(self, x, y):
Box.update(self, x, y)
pos = vec2(x, y)
self.a, self.b, self.c = a, b, c = self.get_vertices(x, y)
self.left_triangle = Triangle(a, b, pos, self.color, self.batch)
self.bottom_triangle = Triangle(b, c, pos, self.color, self.batch)
self.right_triangle = Triangle(c, a, pos, self.color, self.batch)
self.glow = self.batch.add_indexed(6, pyglet.gl.GL_TRIANGLES, None, [0, 1, 3, 1, 4, 3, 1, 2, 4, 2, 5, 4, 2, 0, 5, 0, 3, 5],
('v2f', (a.x-255, a.y+512 , b.x-255, b.y-255, c.x+512, c.y-255, a.x, a.y, b.x, b.y, c.x, c.y)),
('c4f', (self.color+(0.0,))*3+(self.color+(1.0,))*3)
)
self.leftattach = (b.x, y)
self.bottomattach = (x, b.y)
self.rightattach = (x+self.s1, y+self.s1)
def draw(self):
self.batch.draw()
if self.rightline:
self.rightline.draw()
if self.leftline:
self.leftline.draw()
def gethover(self, x, y):
hovered = False
if x > self.a.x and x < self.c.x and y > self.b.y and y < self.a.y: #bounding box check
if self.left_triangle.gethover(vec2(x, y)):
hovered = self, self.leftattach
if self.bottom_triangle.gethover(vec2(x, y)):
hovered = self, self.bottomattach
if self.right_triangle.gethover(vec2(x, y)):
hovered = self, self.rightattach
else:
self.left_triangle.highlight(False)
self.bottom_triangle.highlight(False)
self.right_triangle.highlight(False)
return hovered
def gethover_recursive(self, x, y):
hovered = self.gethover(x, y)
if hovered:
return hovered
else:
if self.rightline:
rightline_hover = self.rightline.gethover_recursive(x, y)
if rightline_hover:
return rightline_hover
else:
if self.leftline:
leftline_hover = self.leftline.gethover_recursive(x, y)
if leftline_hover:
return leftline_hover
else:
return False
def drag_end(self, x, y):
pass
def setUp(self):
path = tempfile.mktemp('.ldb')
db = leveldb.LevelDB(path)
self.triangle = Triangle(db)
class CoffeeData(flask.views.MethodView):
@login_required
def get(self):
return flask.render_template('coffeedata.html')
# Routes
app.add_url_rule('/',
view_func=Login.as_view('login'),
methods=["GET", "POST"])
app.add_url_rule('/remote/',
view_func=Remote.as_view('remote'),
methods=["GET", "POST"])
app.add_url_rule('/triangle/',
view_func=Triangle.as_view('triangle'),
methods=["GET", "POST"])
app.add_url_rule('/music/',
view_func=Music.as_view('music'),
methods=["GET"])
app.add_url_rule('/asteroids/',
view_func=Asteroids.as_view('asteroids'),
methods=["GET"])
app.add_url_rule('/remotezsnes/',
view_func=RemoteZsnes.as_view('remotezsnes'),
methods=["GET"])
app.add_url_rule('/asteroids/',
view_func=CoffeeData.as_view('coffeedata'),
methods=["GET"])
@app.errorhandler(404)
#!/usr/bin/env python
import sys
import time
from triangle import Triangle
arr = [[6],[3,5],[9,7,1],[4,6,8,4]]
t = time.time()
Triangle = Triangle(arr)
(sum,path) = Triangle.maximumTotal()
t = time.time() - t
print("========== results ==========")
print(" triangle: %s " % (arr))
print(" maximum total: %d" % (sum))
print(" path: %s " % (path))
print(" execution time: %fs" % (t))
print("=============================")
def main():
Lines=1
Lines_valid=0
total_perimeter=0
total_area=0
largest_perimeter=0
largest_perimeters_area=0
largest_area=0
largest_areas_perimeter=0
triangle_perimeter=''
triangle_area=''
for line in fo:
line = "".join(c for c in line if c not in ('(',')',' '))
linelist=line.strip().replace(' ', '').split(',')
print("Line ",Lines,": ",line)
sideA=linelist[0]
sideB=linelist[1]
sideC=linelist[2]
triangle=Triangle(sideA,sideB,sideC)
if triangle.is_valid()==True:
Lines_valid+=1
total_perimeter+=triangle.perimeter()
total_area+=triangle.area()
if triangle.perimeter()>largest_perimeter:
largest_perimeter=triangle.perimeter()
largest_perimeters_area=triangle.area()
triangle_perimeter=line
if triangle.area()>largest_area:
largest_area=triangle.area()
largest_areas_perimeter=triangle.perimeter()
triangle_area=line
print("This Triangle's perimeter= {}, and area= {}".format(triangle.perimeter(),triangle.area()))
else:
print("Triangle is not valid")
Lines+=1
print("")
print("Total lines processed: ",Lines)
print("Total valid triangles processed: ",Lines_valid)
