def drawImage3D(image,nx=0,ny=0,pixel='dot'):
"""Draw an image as a colored Formex
Draws a raster image as a colored Formex. While there are other and
better ways to display an image in pyFormex (such as using the imageView
widget), this function allows for interactive handling the image using
the OpenGL infrastructure.
Parameters:
- `image`: a QImage or any data that can be converted to a QImage,
e.g. the name of a raster image file.
- `nx`,`ny`: width and height (in cells) of the Formex grid.
If the supplied image has a different size, it will be rescaled.
Values <= 0 will be replaced with the corresponding actual size of
the image.
- `pixel`: the Formex representing a single pixel. It should be either
a single element Formex, or one of the strings 'dot' or 'quad'. If 'dot'
a single point will be used, if 'quad' a unit square. The difference
will be important when zooming in. The default is 'dot'.
Returns the drawn Actor.
See also :func:`drawImage`.
"""
pf.GUI.setBusy()
from pyformex.plugins.imagearray import qimage2glcolor, resizeImage
from pyformex.opengl.colors import GLcolorA
# Create the colors
#print("TYPE %s" % type(image))
if isinstance(image,np.ndarray):
# undocumented feature: allow direct draw of 2d array
color = GLcolorA(image)
nx,ny = color.shape[:2]
colortable = None
print(color)
else:
image = resizeImage(image, nx, ny)
nx, ny = image.width(), image.height()
color, colortable = qimage2glcolor(image)
# Create a 2D grid of nx*ny elements
# !! THIS CAN PROBABLY BE DONE FASTER
if isinstance(pixel, Formex) and pixel.nelems()==1:
F = pixel
elif pixel == 'quad':
F = Formex('4:0123')
else:
F = Formex('1:0')
F = F.replic2(nx, ny).centered()
F._imageshape_ = (nx,ny)
# Draw the grid using the image colors
FA = draw(F, color=color, colormap=colortable, nolight=True)
pf.GUI.setBusy(False)
return FA
def sector(r, t, nr, nt, h=0., diag=None):
"""Constructs a Formex which is a sector of a circle/cone.
A sector with radius r and angle t is modeled by dividing the
radius in nr parts and the angle in nt parts and then creating
straight line segments.
If a nonzero value of h is given, a conical surface results with its
top at the origin and the base circle of the cone at z=h.
The default is for all points to be in the (x,y) plane.
By default, a plex-4 Formex results. The central quads will collapse
into triangles.
If diag='up' or diag = 'down', all quads are divided by an up directed
diagonal and a plex-3 Formex results.
"""
r = float(r)
t = float(t)
p = Formex(regularGrid([0., 0., 0.], [r, 0., 0.], [nr, 0, 0],swapaxes=True).reshape(-1, 3))
if h != 0.:
p = p.shear(2, 0, h / r)
q = p.rotate(t / nt)
if isinstance(diag, str):
diag = diag[0]
if diag == 'u':
F = connect([p, p, q], bias=[0, 1, 1]) + \
connect([p, q, q], bias=[1, 2, 1])
elif diag == 'd':
F = connect([q, p, q], bias=[0, 1, 1]) + \
connect([p, p, q], bias=[1, 2, 1])
else:
F = connect([p, p, q, q], bias=[0, 1, 1, 0])
F = Formex.concatenate([F.rotate(i * t / nt) for i in range(nt)])
return F
def boxes(x):
"""Create a set of cuboid boxes.
`x`: Coords with shape (nelems,2,3), usually with x[:,0,:] < x[:,1,:]
Returns a Formex with shape (nelems,8,3) and of type 'hex8',
where each element is the cuboid box which has x[:,0,:]
as its minimum coordinates and x[:,1,:] as the maximum ones.
Note that the elements may be degenerate or reverted if the minimum
coordinates are not smaller than the maximum ones.
This function can be used to visualize the bboxes() of a geometry.
"""
x = Coords(x).reshape(-1, 2, 3)
i = [[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[0, 1, 0],
[0, 0, 1],
[1, 0, 1],
[1, 1, 1],
[0, 1, 1]]
j = [0, 1, 2]
return Formex(x[:, i, j], eltype='hex8')
def boxes2d(x):
"""Create a set of rectangular boxes.
