/*!

\page tui_complex_objs_page Complex Objects

\anchor tui_creation_prism
<br><h2>Creation of a Prism</h2>

\code
import geompy
import salome
gg = salome.ImportComponentGUI("GEOM")

# create a vertex and a vector
p1 = geompy.MakeVertex(   0.,   0.,   0.)
p2 = geompy.MakeVertex( 100.,   0.,   0.)
p3 = geompy.MakeVertex( 100., 100.,   0.)
p4 = geompy.MakeVertex(   0., 100.,   0.)
p5 = geompy.MakeVertex(   0.,   0.,  60.)
p6 = geompy.MakeVertex(-100.,   0.,   0.)
p7 = geompy.MakeVertex(-100.,-100.,   0.)
p8 = geompy.MakeVertex(   0.,-100.,   0.)

# create a vector from the given components
vector = geompy.MakeVectorDXDYDZ(50., 50., 50.)

#create vectors from two points
vector1_arc1 = geompy.MakeVector(p1, p2)
vector2_arc1 = geompy.MakeVector(p1, p4)
vector1_arc2 = geompy.MakeVector(p1, p6)
vector2_arc2 = geompy.MakeVector(p1, p8)

# create arcs from three points
arc1 = geompy.MakeArc(p2, p3, p4)
arc2 = geompy.MakeArc(p6, p7, p8)

# create wires
wire1 = geompy.MakeWire([vector1_arc1, arc1, vector2_arc1])
wire2 = geompy.MakeWire([vector1_arc2, arc2, vector2_arc2])

# create faces
isPlanarWanted = 1
face1 = geompy.MakeFace(wire1, isPlanarWanted)
face2 = geompy.MakeFace(wire2, isPlanarWanted)

# create prisms
prism1 = geompy.MakePrism(face2, p1, p5)
prism2 = geompy.MakePrismVecH(face1, vector, 50)
prism3 = geompy.MakePrismVecH2Ways(face1, vector, 50)

# add objects in the study
id_face1   = geompy.addToStudy(face1,"Face1")
id_face2   = geompy.addToStudy(face2,"Face2")
id_prism1 = geompy.addToStudy(prism1,"Prism1")
id_prism2 = geompy.addToStudy(prism2,"Prism2")
id_prism3 = geompy.addToStudy(prism3,"Prism3")

# display cylinders
gg.createAndDisplayGO(id_face1)
gg.setDisplayMode(id_face1,1)
gg.createAndDisplayGO(id_face2)
gg.setDisplayMode(id_face2,1)
gg.createAndDisplayGO(id_prism1)
gg.setDisplayMode(id_prism1,1)
gg.createAndDisplayGO(id_prism2)
gg.setDisplayMode(id_prism2,1) 
gg.createAndDisplayGO(id_prism3)
gg.setDisplayMode(id_prism3,1) 
\endcode

\anchor tui_creation_revolution
<br><h2>Creation of a Revolution</h2>

\code
import geompy
import salome
gg = salome.ImportComponentGUI("GEOM")

# create a vertex and a vector
p1 = geompy.MakeVertex(  10.,  10.,  10.)
p2 = geompy.MakeVertex(  15.,  15.,  50.)
p3 = geompy.MakeVertex(  40.,  40.,   0.)

#create vectors from two points
vector1 = geompy.MakeVector(p1, p2)
vector2 = geompy.MakeVector(p1, p3)

# create a vector from the given components
vector3 = geompy.MakeVectorDXDYDZ(-20., -20., 100.)

# create a wire
wire = geompy.MakeWire([vector1, vector2])

# create a revolution
revolution = geompy.MakeRevolution(wire, vector3, 2.3)

# add objects in the study
id_vector3    = geompy.addToStudy(vector3,"Axis")
id_wire       = geompy.addToStudy(wire,"Wire")
id_revolution = geompy.addToStudy(revolution,"Revolution")

# display the vector, the wire and the revolution
gg.createAndDisplayGO(id_vector3)
gg.createAndDisplayGO(id_wire)
gg.createAndDisplayGO(id_revolution)
gg.setDisplayMode(id_revolution,1) 
\endcode

\anchor tui_creation_filling
<br><h2>Creation of a Filling</h2>

\code
import geompy
import salome
gg = salome.ImportComponentGUI("GEOM")

mindeg = 2
maxdeg = 5
tol3d  = 0.0001
tol2d  = 0.0001
nbiter = 5

# create a vertex and a vector
p1 = geompy.MakeVertex(  -30.,  -30.,  50.)
p2 = geompy.MakeVertex(  -60.,  -60.,  30.)
p3 = geompy.MakeVertex(  -30.,  -30.,  10.)