avg_perimeter=total_perimeter/Lines_valid
avg_area=total_area/Lines_valid
print("Average perimeter: ",avg_perimeter)
print("Average area: ",avg_area)
print("The Triangle with the largest perimeter= ",largest_perimeter," had a area= ",largest_perimeters_area," with sides: ",triangle_perimeter)
print("The Triangle with the largest area= ",largest_area," had a perimeter= ",largest_areas_perimeter," with sides: ",triangle_area)
def __init__(self):
ShowBase.__init__(self)
winProps = WindowProperties()
winProps.setTitle("Triangle and SimpleCircle Unittest")
# base.win.requestProperties(winProps) (same as below e.g. self == base)
self.win.requestProperties(winProps)
# 1) create GeomVertexData
frmt = GeomVertexFormat.getV3n3cp()
vdata = GeomVertexData('triangle_developer', frmt, Geom.UHDynamic)
# 2) create Writers/Rewriters (must all be created before any readers and readers are one-pass-temporary)
vertex = GeomVertexRewriter(vdata, 'vertex')
normal = GeomVertexRewriter(vdata, 'normal')
color = GeomVertexRewriter(vdata, 'color')
zUp = Vec3(0, 0, 1)
wt = Vec4(1.0, 1.0, 1.0, 1.0)
gr = Vec4(0.5, 0.5, 0.5, 1.0)
# 3) write each column on the vertex data object (for speed, have a different writer for each column)
def addPoint(x, y, z):
vertex.addData3f(x, y, z)
normal.addData3f(zUp)
color.addData4f(wt)
addPoint(0.0, 0.0, 0.0)
addPoint(5.0, 0.0, 0.0)
addPoint(0.0, 5.0, 0.0)
addPoint(15.0, 15.0, 0.0)
# 4) create a primitive and add the vertices via index (not truely associated with the actual vertex table, yet)
tris = GeomTriangles(Geom.UHDynamic)
t1 = Triangle(0, 1, 2, vdata, tris, vertex)
t2 = Triangle(2, 1, 3, vdata, tris, vertex)
c1 = t1.getCircumcircle()
t1AsEnum = t1.asPointsEnum()
r0 = (t1AsEnum.point0 - c1.center).length()
r1 = (t1AsEnum.point1 - c1.center).length()
r2 = (t1AsEnum.point2 - c1.center).length()
assert abs(r0 - r2) < utilities.EPSILON and abs(r0 - r1) < utilities.EPSILON
t2AsEnum = t2.asPointsEnum()
c2 = t2.getCircumcircle()
r0 = (t2AsEnum.point0 - c2.center).length()
r1 = (t2AsEnum.point1 - c2.center).length()
r2 = (t2AsEnum.point2 - c2.center).length()
assert abs(r0 - r2) < utilities.EPSILON and abs(r0 - r1) < utilities.EPSILON
assert t1.getAngleDeg0() == 90.0
assert t1.getAngleDeg1() == t1.getAngleDeg2()
oldInd0 = t1.pointIndex0
oldInd1 = t1.pointIndex1
oldInd2 = t1.pointIndex2
t1.pointIndex0 = t1.pointIndex1
t1.pointIndex1 = oldInd0
assert t1.pointIndex0 == oldInd1
assert t1.pointIndex1 == oldInd0
assert t1.pointIndex0 != t1.pointIndex1
t1.reverse()
assert t1.pointIndex1 == oldInd2
# 5.1) (adding to scene) create a Geom and add primitives of like base-type i.e. triangles and triangle strips
geom = Geom(vdata)
geom.addPrimitive(tris)
# 5.2) create a GeomNode to hold the Geom(s) and add the Geom(s)
gn = GeomNode('gnode')
gn.addGeom(geom)
# 5.3) attache the node to the scene
gnNodePath = render.attachNewNode(gn)
# setup a wire frame
wireNP = render.attachNewNode('wire')
wireNP.setPos(0.0, 0.0, .1)
wireNP.setColor(0.1, 0.1, 0.1, 1)
wireNP.setRenderMode(RenderModeAttrib.MWireframe, .5, 0)
gnNodePath.instanceTo(wireNP)
# test and draw intersections and circles
pt1 = Point3(0.0, 5.0, 0.0)
pt2 = Point3(1.0, 5.0, 0.0)
intersection = t2.getIntersectionsWithCircumcircle(pt1, pt2)
circle = t2.getCircumcircle()
cuts = 128
border = circle.getBorder(cuts, closed=True)
assert len(border) == cuts or (len(border) == cuts + 1 and border[0] == border[len(border) - 1])
n = len(border)
xMid = yMid = 0
for p in border:
xMid += p.x
yMid += p.y
mid = Point3(xMid / n, yMid / n, border[0].z)
assert mid.almostEqual(circle.center, 0.06)
assert t2.isCcw()
assert t1.containsPoint(c1.center) != t1.containsPoint(c1.center, includeEdges=False)
circleSegs = LineSegs("circleLines")
circleSegs.setColor(1.0, 0.0, 0.0, 1.0)
for p in border:
circleSegs.drawTo(*p)
circleNode = circleSegs.create(False)
circleNP = render.attachNewNode(circleNode)
circleNP.setZ(-5)
originSpot = LineSegs("intersection")
originSpot.setColor(1.0, 0.0, 0.0, 1.0)
originSpot.setThickness(10)