Parameters:
- `x`: Coords with shape (nelems,2,3), usually with x[:,0,:] < x[:,1,:]
and x[:,:,2] == 0.
Returns a Formex with shape (nelems,4,3) and of type 'quad4',
where each element is the rectangular box which has x[:,0,:]
as its minimum coordinates and x[:,1,:] as the maximum ones.
Note that the elements may be degenerate or reverted if the minimum
coordinates are not smaller than the maximum ones.
This function is a 2D version of :meth:`bboxes`.
"""
x = Coords(x).reshape(-1, 2, 3)
i = [[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[0, 1, 0]]
j = [0, 1, 2]
return Formex(x[:, i, j], eltype='quad4')
def line(p1=[0., 0., 0.], p2=[1., 0., 0.], n=1):
"""Return a Formex which is a line between two specified points.
p1: first point, p2: second point
The line is split up in n segments.
"""
return Formex([[p1, p2]]).divide(n)
def circle(a1=2., a2=0., a3=360., r=None, n=None, c=None, eltype='line2'):
"""A polygonal approximation of a circle or arc.
All points generated by this function lie on a circle with unit radius at
the origin in the x-y-plane.
- `a1`: the angle enclosed between the start and end points of each line
segment (dash angle).
- `a2`: the angle enclosed between the start points of two subsequent line
segments (module angle). If ``a2==0.0``, `a2` will be taken equal to `a1`.
- `a3`: the total angle enclosed between the first point of the first
segment and the end point of the last segment (arc angle).
All angles are given in degrees and are measured in the direction from
x- to y-axis. The first point of the first segment is always on the x-axis.
The default values produce a full circle (approximately).
If $a3 < 360$, the result is an arc.
Large values of `a1` and `a2` result in polygons. Thus
`circle(120.)` is an equilateral triangle and `circle(60.)`
is regular hexagon.
Remark that the default a2 == a1 produces a continuous line,
while a2 > a1 results in a dashed line.
Three optional arguments can be added to scale and position the circle
in 3D space:
- `r`: the radius of the circle
- `n`: the normal on the plane of the circle
- `c`: the center of the circle
"""
if a2 == 0.0:
a2 = a1
ns = round(a3/a2)
a1 *= pi/180.
if eltype=='line2':
F = Formex([[[1., 0., 0.], [cos(a1), sin(a1), 0.]]]).rosette(ns, a2, axis=2, point=[0., 0., 0.])
elif eltype=='line3':
F = Formex([[[1., 0., 0.], [cos(a1/2.), sin(a1/2.), 0.], [cos(a1), sin(a1), 0.]]], eltype=eltype).rosette(ns, a2, axis=2, point=[0., 0., 0.])
if r is not None:
F = F.scale(r)
if n is not None:
F = F.swapAxes(0, 2).rotate(rotMatrix(n))
if c is not None:
F = F.trl(c)
return F
def __init__(self,
x1,
y1,
x2,
y2,
nx=1,
ny=1,
lighting=False,
rendertype=2,
**kargs):
F = Formex([[[x1,y1],[x1,y2]]]).replic(nx+1,step=float(x2-x1)/nx,dir=0) + \
Formex([[[x1,y1],[x2,y1]]]).replic(ny+1,step=float(y2-y1)/ny,dir=1)
Actor.__init__(self,
F,
rendertype=rendertype,
lighting=lighting,
**kargs)
def triangle():
"""An equilateral triangle with base [0,1] on axis 0.
Returns an equilateral triangle with side length 1.
The first point is the origin, the second points is on the axis 0.
The return value is a plex-3 Formex.
"""
return Formex([[[0., 0., 0.], [1., 0., 0.], [0.5, 0.5 * sqrt(3.), 0.]]])
def Cube():
"""Create the surface of a cube
Returns a TriSurface representing the surface of a unit cube.
Each face of the cube is represented by two triangles.
"""
from pyformex.trisurface import TriSurface
back = Formex('3:012934')
fb = back.reverse() + back.translate(2, 1)
faces = fb + fb.rollAxes(1) + fb.rollAxes(2)
return TriSurface(faces)
def shape(name):
"""Return a Formex with one of the predefined named shapes.