# create an arc from three points
arc = geompy.MakeArc(p1, p2, p3)
ShapeListCompound = []
i = 0
while i <= 3 :
    S = geompy.MakeTranslation(arc, i * 50., 0., 0.)
    ShapeListCompound.append(S)
    i = i + 1

compound = geompy.MakeCompound(ShapeListCompound)

# create a filling
filling = geompy.MakeFilling(compound, mindeg, maxdeg, tol3d, tol2d, nbiter)

# add objects in the study
id_compound = geompy.addToStudy(compound,"Compound")
id_filling = geompy.addToStudy(filling,"Filling")

# display the compound and the filling
gg.createAndDisplayGO(id_compound)
gg.createAndDisplayGO(id_filling)
gg.setDisplayMode(id_filling,1) 
\endcode
 
\anchor tui_creation_pipe
<br><h2>Creation of a Pipe</h2>

\code
import geompy
import salome
gg = salome.ImportComponentGUI("GEOM")

# create vertices
p0   = geompy.MakeVertex(0.  , 0.  , 0.  )
px   = geompy.MakeVertex(100., 0.  , 0.  )
py   = geompy.MakeVertex(0.  , 100., 0.  )
pz   = geompy.MakeVertex(0.  , 0.  , 100.)
pxyz = geompy.MakeVertex(100., 100., 100.)

# create a vector from two points
vxy = geompy.MakeVector(px, py)

# create an arc from three points
arc = geompy.MakeArc(py, pz, px)

# create a wire
wire = geompy.MakeWire([vxy, arc])

# create an edge
edge = geompy.MakeEdge(p0, pxyz)

# create a pipe
pipe = geompy.MakePipe(wire, edge)

# add objects in the study
id_wire = geompy.addToStudy(wire,"Wire")
id_edge = geompy.addToStudy(edge,"Edge")
id_pipe = geompy.addToStudy(pipe,"Pipe")

# display the wire, the edge (path) and the pipe
gg.createAndDisplayGO(id_wire)
gg.createAndDisplayGO(id_edge)
gg.createAndDisplayGO(id_pipe)
gg.setDisplayMode(id_pipe,1) 
\endcode

\anchor tui_creation_pipe_with_diff_sec
<br><h2>Creation of a PipeWithDifferentSections</h2>

\code
import geompy
import salome
gg = salome.ImportComponentGUI("GEOM")

Wire_1 = geompy.MakeSketcher("Sketcher:F 0 0:TT 100 0:R 0:C 100 90:T 0 200", [0, 0, 0, 0, 0, 1, 1, 0, -0])
edges = geompy.SubShapeAll(Wire_1, geompy.ShapeType["EDGE"])
vertices = geompy.SubShapeAll(Wire_1, geompy.ShapeType["VERTEX"])

# create sections
circles=[]
circles.append(geompy.MakeCircle(vertices[0], edges[0], 20))
circles.append(geompy.MakeCircle(vertices[1], edges[0], 40))
circles.append(geompy.MakeCircle(vertices[2], edges[2], 30))
circles.append(geompy.MakeCircle(vertices[3], edges[2], 20))

# create pipe
Pipe = geompy.MakePipeWithDifferentSections(circles, vertices, Wire_1, 0, 0)

# add objects in the study
geompy.addToStudy(circles[0], "circles1")
geompy.addToStudy(circles[1], "circles2")
geompy.addToStudy(circles[2], "circles3")
geompy.addToStudy(circles[3], "circles4")
id_wire = geompy.addToStudy(Wire_1, "Path")
id_pipe = geompy.addToStudy(Pipe, "Pipe")

# display the wire(path) and the pipe
gg.createAndDisplayGO(id_wire)
gg.createAndDisplayGO(id_pipe)
gg.setDisplayMode(id_pipe,1) 
\endcode