for p in intersection:
originSpot.drawTo(p)
spotNode = originSpot.create(False)
spotNP = render.attachNewNode(spotNode)
circleNP.setZ(-0.75)
# fix the camera rot/pos
PHF.PanditorDisableMouseFunc()
camera.setPos(0.0, 0.0, 50.0)
camera.lookAt(c2.center)
PHF.PanditorEnableMouseFunc()
def testTriangleArea(self):
t = Triangle(Node((1,1),(0,0)), Node((0,0),(0,0)), Node((1,0),(0,0)))
self.assertEqual(t.getArea(), 0.5)
from triangle import Triangle from camera import Camera from random import random from math import pi, tan from vector3f import Vector3f #cam = Camera() tri = Triangle() vec1 = Vector3f(0.556, 0.401054805321, 0.40692763018) vec2 = Vector3f(-0.745565615449, 0.432850996024, -0.506726680076) print tri.get_intersection(vec1, vec2) tri.get_sample_point().echovec() print tri.area tri.tangent.echovec() tri.normal.echovec()
def test_maximumTotal_return_true_result2(self):
triangle = [[6],[3,5]]
T = Triangle(triangle)
(val, path) = T.maximumTotal()
self.assertEqual(val,11)
self.assertEqual(path, [0, 1] )
from triangle import Triangle
scalene_triangle=Triangle(10.0,4.0,7.0)
print('A Triangle with side lengths of: ',scalene_triangle)
print('Is this a valid triangle?')
print(scalene_triangle.is_valid())
print('')
print('Is the Triangle equilateral?')
print(scalene_triangle.is_equilateral())
print('Is the Triangle isosceles?')
print(scalene_triangle.is_isosceles())
print('Is the Triangle scalene?')
print(scalene_triangle.is_scalene())
print('')
print('What are the lengths of this Triangle again..?')
print(scalene_triangle.sides())
print('What are the interior angles of this triangle?')
print(scalene_triangle.angles())
print('What is the perimeter of this triangle?')
print(scalene_triangle.perimeter())
print('What is the area of this triangle?')
print(scalene_triangle.area())
class Delaunay(object):
'''
Delaunay Triangulation
ref: http://www.cs.cornell.edu/home/chew/Delaunay.html
'''
# INT => MAX=+(pow(2,31) - 1)(2147483647) & MIN=-pow(2,31)(-2147483648)
# inf = 1000000 was empirically limited due to pygame simulator
# inf = 2^16 was empirically limited due to float point precision
def __init__(self, inf = 65536, test = False):
self._initTriangle = Triangle(Point2D(-inf, -inf),
Point2D(inf, -inf),
Point2D(0, inf))
self.neighborhood = {self._initTriangle: {}}
self.lock = threading.RLock()
self.main_site = None
self.fail_site = None
self.fail_triangle = None
self.fail_witness = None
self.version = 0
self.check_triangulation = test
def __repr__(self):
return 'Triangulation with ' + str(len(self.neighborhood)) + \
' triangles'
def __str__(self):
return self.__repr__()
def _new_version(self):
self.version += 1
# cicle version
if self.version > 2147483640:
self.version = 0
def updated_since(self, version):
return (version != self.version)
def has_error(self):
return self.fail_site is not None
def include(self, site):
'''
Add a site to triangulation
'''
if self.fail_site is not None:
return False
with self.lock:
triangle = self._find_triangle_circumscribe(site)
return self._add(site, triangle)
def remove_far_sites(self, from_site):
'''
Remove all sites that do not affect a "from site" cell
Returns the number of removed sites
'''
if self.fail_site is not None:
return False
with self.lock:
from_triangle = self._find_triangle_by_vertex(from_site)
if (from_triangle is None):
return 0
triangles, points = \
self.surrounding_triangles(from_site, from_triangle)
# search irrlevant sites
dispensables = []
for triangle in self.neighborhood.keys():
if (not triangle in triangles):
dispensable = True
for vertex in triangle:
if not vertex in points:
dispensables.append(vertex)
# remove irrlevant sites
removed = 0
for site in dispensables:
if not self._initTriangle.contains(site):
self.remove(site)
removed += 1
return removed
def include_near(self, site, from_site):
'''
Add a site only if it will affect a "from site" cell
'''
if self.fail_site is not None:
return False
with self.lock:
triangle = self._find_triangle_by_vertex(from_site)
if (triangle is None):
raise Exception("'From site' don't found.")