This is a convenience function returning a plex-2 Formex constructed
from one of the patterns defined in the simple.Pattern dictionary.
Currently, the following pattern names are defined:
'line', 'angle', 'square', 'plus', 'cross', 'diamond', 'rtriangle', 'cube',
'star', 'star3d'.
See the Pattern example.
"""
return Formex(Pattern[name])
def read_gts_intersectioncurve(fn):
import re
from pyformex.formex import Formex
RE = re.compile("^VECT 1 2 0 2 0 (?P<data>.*)$")
r = []
for line in open(fn, 'r'):
m = RE.match(line)
if m:
r.append(m.group('data'))
nelems = len(r)
x = fromstring('\n'.join(r), sep=' ').reshape(-1, 2, 3)
F = Formex(x)
return F
def readFormex(self, nelems, nplex, props, eltype, sep):
"""Read a Formex from a pyFormex geometry file.
The coordinate array for nelems*nplex points is read from the file.
If present, the property numbers for nelems elements are read.
From the coords and props a Formex is created and returned.
"""
ndim = 3
f = at.readArray(self.fil, at.Float, (nelems, nplex, ndim), sep=sep)
if props:
p = at.readArray(self.fil, at.Int, (nelems,), sep=sep)
else:
p = None
return Formex(f, p, eltype)
def rectangle(nx=1, ny=1, b=None, h=None, bias=0., diag=None):
"""Return a Formex representing a rectangular surface.
The rectangle has a size(b,h) divided into (nx,ny) cells.
The default b/h values are equal to nx/ny, resulting in a modular grid.
The rectangle lies in the (x,y) plane, with one corner at [0,0,0].
By default, the elements are quads. By setting diag='u','d' of 'x',
diagonals are added in /, resp. \ and both directions, to form triangles.
"""
if diag == 'x':
base = Formex([[[0.0, 0.0, 0.0], [1.0, -1.0, 0.0], [1.0, 1.0, 0.0]]]).rosette(4, 90.).translate([-1.0, -1.0, 0.0]).scale(0.5)
else:
base = Formex({'u': '3:012934', 'd': '3:016823'}.get(diag, '4:0123'))
if b is None:
sx = 1.
else:
sx = float(b) / nx
if h is None:
sy = 1.
else:
sy = float(h) / ny
return base.replic2(nx, ny, bias=bias).scale([sx, sy, 0.])
def inside(self,pts,atol='auto',multi=True):
"""Test which of the points pts are inside the surface.
Parameters:
- `pts`: a (usually 1-plex) Formex or a data structure that can be used
to initialize a Formex.
Returns an integer array with the indices of the points that are
inside the surface. The indices refer to the onedimensional list
of points as obtained from pts.points().
"""
from pyformex.formex import Formex
if not isinstance(pts, Formex):
pts = Formex(pts)
if atol == 'auto':
atol = pts.dsize()*0.001
# determine bbox of common space of surface and points
bb = bboxIntersection(self, pts)
if (bb[0] > bb[1]).any():
# No bbox intersection: no points inside
return array([], dtype=Int)
# Limit the points to the common part
# Add point numbers as property, to allow return of original numbers
pts.setProp(arange(pts.nelems()))
pts = pts.clip(testBbox(pts, bb, atol=atol))
ins = zeros((3, pts.nelems()), dtype=bool)
if pf.scriptMode == 'script' or not multi:
for i in range(3):
dirs = roll(arange(3), -i)[1:]
# clip the surface perpendicular to the shooting direction
# !! gtsinside seems to fail sometimes when using clipping
S = self#.clip(testBbox(self,bb,dirs=dirs,atol=atol),compact=False)
# find inside points shooting in direction i
ok = gtsinside(S, pts, dir=i)
ins[i, ok] = True
else:
tasks = [(gtsinside, (self, pts, i)) for i in range(3)]
ind = multitask(tasks, 3)
for i in range(3):
ins[i, ind[i]] = True
ok = where(ins.sum(axis=0) > 1)[0]
return pts.prop[ok]
def sphere3(nx, ny, r=1, bot=-90., top=90.):
"""Return a sphere consisting of surface triangles
A sphere with radius r is modeled by the triangles formed by a regular
grid of nx longitude circles, ny latitude circles and their diagonals.