\anchor tui_creation_pipe_with_shell_sec
<br><h2>Creation of a PipeWithShellSections</h2>

\code
import geompy
import salome
gg = salome.ImportComponentGUI("GEOM")

# create path
WirePath = geompy.MakeSketcher("Sketcher:F 0 0:TT 100 0:R 0:C 100 90:T 0 200", [0, 0, 0, 0, 0, 1, 1, 0, -0])

#=======================================================
#                 Create shell sections
#=======================================================
ps = [Vertex_1,Vertex_2,Vertex_3,Vertex_4]
theLocations = [Vertex_1, Vertex_2, Vertex_3, Vertex_4]
VC = geompy.MakeCompound(theLocations)
geompy.addToStudy(VC,"VC")
vs = [Edge_1,Edge_1,Edge_3,Edge_3]
hs = [20,40,30,20]
shells = []
subbases = []

# 1 section
c0 = geompy.PointCoordinates(ps[0])
c1 = geompy.PointCoordinates(ps[1])
nx = c1[0] - c0[0]
ny = c1[1] - c0[1]
nz = c1[2] - c0[2]

faces = []
f1 = geompy.MakeSketcher("Sketcher:F 0 0:TT 20 0:TT 20 20:TT 0 20:WF",
                         [c0[0], c0[1], c0[2], nx, ny, nz, 0, 0, 1])
f2 = geompy.MakeSketcher("Sketcher:F 0 0:TT 0 20:TT -20 20:TT -20 0:WF",
                         [c0[0], c0[1], c0[2], nx, ny, nz, 0, 0, 1])
f3 = geompy.MakeSketcher("Sketcher:F 0 0:TT -20 0:TT -20 -20:TT 0 -20:WF",
                         [c0[0], c0[1], c0[2], nx, ny, nz, 0, 0, 1])
f4 = geompy.MakeSketcher("Sketcher:F 0 0:TT 0 -20:TT 20 -20:TT 20 0:WF",
                         [c0[0], c0[1], c0[2], nx, ny, nz, 0, 0, 1])
faces.append(f1)
faces.append(f2)
faces.append(f3)
faces.append(f4)
shell = geompy.MakeSewing(faces,1.e-6)
shells.append(shell)
faces = geompy.SubShapeAllSorted(shell, geompy.ShapeType["FACE"])
subbases.append(faces[0])

# 2 section
faces = []

w = geompy.MakeSketcher("Sketcher:F 20 20:TT 0 20:TT 0 0:TT 20 0",
                         [c1[0], c1[1], c1[2], nx, ny, nz, 0, 0, 1])
[e1,e2,e3] = geompy.SubShapeAll(w, geompy.ShapeType["EDGE"])
arc = MakeArc(w,3,-1)
w = geompy.MakeWire([e1,e2,e3,arc])
f1 = geompy.MakeFace(w,1)

w = geompy.MakeSketcher("Sketcher:F -20 0:TT 0 0:TT 0 20:TT -20 20",
                         [c1[0], c1[1], c1[2], nx, ny, nz, 0, 0, 1])
[e1,e2,e3] = geompy.SubShapeAll(w, geompy.ShapeType["EDGE"])
arc = MakeArc(w,3,-1)
w = geompy.MakeWire([e1,e2,e3,arc])
f2 = geompy.MakeFace(w,1)

w = geompy.MakeSketcher("Sketcher:F 20 0:TT 0 0:TT 0 -20:TT 20 -20",
                         [c1[0], c1[1], c1[2], nx, ny, nz, 0, 0, 1])
[e1,e2,e3] = geompy.SubShapeAll(w, geompy.ShapeType["EDGE"])
arc = MakeArc(w,3,-1)
w = geompy.MakeWire([e1,e2,e3,arc])
f3 = geompy.MakeFace(w,1)

w = geompy.MakeSketcher("Sketcher:F -20 -20:TT 0 -20:TT 0 0:TT -20 0",
                         [c1[0], c1[1], c1[2], nx, ny, nz, 0, 0, 1])
[e1,e2,e3] = geompy.SubShapeAll(w, geompy.ShapeType["EDGE"])
arc = MakeArc(w,3,-1)
w = geompy.MakeWire([e1,e2,e3,arc])
f4 = geompy.MakeFace(w,1)

faces.append(f1)
faces.append(f2)
faces.append(f3)
faces.append(f4)
shell = geompy.MakeSewing(faces,1.e-6)
shells.append(shell)
faces = geompy.SubShapeAllSorted(shell, geompy.ShapeType["FACE"])
subbases.append(faces[0])