triangles, points = \
self.surrounding_triangles(from_site, triangle)
# verify site influence
for triangle in triangles:
if triangle.circumscribe(site):
return self._add(site, triangle)
return False
def remove(self, site):
'''
Remove a site from triagulation
'''
if self.fail_site is not None:
return False
with self.lock:
triangle = self._find_triangle_by_vertex(site)
if triangle is not None:
triangles, points = self.surrounding_triangles(site, triangle)
self._remove(site, points, triangles)
return True
return False
def _find_triangle_circumscribe(self, site):
'''
Search the triangle that circumcircle the point
'''
for triangle in self.neighborhood:
if triangle.circumscribe(site) or triangle.contains(site):
return triangle
raise Exception("Site out of the valid area.")
def _find_triangle_by_vertex(self, site):
'''
Search the triangle that contains the point as a vertex
'''
for triangle in self.neighborhood.keys():
if triangle.contains(site):
return triangle
return None
def _cavity(self, site, triangle):
'''
Determine the cavity caused by site.
'''
encroached = {}
toBeChecked = [triangle]
marked = {triangle: None}
while (len(toBeChecked) > 0):
triangle = toBeChecked.pop()
# Site outside triangle => triangle not in cavity
if not triangle.circumscribe(site):
continue
encroached[triangle] = None
# Check the neighborhood
for neighbor in self.neighborhood[triangle]:
if neighbor not in marked:
marked[neighbor] = None
toBeChecked.append(neighbor)
return encroached
def _add(self, site, triangle):
'''
Add a site to triangulation with specific triangle
'''
if not triangle.contains(site):
cavity = self._cavity(site, triangle)
self._insert(site, cavity)
return True
return False
def _add_triangle(self, t1, t2):
'''
Add a triangle to neighborhood control
'''
if t1 not in self.neighborhood:
self.neighborhood[t1] = {t2}
else:
self.neighborhood[t1][t2] = None
def _del_triangle(self, triangle):
'''
Remove a triangle from neighborhood control
'''
del self.neighborhood[triangle]
for neighbor in self.neighborhood.values():
if triangle in neighbor:
del neighbor[triangle]
def _link_triangles(self, t1, t2):
'''
Include mutual neighbor triangles
'''
self._add_triangle(t1, t2)
self._add_triangle(t2, t1)
def _insert(self, site, cavity):
'''
Update the triangulation by removing the cavity triangles and then
filling the cavity with new triangles.
'''
boundary = {}
triangles = {}
# Find boundary facets and adjacent triangles
for triangle in cavity:
for neighbor in self.neighborhood[triangle]:
# Adj triangles only
if neighbor not in cavity:
triangles[neighbor] = None
for point in triangle:
facet = triangle.opposite_facet(point)
if facet in boundary:
del boundary[facet]
else:
boundary[facet] = None
# Remove the cavity triangles from the triangulation
for triangle in cavity:
self._del_triangle(triangle)
# Build each new triangle and include it to the triangulation
new_triangles = {}
for facet in boundary.keys():
newTriangle = Triangle(facet[0], facet[1], site)
self.neighborhood[newTriangle] = {}
new_triangles[newTriangle] = None
# Adj triangle + new triangles
triangles[newTriangle] = None
# Update the graph links for each new triangle
for triangle in new_triangles:
for other in triangles:
if triangle.is_neighbor(other):
self._link_triangles(triangle, other)
if self.main_site is None:
self.main_site = site
self._new_version()
if self.check_triangulation:
if not self.valid():
print "### Including failure"
def _remove(self, site, points, triangles):
'''
Update the triangulation by removing the surrounding triangles
and then filling this cavity with new Delaunay triangles.
Challenge: Maintain neighborhood control.
Ref: Mir Abolfazl Mostafavi, Christopher Gold, and Maciej Dakowicz.
2003. Delete and insert operations in Voronoi/Delaunay methods
and applications. Comput. Geosci. 29, 4 (May 2003), 523-530.