The two sets of triangles can be distinguished by their property number:
1: horizontal at the bottom, 2: horizontal at the top.
The sphere caps can be cut off by specifying top and bottom latitude
angles (measured in degrees from 0 at north pole to 180 at south pole.
"""
base = Formex([[[0, 0, 0], [1, 0, 0], [1, 1, 0]],
[[1, 1, 0], [0, 1, 0], [0, 0, 0]]],
[1, 2])
grid = base.replic2(nx, ny, 1, 1)
s = float(top - bot) / ny
return grid.translate([0, bot / s, 1]).spherical(scale=[360. / nx, s, r])
def sphere2(nx, ny, r=1, bot=-90, top=90):
"""Return a sphere consisting of line elements.
A sphere with radius r is modeled by a regular grid of nx
longitude circles, ny latitude circles and their diagonals.
The 3 sets of lines can be distinguished by their property number:
1: diagonals, 2: meridionals, 3: horizontals.
The sphere caps can be cut off by specifying top and bottom latitude
angles (measured in degrees from 0 at north pole to 180 at south pole.
"""
base = Formex('l:543', [1, 2, 3]) # single cell
d = base.select([0]).replic2(nx, ny, 1, 1) # all diagonals
m = base.select([1]).replic2(nx, ny, 1, 1) # all meridionals
h = base.select([2]).replic2(nx, ny + 1, 1, 1) # all horizontals
grid = m + d + h
s = float(top - bot) / ny
return grid.translate([0, bot / s, 1]).spherical(scale=[360. / nx, s, r])
def __init__(self,
n=(1.0, 0.0, 0.0),
P=(0.0, 0.0, 0.0),
sz=(1., 1., 0.),
color='white',
alpha=0.5,
mode='flatwire',
linecolor='black',
**kargs):
"""A plane perpendicular to the x-axis at the origin."""
from pyformex.formex import Formex
F = Formex('4:0123').replic2(2, 2).centered().scale(sz).rotate(
90., 1).rotate(at.rotMatrix(n)).trl(P)
F.attrib(mode=mode,
lighting=False,
color=color,
alpha=alpha,
linecolor=linecolor)
print("kargs")
print(kargs)
Actor.__init__(self, F, **kargs)
def __init__(self,val,pos,prefix='',**kargs):
# Make sure we have strings
val = [ str(i) for i in val ]
pos = at.checkArray(pos,shape=(len(val),-1))
if len(val) != pos.shape[0]:
raise ValueError("val and pos should have same length")
# concatenate all strings
val = [ prefix+str(v) for v in val ]
cs = at.cumsum([0,] + [ len(v) for v in val ])
val = ''.join(val)
nc = cs[1:] - cs[:-1]
pos = [ at.multiplex(p,n,0) for p,n in zip(pos,nc) ]
pos = np.concatenate(pos,axis=0)
pos = at.multiplex(pos,4,1)
# Create the grids for the strings
F = Formex('4:0123')
grid = Formex.concatenate([ F.replic(n) for n in nc ])
# Create a text with the concatenation
Text.__init__(self,val,pos=pos,grid=grid,**kargs)
def area(self):
"""Compute area inside a polygon.
"""
from pyformex.plugins.section2d import PlaneSection
return PlaneSection(Formex(self.coords)).sectionChar()['A']
def __init__(self,text,pos,gravity=None,size=18,width=None,font=None,lineskip=1.0,grid=None,texmode=4,**kargs):
"""Initialize the Text actor."""
