# [Matplotlib-users] Matplotlib with invalid triangulations

Pat Prodanovic pprodano at gmail.com
Mon Nov 21 06:45:06 EST 2016

```Hi Ian,

Thank you for your reply.

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.

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?

Thanks,

Pat

import matplotlib.tri as mtri
import numpy as np

# manually construct an invalid triangulation
x = np.array([0.0, 1.0, 1.0, 1.0, 2.0])
y = np.array([1.0, 0.0, 2.0, 1.0, 1.0])
z = np.zeros(5)

# slightly modified from what I originally posted
triangles = np.array( [[0, 1, 4], [2, 3, 4], [0, 3, 2], [0, 4, 3]])

# create a Matplotlib Triangulation
triang = mtri.Triangulation(x,y,triangles)

# ---------- start of new code ----------
xy = np.dstack((triang.x[triang.triangles], triang.y[triang.triangles]))
#shape (ntri,3,2)
twice_area = np.cross(xy[:,1,:] - xy[:,0,:], xy[:,2,:] - xy[:,0,:])  #
shape (ntri)
mask = twice_area < 1e-10  # shape (ntri)

if np.any(mask):
triang.set_mask(mask)
# ---------- end of new code ----------

# to perform the linear interpolation
interpolator = mtri.LinearTriInterpolator(triang, z)
m_z = interpolator(1.0, 1.0)

On 11/21/2016 03:47 AM, Ian Thomas wrote:
> Hello Pat,
>
> 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:
>
> # +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
> import matplotlib.tri as mtri
> import numpy as np
>
> # manually construct an invalid triangulation having a zero area element
> x = np.array([0.0, 1.0, 1.0, 1.0, 2.0])
> y = np.array([1.0, 0.0, 2.0, 1.0, 1.0])
> z = np.zeros(5)
>
> triangles = np.array( [[0, 1, 2], [1, 3, 2], [1, 4, 2], [0, 4, 1]])
>
> # create a Matplotlib Triangulation
> triang = mtri.Triangulation(x,y,triangles)
>
> # ---------- start of new code ----------
> xy = np.dstack((triang.x[triang.triangles],
> triang.y[triang.triangles]))  # shape (ntri,3,2)
> twice_area = np.cross(xy[:,1,:] - xy[:,0,:], xy[:,2,:] - xy[:,0,:])  #
> shape (ntri)
> mask = twice_area < 1e-10  # shape (ntri)
>
> if np.any(mask):
>     triang.set_mask(mask)
> # ---------- end of new code ----------
>
> # to perform the linear interpolation
> interpolator = mtri.LinearTriInterpolator(triang, z)
> m_z = interpolator(1.0, 1.0)
> # +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
>
> 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.
>
> Ian
>
>
> On 19 November 2016 at 12:24, Pat Prodanovic <pprodano at gmail.com
> <mailto:pprodano at gmail.com>> wrote:
>
>     Hello,
>
>     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.
>
>     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.
>
>     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.
>
>     I've reproduced the following example that illustrates the problem
>     in a small code snippet. Any suggestions?
>
>     Thanks,
>
>     Pat Prodanovic
>
>     #
>     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
>     import matplotlib.tri as mtri
>     import numpy as np
>
>     # manually construct an invalid triangulation having a zero area
>     element
>     x = np.array([0.0, 1.0, 1.0, 1.0, 2.0])
>     y = np.array([1.0, 0.0, 2.0, 1.0, 1.0])
>     z = np.zeros(5)
>
>     triangles = np.array( [[0, 1, 2], [1, 3, 2], [1, 4, 2], [0, 4, 1]])
>
>     # create a Matplotlib Triangulation
>     triang = mtri.Triangulation(x,y,triangles)
>
>     # to perform the linear interpolation
>     interpolator = mtri.LinearTriInterpolator(triang, z)
>     m_z = interpolator(1.0, 1.0)
>     #
>     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
>
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