DOI=10.1016/S0098-3004(03)00017-7
http://dx.doi.org/10.1016/S0098-3004(03)00017-7
'''
# verify compatibility of surrounding points and old triangles
if len(points) != len(triangles):
raise Exception("Triangulation has different sizes.")
# verify is the triangulation is empty (or insufficient?)
if len(points) < 3:
return
# initialize new triangulation controls
i = -1
new_triangles = {}
# while there are points to form more than the last triangle
while len(points) > 3:
# checks the possible triangles considering
# all three consecutive points (i, i1, i2 in a cycle)
# of surrounding points of the site
i += 1
npoints = len(points)
if (i >= npoints):
raise Exception("Inexists a valid ear? Is it possible?")
i1 = (i + 1) % npoints
i2 = (i1 + 1) % npoints
# verify if points represent a valid triangle to site,
# like a ear listen to the site:
# 1: gets triangle orientation (CW or CCW)
o_ear = Triangle.orientation(points[i], points[i1], points[i2])
# 2: gets direction of triangle to the site (CW or CCW)
o_ear_site = Triangle.orientation(points[i], points[i2], site)
# 3: if points are collinear, try another edge as a reference
# ??why don't take this edge at first place??
if o_ear_site == 0:
o_ear_site = Triangle.orientation(points[i], points[i1], site)
# 4: the directions is the same?
if (o_ear * o_ear_site) > 0:
# if so, this a valid ear (possible triangulation)
valid_ear = Triangle(points[i], points[i1], points[i2])
# verify if this ear is a Delaunay Triangulation
ear_is_delaunay = True
# 1. for all other surrounding points
for p in points:
# 1.1: is this other point (not in ear)?
if not valid_ear.contains(p):
# verify if ear won't circumcircle it
if valid_ear.circumscribe(p):
# if circumcircle, ear is not a Delaunay triangle
ear_is_delaunay = False
break
# if it is a Delaunay triangle...
if ear_is_delaunay:
# include to new triangle control
new_triangles[valid_ear] = None
# include to neighborhood control
self.neighborhood[valid_ear] = {}
# link to the opposite triangles from the removed vertices
self._link_ear(site, valid_ear, triangles[i],
new_triangles)
self._link_ear(site, valid_ear, triangles[i1],
new_triangles)
# change triangle related to vertex by the new one
# remove old triangle by switching the diagonal
triangles[i] = valid_ear
# remove middle point (leave the corners)
del points[i1]
del triangles[i1]
# restart cycle of surrounding points
i = -1
# if has only three neighbours remaining in the surrounding points,
# merged these three points (triangles) into last triangulation
last_ear = Triangle(points[0], points[1], points[2])
self.neighborhood[last_ear] = {}
new_triangles[last_ear] = None
# last triangle closes the triangulation and
# needs update the link with all sides (neighborhood)
self._link_ear(site, last_ear, triangles[0], new_triangles)
self._link_ear(site, last_ear, triangles[1], new_triangles)
self._link_ear(site, last_ear, triangles[2], new_triangles)
if self.main_site is not None:
if self.main_site == site:
self.main_site = None
self._new_version()
if self.check_triangulation:
if not self.valid():
print "### Removing failure"
def _link_ear(self, site, ear, triangle, new_triangles):
# check if the triangle has neighbor that is opposite from the site
neighbor = self.neighbor_opposite(site, triangle)
# if not, it's a external triangulation (from initial triangle)
# or it's a new triangulation...
if neighbor is None:
# if the triangle related to the vertex is new
if triangle in new_triangles:
# update neighborhood with the new triangle
self._link_triangles(ear, triangle)
else:
# otherwise, old triangle doesn't had a neighbor:
# ignore its neighborhood and delete it
self._del_triangle(triangle)
else:
# update neighborhood of new triangle (ear)
self._link_triangles(ear, neighbor)
# delete old voronoi cell triangle
self._del_triangle(triangle)
def neighbor_opposite(self, site, triangle):
'''
Report neighbor opposite the given vertex of triangle.
'''
if site not in triangle:
return None
with self.lock:
for neighbor in self.neighborhood[triangle]:
if not neighbor.contains(site):
return neighbor
return None
def surrounding_triangles(self, site, triangle):
'''
Report triangles and points surrounding site in order (cw or ccw).