# split the string on newlines
text = str(text).split('\n')
# set pos and offset3d depending on pos type (2D vs 3D rendering)
pos = at.checkArray(pos)
if pos.shape[-1] == 2:
rendertype = 2
pos = [pos[0],pos[1],0.]
offset3d = None
else:
rendertype = 1
offset3d = Coords(pos)
pos = [0.,0.,0.]
if offset3d.ndim > 1:
if offset3d.shape[0] != len(text[0]):
raise ValueError("Length of text(%s) and pos(%s) should match!" % (len(text),len(pos)))
# Flag vertex offset to shader
rendertype = -1
# set the font characteristics
if font is None:
font = FontTexture.default(size)
if isinstance(font,(str,unicode)):
font = FontTexture(font,size)
if width is None:
#print("Font %s / %s" % (font.height,font.width))
aspect = float(font.width) / font.height
width = size * aspect
self.width = width
# set the alignment
if gravity is None:
gravity = 'E'
alignment = ['0','0','0']
if 'W' in gravity:
alignment[0] = '+'
elif 'E' in gravity:
alignment[0] = '-'
if 'S' in gravity:
alignment[1] = '+'
elif 'N' in gravity:
alignment[1] = '-'
alignment = ''.join(alignment)
# record the lengths of the lines, join all characters
# together, create texture coordinates for all characters
# create a geometry grid for the longest line
lt = [ len(t) for t in text ]
text = ''.join(text)
texcoords = font.texCoords(text)
if grid is None:
grid = Formex('4:0123').replic(max(lt))
grid = grid.scale([width,size,0.])
# create the actor for the first line
l = lt[0]
g = grid.select(range(l)).align(alignment,pos)
Actor.__init__(self,g,rendertype=rendertype,texture=font,texmode=texmode,texcoords=texcoords[:l],opak=False,ontop=True,offset3d=offset3d,**kargs)
for k in lt[1:]:
# lower the canvas y-value
pos[1] -= font.height * lineskip
g = grid.select(range(k)).align(alignment,pos)
C = Actor(g,rendertype=rendertype,texture=font,texmode=texmode,texcoords=texcoords[l:l+k],opak=False,ontop=True,offset3d=offset3d,**kargs)
self.children.append(C)
# do next line
l += k
def tetrahedral_inertia(x,density=None,center_only=False):
"""Return the inertia of the volume of a 4-plex Formex.
Parameters:
- `x`: an (ntet,4,3) shaped float array, representing ntet tetrahedrons.
- `density`: optional mass density (ntet,) per tetrahedron
- `center_only`: bool. If True, returns only the total volume, total mass
and center of gravity. This may be used on large models when only these
quantities are required.
Returns a tuple (V,M,C,I) where V is the total volume, M is the total mass,
C is the center of mass (3,) and I is the inertia tensor (6,) of the
tetrahedral model.
Formulas for inertia were based on F. Tonon, J. Math & Stat, 1(1):8-11,2005
Example:
>>> x = Coords([
... [ 8.33220, -11.86875, 0.93355 ],
... [ 0.75523, 5.00000, 16.37072 ],
... [ 52.61236, 5.00000, -5.38580 ],
... [ 2.000000, 5.00000, 3.00000 ],
... ])
>>> F = Formex([x])
>>> print(tetrahedral_center(F.coords))
[ 15.92 0.78 3.73]
>>> print(tetrahedral_volume(F.coords))
[ 1873.23]
>>> print(*tetrahedral_inertia(F.coords))
1873.23 1873.23 [ 15.92 0.78 3.73] [ 43520.32 194711.28 191168.77 4417.66 -46343.16 11996.2 ]
"""
def K(x,y):
x1,x2,x3,x4 = x[:,0], x[:,1], x[:,2], x[:,3]
y1,y2,y3,y4 = y[:,0], y[:,1], y[:,2], y[:,3]
return x1 * (y1+y2+y3+y4) + \
x2 * ( y2+y3+y4) + \
x3 * ( y3+y4) + \
x4 * ( y4)
x = at.checkArray(x,shape=(-1,4,3),kind='f')
v = tetrahedral_volume(x)
V = v.sum()
if density:
v *= density
c = Formex(x).centroids()
M = v.sum()
C = (c*v[:,np.newaxis]).sum(axis=0) / M
if center_only:
return V,M,C
x -= C
aa = 2 * K(x,x) * v.reshape(-1,1)
aa = aa.sum(axis=0)
a0 = aa[1] + aa[2]
a1 = aa[0] + aa[2]
a2 = aa[0] + aa[1]
x0,x1,x2 = x[...,0],x[...,1],x[...,2]
a3 = (( K(x1,x2) + K(x2,x1) ) * v).sum(axis=0)
a4 = (( K(x2,x0) + K(x0,x2) ) * v).sum(axis=0)
a5 = (( K(x0,x1) + K(x1,x0) ) * v).sum(axis=0)
I = np.array([a0,a1,a2,a3,a4,a5]) / 20.