# 3 section
faces = []
c2 = geompy.PointCoordinates(ps[2])
c3 = geompy.PointCoordinates(ps[3])
nx = c3[0] - c2[0]
ny = c3[1] - c2[1]
nz = c3[2] - c2[2]

w = geompy.MakeSketcher("Sketcher:F 20 20:TT 0 20:TT 0 0:TT 20 0",
                         [c2[0], c2[1], c2[2], nx, ny, nz, 0, 0, 1])
[e1,e2,e3] = geompy.SubShapeAll(w, geompy.ShapeType["EDGE"])
arc = MakeArc(w,3,1)
w = geompy.MakeWire([e1,e2,e3,arc])
f1 = geompy.MakeFace(w,1)

w = geompy.MakeSketcher("Sketcher:F -20 0:TT 0 0:TT 0 20:TT -20 20",
                         [c2[0], c2[1], c2[2], nx, ny, nz, 0, 0, 1])
[e1,e2,e3] = geompy.SubShapeAll(w, geompy.ShapeType["EDGE"])
arc = MakeArc(w,3,1)
w = geompy.MakeWire([e1,e2,e3,arc])
f2 = geompy.MakeFace(w,1)

w = geompy.MakeSketcher("Sketcher:F 20 0:TT 0 0:TT 0 -20:TT 20 -20",
                         [c2[0], c2[1], c2[2], nx, ny, nz, 0, 0, 1])
[e1,e2,e3] = geompy.SubShapeAll(w, geompy.ShapeType["EDGE"])
arc = MakeArc(w,3,1)
w = geompy.MakeWire([e1,e2,e3,arc])
f3 = geompy.MakeFace(w,1)

w = geompy.MakeSketcher("Sketcher:F -20 -20:TT 0 -20:TT 0 0:TT -20 0",
                         [c2[0], c2[1], c2[2], nx, ny, nz, 0, 0, 1])
[e1,e2,e3] = geompy.SubShapeAll(w, geompy.ShapeType["EDGE"])
arc = MakeArc(w,3,1)
w = geompy.MakeWire([e1,e2,e3,arc])
f4 = geompy.MakeFace(w,1)

faces.append(f1)
faces.append(f2)
faces.append(f3)
faces.append(f4)
shell = geompy.MakeSewing(faces,1.e-6)
shells.append(shell)
faces = geompy.SubShapeAllSorted(shell, geompy.ShapeType["FACE"])
subbases.append(faces[2])

# 4 section
faces = []

kk = 4
dx = c3[0] - nx/kk
dy = c3[1] - ny/kk
dz = c3[2] - nz/kk
rad = math.sqrt(nx*nx+ny*ny+nz*nz)
vc = geompy.MakeVertex(dx,dy,dz)
sph = geompy.MakeSpherePntR(vc,rad/kk)
shellsph = geompy.SubShapeAll(sph, geompy.ShapeType["SHELL"])

fs = []
vec = geompy.MakeVectorDXDYDZ(0,0,1)
ff = geompy.MakePlane(ps[3],vec,40)
fs.append(ff)
vp = geompy.MakeVertex(c3[0],c3[1],c3[2]+20)
ff = geompy.MakePlane(vp,vec,40)
fs.append(ff)
vp = geompy.MakeVertex(c3[0],c3[1],c3[2]-20)
ff = geompy.MakePlane(vp,vec,40)
fs.append(ff)
vec = geompy.MakeVectorDXDYDZ(1,0,0)
ff = geompy.MakePlane(ps[3],vec,40)
fs.append(ff)
vp = geompy.MakeVertex(c3[0]+20,c3[1],c3[2])
ff = geompy.MakePlane(vp,vec,40)
fs.append(ff)
vp = geompy.MakeVertex(c3[0]-20,c3[1],c3[2])
ff = geompy.MakePlane(vp,vec,40)
fs.append(ff)
aPartition = geompy.MakePartition(shellsph,fs)
fs = geompy.SubShapeAllSorted(aPartition, geompy.ShapeType["FACE"])

faces.append(fs[0])
faces.append(fs[1])
faces.append(fs[2])
faces.append(fs[3])
shell = geompy.MakeSewing(faces,1.e-6)
shells.append(shell)
faces = geompy.SubShapeAllSorted(shell, geompy.ShapeType["FACE"])