'''
if site not in triangle:
raise Exception("Site not in triangle.")
with self.lock:
points = []
triangles = []
start = triangle
# cw or cww (pay attention)
guide = triangle.next_vertex_except({site})
while triangle is not None:
triangles.append(triangle)
points.append(guide)
previous = triangle
triangle = self.neighbor_opposite(guide, triangle)
guide = previous.next_vertex_except({site, guide})
if (triangle == start):
break
return triangles, points
def voronoi_cells(self):
'''
Report polygons of each voronoi cell
'''
with self.lock:
cells = {}
ignore = {} #x:None for x in self._initTriangle}
for triangle in self.neighborhood.keys():
for site in triangle:
if site in ignore:
continue
ignore[site] = None
triangles, points = self.surrounding_triangles(site,
triangle)
cell = []
for tri in triangles:
cell.append(tri.circumcenter())
cells[site] = cell
return cells
def voronoi_cell_trinagulation(self, site):
'''
Test purpose only
'''
with self.lock:
triangle = self._find_triangle_by_vertex(site)
triangles, points = self.surrounding_triangles(site, triangle)
return triangles, triangle
def valid(self):
for triangle in self.neighborhood.keys():
for other in self.neighborhood.keys():
if (other != triangle):
for vertex in other:
if not triangle.contains(vertex):
if triangle.circumscribe(vertex):
self.fail_site = vertex
self.fail_triangle = triangle
self.fail_witness = other
print "Triangle : " + str(triangle)
print "Other : " + str(other)
print "Other vertex : " + str(vertex)
triangle.debug_distance(vertex)
return False
return True
def setUp(self):
self.triangle = Triangle()
def test_if_list_is_empty(self): triangle = [] T = Triangle(triangle) (res) = T.maximumTotal() self.assertEqual(res,False)
class TriangleTest(unittest.TestCase):
def setUp(self):
path = tempfile.mktemp('.ldb')
db = leveldb.LevelDB(path)
self.triangle = Triangle(db)
def test_it_exists(self):
self.assertTrue(self.triangle)
def test_insertion(self):
wb = mock.Mock()
self.triangle.db = mock.Mock()
with mock.patch('triangle.leveldb.WriteBatch', return_value=wb):
self.triangle.insert(s='Daniel', p='loves', o='Cheese')
self.assertEqual(
sorted(i[0][0] for i in wb.Put.call_args_list),
sorted(['spo::Daniel::loves::Cheese',
'sop::Daniel::Cheese::loves',
'pso::loves::Daniel::Cheese',
'pos::loves::Cheese::Daniel',
'osp::Cheese::Daniel::loves',
'ops::Cheese::loves::Daniel'])
)
def test_retreival(self):
self.triangle.insert(s='Daniel', p='loves', o='Cheese')
self.triangle.insert(s='Daniel', p='loves', o='Sushi')
self.assertEqual(set(self.triangle.start(s='Daniel')), {
('Daniel', 'loves', 'Cheese'),
('Daniel', 'loves', 'Sushi')
})
self.assertEqual(set(self.triangle.start(o='Sushi')), {
('Daniel', 'loves', 'Sushi')
})
def test_retreival_2(self):
self.triangle.insert(s='Daniel', p='loves', o='Cheese')
self.triangle.insert(s='Daniel', p='loves', o='Sushi')
self.assertEqual(set(self.triangle.start(s='Daniel').traverse(o='Cheese')), {
('Daniel', 'loves', 'Cheese'),
})
def test_batch_insert(self):
with self.triangle.batch_insert() as f:
f.insert(s='Daniel', p='loves', o='Cheese')
f.insert(s='Daniel', p='loves', o='Sushi')
self.assertEqual(set(self.triangle.start(s='Daniel')), {
('Daniel', 'loves', 'Cheese'),
('Daniel', 'loves', 'Sushi')
})
def test_exception_rolls_back(self):
try:
with self.triangle.batch_insert() as f:
f.insert(s='Daniel', p='loves', o='Cheese')
f.insert(s='Daniel', p='loves', o='Sushi')
0/0
except ZeroDivisionError:
pass
self.assertEqual(len(set(self.triangle.start(s='Daniel'))), 0)
def test_graph_of_the_gods(self):
path = os.path.join(
os.path.dirname(os.path.abspath(__file__)),
'data/graph_of_the_gods.json'
)
with open(path) as f:
graph = json.loads(f.read())
vertex_map = {}
for v in graph['node']:
vertex_map[v['-id']] = v['data'][1]['#text'] + ':' + v['data'][0]['#text']
with self.triangle.batch_insert() as h:
for e in graph['edge']:
s = vertex_map[e['-source']]
o = vertex_map[e['-target']]
p = e['-label']
h.insert(s=s, p=p, o=o)
# Where do gods live?
self.assertEqual(
sorted(list(self.triangle.start(s='god').traverse(p='lives'))),
sorted([('god:jupiter', 'lives', 'location:sky'),
('god:neptune', 'lives', 'location:sea'),
('god:pluto', 'lives', 'location:tartarus')])
)
# Usually gods live in the sky
self.assertEqual(
list(self.triangle.start(s='god').traverse(p='lives').traverse(o='location:sky')),
[('god:jupiter', 'lives', 'location:sky')]
)
result = (
vs(self.triangle.start(s='demigod')) &
vs(self.triangle.start(p='mother').traverse(o='human:alcmene'))
)
self.assertEqual(result, {'demigod:hercules'})
def _remove(self, site, points, triangles):
'''
Update the triangulation by removing the surrounding triangles
and then filling this cavity with new Delaunay triangles.