return V,M,C,I
def __init__(self,pos,tex,size,opak=False,ontop=True,**kargs):
self.pos = pos
F = Formex([[[0,0],[1,0],[1,1],[0,1]]]).scale(size).align('000')
Actor.__init__(self,F,rendertype=1,texture=tex,texmode=4,offset3d=pos,opak=opak,ontop=ontop,lighting=False,**kargs)
def Grid(nx=(1, 1, 1),
ox=(0.0, 0.0, 0.0),
dx=(1.0, 1.0, 1.0),
lines='b',
planes='b',
linecolor=colors.black,
planecolor=colors.white,
alpha=0.3,
**kargs):
"""Creates a (set of) grid(s) in (some of) the coordinate planes.
Parameters:
- `nx`: a list of 3 integers, specifying the number of divisions of the
grid in the three coordinate directions. A zero value may be specified
to avoid the grid to extend in that direction. Thus, setting the last
value to zero will result in a planar grid in the xy-plane.
- `ox`: a list of 3 floats: the origin of the grid.
- `dx`: a list of 3 floats: the step size in each coordinate direction.
- `planes`: one of 'first', 'box', 'all', 'no' (the string can be
shortened to the first chartacter): specifies how many planes are
drawn in each direction: 'f' only draws the first, 'b' draws the first
and the last, resulting in a box, 'a' draws all planes,
'n' draws no planes.
Returns a list with up to two Meshes: the planes, and the lines.
"""
from pyformex import simple
from pyformex.olist import List
from pyformex.mesh import Mesh
G = List()
planes = planes[:1].lower()
P = []
L = []
for i in range(3):
n0, n1, n2 = np.roll(nx, i)
d0, d1, d2 = np.roll(dx, i)
if n0 * n1:
if planes != 'n':
M = simple.rectangle(b=n0 * d0, h=n1 * d1)
if n2:
if planes == 'b':
M = M.replic(2, dir=2, step=n2 * d2)
elif planes == 'a':
M = M.replic(n2 + 1, dir=2, step=d2)
P.append(M.rollAxes(-i).toMesh())
if lines != 'n':
M = Formex('1').scale(n0*d0).replic(n1+1,dir=1,step=d1) + \
Formex('2').scale(n1*d1).replic(n0+1,dir=0,step=d0)
if n2:
if lines == 'b':
M = M.replic(2, dir=2, step=n2 * d2)
elif lines == 'a':
M = M.replic(n2 + 1, dir=2, step=d2)
L.append(M.rollAxes(-i).toMesh())
if P:
M = Mesh.concatenate(P)
M.attrib(name='__grid_planes__',
mode='flat',
lighting=False,
color=planecolor,
alpha=alpha,
**kargs)
G.append(M)
if L:
M = Mesh.concatenate(L)
M.attrib(name='__grid_lines__',
mode='flat',
lighting=False,
color=linecolor,
alpha=0.6,
**kargs)
G.append(M)
return G.trl(ox)
def __init__(self, x1, y1, x2, y2, **kargs):
F = Formex([[[x1, y1], [x2, y2]]])
Actor.__init__(self, F, rendertype=2, **kargs)
def __init__(self, data, color=None, linewidth=None, **kargs):
"""Initialize a Lines."""
F = Formex(data)
Actor.__init__(self, F, rendertype=2, **kargs)
def point(x=0., y=0., z=0.):
"""Return a Formex which is a point, by default at the origin.
Each of the coordinates can be specified and is zero by default.
"""
return Formex([[[x, y, z]]])
def toFormex(self):
from pyformex.formex import Formex
x = stack([self.coords, roll(self.coords, -1, axis=0)], axis=1)
return Formex(x)