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<p>Hi Ian,</p>
<p>Thank you for your reply.</p>
<p>The modification you provided correctly finds the zero area
element, and masks it from the triangulation. In the example from
the previous post, masking the zero area element works.</p>
<p>When I try and make a slightly different triangulation (see
below), and try to mask the zero area elements, I still get an
invalid triangulation. I am using v1.4.2. Do you have a sense as
to what could be going on here?</p>
<p>Thanks,<br>
</p>
<p>Pat</p>
<p>import matplotlib.tri as mtri<br>
import numpy as np<br>
<br>
# manually construct an invalid triangulation<br>
x = np.array([0.0, 1.0, 1.0, 1.0, 2.0])<br>
y = np.array([1.0, 0.0, 2.0, 1.0, 1.0])<br>
z = np.zeros(5)<br>
<br>
# slightly modified from what I originally posted<br>
triangles = np.array( [[0, 1, 4], [2, 3, 4], [0, 3, 2], [0, 4,
3]])<br>
<br>
# create a Matplotlib Triangulation<br>
triang = mtri.Triangulation(x,y,triangles)<br>
<br>
# ---------- start of new code ----------<br>
xy = np.dstack((triang.x[triang.triangles],
triang.y[triang.triangles])) #shape (ntri,3,2)<br>
twice_area = np.cross(xy[:,1,:] - xy[:,0,:], xy[:,2,:] -
xy[:,0,:]) # shape (ntri)<br>
mask = twice_area < 1e-10 # shape (ntri)<br>
<br>
if np.any(mask):<br>
triang.set_mask(mask)<br>
# ---------- end of new code ----------<br>
<br>
# to perform the linear interpolation<br>
interpolator = mtri.LinearTriInterpolator(triang, z)<br>
m_z = interpolator(1.0, 1.0)<br>
</p>
<div class="moz-cite-prefix">On 11/21/2016 03:47 AM, Ian Thomas
wrote:<br>
</div>
<blockquote
cite="mid:CAH53=NYQnxNofi-tkJ7v6aHcZrQwyins3nE3=RkgYK2WNoQu-g@mail.gmail.com"
type="cite">
<div dir="ltr">
<div>
<div>
<div>Hello Pat,<br>
<br>
</div>
The solution is to use the function Triangulation.set_mask()
to mask out the zero-area triangles. The masked-out
triangles will be ignored in subsequent calls to
LinearTriInterpolator, tricontourf, etc. For example:<br>
<br>
# +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-<wbr>+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-<wbr>+-+-+-+-+-<br>
import matplotlib.tri as mtri<br>
import numpy as np<br>
<br>
# manually construct an invalid triangulation having a zero
area element<br>
x = np.array([0.0, 1.0, 1.0, 1.0, 2.0])<br>
y = np.array([1.0, 0.0, 2.0, 1.0, 1.0])<br>
z = np.zeros(5)<br>
<br>
triangles = np.array( [[0, 1, 2], [1, 3, 2], [1, 4, 2], [0,
4, 1]])<br>
<br>
# create a Matplotlib Triangulation<br>
triang = mtri.Triangulation(x,y,triangles)<br>
<br>
# ---------- start of new code ----------<br>
xy = np.dstack((triang.x[triang.triangles],
triang.y[triang.triangles])) # shape (ntri,3,2)<br>
twice_area = np.cross(xy[:,1,:] - xy[:,0,:], xy[:,2,:] -
xy[:,0,:]) # shape (ntri)<br>
mask = twice_area < 1e-10 # shape (ntri)<br>
<br>
if np.any(mask):<br>
triang.set_mask(mask)<br>
# ---------- end of new code ----------<br>
<br>
# to perform the linear interpolation<br>
interpolator = mtri.LinearTriInterpolator(triang, z)<br>
m_z = interpolator(1.0, 1.0)<br>
# +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-<wbr>+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-<wbr>+-+-+-+-+-<br>
<br>
</div>
Note that I have used a small positive number to test the
triangle areas against rather than zero. This is to avoid
problems with rounding errors. You may need to alter this
threshold.<br>
<br>
</div>
Ian<br>
<div>
<div><br>
</div>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On 19 November 2016 at 12:24, Pat
Prodanovic <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:pprodano@gmail.com" target="_blank">pprodano@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">Hello,<br>
<br>
I am using JR Shewchuk's Triangle to create triangulations
for use in floodplain modeling. I am using a city's
digital terrain model with hundreds of thousands of
breaklines that constrain where triangles can form in the
triangulations (streets, rivers, etc). Triangle does this
very efficiently.<br>
<br>
Sometimes the input topology I am using has bad inputs
which makes Triangle create zero area elements. When I
import these triangulations to Matplotlib I get the error
that such triangulations are invalid (when using the
LinearTriInterpolator() method). I understand the
trapezoid map algorithm implemented requires only valid
triangulations. So far, so good.<br>
<br>
The option of cleaning the input topology before using
Matplotlib exists, but it is really cumbersome. Rather
than topology cleaning, am I am able to somehow throw out
the zero area elements from the call to
LinearTriInterpolator() method, and still use the
triangulation in Matplotlib? My other alternative is to
use something other than trapezoidal map algorithm, but
this is just not computationally efficient.<br>
<br>
I've reproduced the following example that illustrates the
problem in a small code snippet. Any suggestions?<br>
<br>
Thanks,<br>
<br>
Pat Prodanovic<br>
<br>
# +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-<wbr>+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-<wbr>+-+-+-+-+-<br>
import matplotlib.tri as mtri<br>
import numpy as np<br>
<br>
# manually construct an invalid triangulation having a
zero area element<br>
x = np.array([0.0, 1.0, 1.0, 1.0, 2.0])<br>
y = np.array([1.0, 0.0, 2.0, 1.0, 1.0])<br>
z = np.zeros(5)<br>
<br>
triangles = np.array( [[0, 1, 2], [1, 3, 2], [1, 4, 2],
[0, 4, 1]])<br>
<br>
# create a Matplotlib Triangulation<br>
triang = mtri.Triangulation(x,y,triangl<wbr>es)<br>
<br>
# to perform the linear interpolation<br>
interpolator = mtri.LinearTriInterpolator(tri<wbr>ang, z)<br>
m_z = interpolator(1.0, 1.0)<br>
# +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-<wbr>+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-<wbr>+-+-+-+-+-<br>
<br>
______________________________<wbr>_________________<br>
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href="mailto:Matplotlib-users@python.org"
target="_blank">Matplotlib-users@python.org</a><br>
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href="https://mail.python.org/mailman/listinfo/matplotlib-users"
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</blockquote>
</div>
<br>
</div>
</div>
</blockquote>
<br>
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