Challenge: Maintain neighborhood control.
Ref: Mir Abolfazl Mostafavi, Christopher Gold, and Maciej Dakowicz.
2003. Delete and insert operations in Voronoi/Delaunay methods
and applications. Comput. Geosci. 29, 4 (May 2003), 523-530.
DOI=10.1016/S0098-3004(03)00017-7
http://dx.doi.org/10.1016/S0098-3004(03)00017-7
'''
# verify compatibility of surrounding points and old triangles
if len(points) != len(triangles):
raise Exception("Triangulation has different sizes.")
# verify is the triangulation is empty (or insufficient?)
if len(points) < 3:
return
# initialize new triangulation controls
i = -1
new_triangles = {}
# while there are points to form more than the last triangle
while len(points) > 3:
# checks the possible triangles considering
# all three consecutive points (i, i1, i2 in a cycle)
# of surrounding points of the site
i += 1
npoints = len(points)
if (i >= npoints):
raise Exception("Inexists a valid ear? Is it possible?")
i1 = (i + 1) % npoints
i2 = (i1 + 1) % npoints
# verify if points represent a valid triangle to site,
# like a ear listen to the site:
# 1: gets triangle orientation (CW or CCW)
o_ear = Triangle.orientation(points[i], points[i1], points[i2])
# 2: gets direction of triangle to the site (CW or CCW)
o_ear_site = Triangle.orientation(points[i], points[i2], site)
# 3: if points are collinear, try another edge as a reference
# ??why don't take this edge at first place??
if o_ear_site == 0:
o_ear_site = Triangle.orientation(points[i], points[i1], site)
# 4: the directions is the same?
if (o_ear * o_ear_site) > 0:
# if so, this a valid ear (possible triangulation)
valid_ear = Triangle(points[i], points[i1], points[i2])
# verify if this ear is a Delaunay Triangulation
ear_is_delaunay = True
# 1. for all other surrounding points
for p in points:
# 1.1: is this other point (not in ear)?
if not valid_ear.contains(p):
# verify if ear won't circumcircle it
if valid_ear.circumscribe(p):
# if circumcircle, ear is not a Delaunay triangle
ear_is_delaunay = False
break
# if it is a Delaunay triangle...
if ear_is_delaunay:
# include to new triangle control
new_triangles[valid_ear] = None
# include to neighborhood control
self.neighborhood[valid_ear] = {}
# link to the opposite triangles from the removed vertices
self._link_ear(site, valid_ear, triangles[i],
new_triangles)
self._link_ear(site, valid_ear, triangles[i1],
new_triangles)
# change triangle related to vertex by the new one
# remove old triangle by switching the diagonal
triangles[i] = valid_ear
# remove middle point (leave the corners)
del points[i1]
del triangles[i1]
# restart cycle of surrounding points
i = -1
# if has only three neighbours remaining in the surrounding points,
# merged these three points (triangles) into last triangulation
last_ear = Triangle(points[0], points[1], points[2])
self.neighborhood[last_ear] = {}
new_triangles[last_ear] = None
# last triangle closes the triangulation and
# needs update the link with all sides (neighborhood)
self._link_ear(site, last_ear, triangles[0], new_triangles)
self._link_ear(site, last_ear, triangles[1], new_triangles)
self._link_ear(site, last_ear, triangles[2], new_triangles)
if self.main_site is not None:
if self.main_site == site:
self.main_site = None
self._new_version()
if self.check_triangulation:
if not self.valid():
print "### Removing failure"
"""
"""
from point import Point
from line import Line
from triangle import Triangle
__author__ = "liuyang"
if __name__ == "__main__":
points = []
with open("test_case.txt") as f:
ps = map(float, filter(str.isdigit, map(str.strip, f.readlines())))
for i in range(0, len(ps), 2):
points.append(Point(ps[i], ps[i + 1]))
ps = points[9:12]
for point in ps:
print(point)
triangle = Triangle(ps)
print(triangle.isTriangle())
