[Matplotlib-users] Matplotlib with invalid triangulations

[Ian Thomas]

Hi Pat,

That's really unlucky!

Point 3 at (1,1) lies along one edge of triangle (0, 1, 4).  However, due
to rounding error caused by finite-precision maths, there is some test when
creating LinearTriInterpolator for which point 3 lies just inside triangle
(0, 1, 4).  Hence the triangulation is invalid.  You can prove this by
changing the line
    y = np.array([1.0, 0.0, 2.0, 1.0, 1.0])
to
    y = np.array([1.0, 0.0, 2.0, 1.0+1e-10, 1.0])
instead.

Really the only solution if you want to use LinearTriInterpolator is to
ensure that you don't have any very thin triangles before going anywhere
near matplotlib.  This is down to whatever you use to generate your
triangulation and/or whatever preprocessing you perform on it.

Ian


On 21 November 2016 at 11:45, Pat Prodanovic <pprodano at gmail.com> wrote:

> 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> 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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>
>
>
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