#===========================================================
#                   Create Pipe
#===========================================================
subbases = []
Pipe = geompy.MakePipeWithShellSections(shells, subbases, theLocations, WirePath,
                                        theWithContact=0, theWithCorrection=0)

# add objects in the study
resc = geompy.MakeCompound(shells)
id_sec = geompy.addToStudy(resc,"sections")
id_wire = geompy.addToStudy(WirePath,"WirePath")
id_pipe = geompy.addToStudy(Pipe, "Pipe")

# display the wire(path), sections and the pipe
gg.createAndDisplayGO(id_wire)
gg.createAndDisplayGO(id_sec)
gg.createAndDisplayGO(id_pipe)
gg.setDisplayMode(id_pipe,1) 
\endcode


\anchor tui_creation_pipe_without_path
<br><h2>Creation of a PipeShellsWithoutPath</h2>

\code
import geompy
import math
import salome
gg = salome.ImportComponentGUI("GEOM")

# Add a section based on quadrangles
# ----------------------------------
def section(s, p1, p2=None, p3=None, p4=None):
    if p2==None:
        q = p1
    else:
        q = geompy.MakeQuad4Vertices(p1, p2, p3, p4)
        pass
    s.append(q)
    publish(q, "section")
    return q


# find distance between two points
# -------------------------------
def Dist(p1,p2):
    c1 = geompy.PointCoordinates(p1)
    c2 = geompy.PointCoordinates(p2)
    return math.sqrt( (c2[0]-c1[0])*(c2[0]-c1[0]) +
                      (c2[1]-c1[1])*(c2[1]-c1[1]) +
                      (c2[2]-c1[2])*(c2[2]-c1[2]) )


# return middle point
# -------------------------------
def MiddleVert(p1,p2):
    c1 = geompy.PointCoordinates(p1)
    c2 = geompy.PointCoordinates(p2)
    return geompy.MakeVertex( (c2[0]+c1[0])/2, (c2[1]+c1[1])/2, (c2[2]+c1[2])/2 )


# Complex section
# result - 16 quads from lines
# pnt - point from path
# vec - direction from path
def MakeComplexSect(pnt,vec,rmax,rmin,nb):
    dang = 1.0/nb/2
    cmax = geompy.MakeCircle(pnt,vec,rmax)
    cmin = geompy.MakeCircle(pnt,vec,rmin)
    faces = []
    for i in range(0,2*nb,2):
        p1 = geompy.MakeVertexOnCurve(cmin,dang*i)
        p2 = geompy.MakeVertexOnCurve(cmax,dang*(i+1))
        p3 = geompy.MakeVertexOnCurve(cmin,dang*(i+2))
        f = geompy.MakeQuad4Vertices(pnt,p1,p2,p3)
        faces.append(f)
        pass
    shell = geompy.MakeSewing(faces,1.e-6)
    return shell


#=======================================================
#       Create simple path and recieve points
#              for section creation
#=======================================================
WirePath = geompy.MakeSketcher("Sketcher:F 0 0:T 60 0:T 40 0:R 0:C 100 90:",
                               [0, 0, 0, 0, 0, 1, 1, 0, 0])
vs = geompy.SubShapeAll(WirePath, geompy.ShapeType["VERTEX"])

#=======================================================
#                 Create shell sections
#=======================================================
shells = []
subbases = []
locs = []

# 1 section
shell = MakeComplexSect(vs[0], geompy.MakeVectorDXDYDZ(1,0,0), 60, 40, 16)
shells.append(shell)
vs1 = geompy.SubShapeAllSorted(shell,geompy.ShapeType["VERTEX"])
locs.append(vs1[17])

# 2 section
shell = MakeComplexSect(vs[1], geompy.MakeVectorDXDYDZ(1,0,0), 80, 30, 16)
shells.append(shell)
vs2 = geompy.SubShapeAllSorted(shell,geompy.ShapeType["VERTEX"])
locs.append(vs2[17])