def test_maximumTotal_return_true_result(self): triangle = [[6],[3,5],[9,7,1],[4,6,8,4]] T = Triangle(triangle) (val, path) = T.maximumTotal() self.assertEqual(val,26) self.assertEqual(path, [0, 1, 1, 2] )
class App:
def __init__(self, master):
self.dim = 500
#init vars
self.got_edge = 0
#self.move_line = 0
#self.move_oval = 0
self.anistack = deque()
self.moveanistack = deque()
# create paining area
self.canv = Canvas(root, width = self.dim, height = self.dim)
self.canv.bind("<Button-1>", self.clicked)
self.canv.bind("<B1-Motion>", self.moved)
self.canv.bind("<ButtonRelease-1>", self.released)
self.canv.pack()
self.tri = Triangle([50,70],[300,300],[400,100])
self.tri.id = self.canv.create_polygon(self.tri.coo,fill='yellow')
frame = Frame(master)
frame.pack()
self.button = Button(frame, text="QUIT", fg="red", command=frame.quit)
self.button.pack(side=LEFT)
self.hi_there = Button(frame, text="Reset", command=self.reset)
self.hi_there.pack(side=LEFT)
def reset(self):
print "reset isn't yet implemented, please just restart :)"
def clicked(self, event) :
#global xo, yo, got_edge, move_line, move_oval
tol = 40 #egde snap tolerance, in sqrt(tol) = radius
r = 6 #radius of moving animation
#init vars and shortcut
self.xo = xo = event.x
self.yo = yo = event.y
self.p = array([xo,yo])
self.got_edge = 0
tri = self.tri.coo
for i in range(3):
if (xo-tri[i][0])*(xo-tri[i][0])+(yo-tri[i][1])*(yo-tri[i][1]) < tol:
self.got_edge = i+1
#print 'got edge',i
# if not clicking on a edge
if self.got_edge == 0:
isInSide=self.tri.isIn(xo,yo) # collision detection
self.ani(xo,yo,isInSide)
#move_line = self.canv.create_line(xo, yo, xo, yo)
#move_oval = self.canv.create_oval(xo - r, yo - r, xo + r, yo + r)
#self.moveanistack.append([move_line, move_oval])
#this is the simplified crossp
def cp(self,x,y):
return x[0]*y[1]-x[1]*y[0] #collision detection
# collision detection moved to triangle class, as for each object different...
# def colDet(self,xo,yo):
# basic idea: take crossproduct(AP, AC) and crossp(AB, AP)
# if they have the same sign, p is inside a cone
# do the same with (BP, BA) and (BC, BP)
# crossp(A,B) in 2d is simply: Ax*By-Ay*Bx
# x,y have same sign <=> x*y>0 use div because of overflowss occuring
#create some shortcuts
# A=array(self.tri.a)
# B=array(self.tri.b)
# C=array(self.tri.c)
# P=array(self.p)
#print self.tri.a, B, C, P
#print type(self.tri.a), type(B), type(C), type(P)
# if self.cp(P-A,C-A)//self.cp(B-A,P-A)>=0:
# if self.cp(P-B,A-B)//self.cp(C-B,P-B)>=0:
# return True
# return False
def moved(self, event) :
# coordinates moved to
x = event.x
y = event.y
if self.got_edge == 0:pass
#while len(self.moveanistack)>1:
# ml, mo = self.moveanistack.popleft()
# self.canv.delete(ml)
# self.canv.delete(mo)
#ml, mo = self.moveanistack.pop()
#self.canv.coords(ml,xo,yo,x,y)
#self.canv.coords(mo,x - 6, y - 6, x + 6, y + 6)
else:
self.tri.set_coo([[x,y],self.got_edge-1])
self.canv.delete(self.tri.id)
#print '-------------\n',self.tri.coo
area = self.tri.getArea()
area = area*255//(self.dim*self.dim)
if area>255:area=255
#print '-------------\n',area
color = "#%02x%02x%02x" % (255, 255-area, 0)
self.tri.id = self.canv.create_polygon(self.tri.get_c(),fill=color)
self.canv.update()
def released(self, event):
#if self.got_edge == 0:
# while len(self.moveanistack)>0:
# ml, mo = self.moveanistack.popleft()
# self.canv.delete(ml)
# self.canv.delete(mo)
self.got_edge = 0
def ani(self,x,y,isOn):
#clean up the stack, delete all remaining animation artifacts
while len(self.anistack) > 0:
self.canv.delete(self.anistack.popleft())
if isOn: color="green"
else: color = "red"
f = 1 # size factor
for i in range(50,0,-1):
ani = self.canv.create_oval(x - f*i, y - f*i, x + f*i, y + f*i)
self.anistack.append(ani)
self.canv.itemconfigure(ani,fill=color)
self.canv.update()
self.canv.after(5)
if len(self.anistack)>0:
self.canv.delete(self.anistack.pop())