# 3 section
shell = MakeComplexSect(vs[2], geompy.MakeVectorDXDYDZ(1,0,0), 60, 40, 16)
shells.append(shell)
vs3 = geompy.SubShapeAllSorted(shell,geompy.ShapeType["VERTEX"])
locs.append(vs3[17])

# 4 section
shell = MakeComplexSect(vs[3], geompy.MakeVectorDXDYDZ(0,1,0), 40, 35, 16)
shells.append(shell)
vs4 = geompy.SubShapeAllSorted(shell,geompy.ShapeType["VERTEX"])
locs.append(vs4[17])


#===========================================================
#                   Create Pipe
#===========================================================

Pipe = geompy.MakePipeShellsWithoutPath(shells,locs)

# add objects in the study
resc = geompy.MakeCompound(shells)
id_sec = geompy.addToStudy(resc,"sections")
resl = geompy.MakeCompound(locs)
id_loc = geompy.addToStudy(resl,"locations")
id_pipe = geompy.addToStudy(Pipe, "Pipe")

# display the sections, locations and pipe
gg.createAndDisplayGO(id_sec)
gg.createAndDisplayGO(id_loc)
gg.createAndDisplayGO(id_pipe)
gg.setDisplayMode(id_pipe,1) 
\endcode

\anchor tui_creation_pipe_binormal_along_vector
<br><h2>Creation of a PipeBiNormalAlongVector</h2>

\code
def MakeHelix(radius, height, rotation, direction):
    #  - create a helix -
    radius = 1.0 * radius
    height = 1.0 * height
    rotation = 1.0 * rotation
    if direction > 0:
        direction = +1
    else:
        direction = -1
        pass
    from math import sqrt
    length_z  = height
    length_xy = radius*rotation
    length = sqrt(length_z*length_z + length_xy*length_xy)
    import geompy
    nb_steps = 1
    epsilon = 1.0e-6
    while 1:
        z_step = height / nb_steps
        angle_step = rotation / nb_steps
        z = 0.0
        angle = 0.0
        helix_points = []
        for n in range(nb_steps+1):
            from math import cos, sin
            x = radius * cos(angle)
            y = radius * sin(angle)
            p = geompy.MakeVertex(x, y, z)
            helix_points.append( p )
            z += z_step
            angle += direction * angle_step
            pass
        helix = geompy.MakeInterpol(helix_points)
        length_test = geompy.BasicProperties(helix)[0]
        prec = abs(length-length_test)/length
        # print nb_steps, length_test, prec
        if prec < epsilon:
            break
        nb_steps *= 2
        pass
    return helix

def MakeSpring(radius, height, rotation, direction, thread_radius, base_rotation=0.0):
    #  - create a pipe -
    thread_radius = 1.0 * thread_radius
    # create a helix
    helix = MakeHelix(radius, height, rotation, direction)
    # base in the (Ox, Oz) plane
    import geompy
    p0 = geompy.MakeVertex(radius-3*thread_radius, 0.0, -thread_radius)
    p1 = geompy.MakeVertex(radius+3*thread_radius, 0.0, -thread_radius)
    p2 = geompy.MakeVertex(radius+3*thread_radius, 0.0, +thread_radius)
    p3 = geompy.MakeVertex(radius-3*thread_radius, 0.0, +thread_radius)
    e0 = geompy.MakeEdge(p0, p1)
    e1 = geompy.MakeEdge(p1, p2)
    e2 = geompy.MakeEdge(p2, p3)
    e3 = geompy.MakeEdge(p3, p0)
    w = geompy.MakeWire([e0, e1, e2, e3])
    # create a base face
    base = geompy.MakeFace(w, True)
    # create a binormal vector
    binormal = geompy.MakeVectorDXDYDZ(0.0, 0.0, 10.0)
    # create a pipe
    spring = geompy.MakePipeBiNormalAlongVector(base, helix, binormal)
    # Publish in the study
    geompy.addToStudy(base, "base")
    geompy.addToStudy(helix, "helix")
    geompy.addToStudy(binormal, "binormal")
    geompy.addToStudy(spring, "spring")
    return spring

from math import pi

spring = MakeSpring(50, 100, 2*pi, 1, 5, pi/2)
\endcode

*/