Modify control point nudge for 1D elements

[dbrakenhoff]

Currently, the control point locations inside and outside an element are computed by multiplying 1 plus a small number (1E-6) by the absolute value of the coordinate and adding/subtracting that to the location of the element.

self.xcin = self.xc + self.tiny * abs(self.xc) + self.tiny

For large values of the coordinate (which to be fair is probably rare for cross sectional models), this causes large distances between the element and its control points inside/outside, which isn't what we want.

Proposal is to replace the above by just adding/subtracting a small number. Optionally we can consider exposing the small number as a keyword argument in the elements.

self.xcin  = self.xc + self.tiny

[panibillo]

For a small number that is just large enough for Python to distinguish the distance, what about using numpy.spacing(n)? Where n is some small number that lets your tests pass.

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On Mon, Nov 11, 2024 at 7:30 AM Davíd Brakenhoff ***@***.***> wrote: Currently, the control point locations inside and outside an element are computed by multiplying 1 plus a small number (1E-6) by the absolute value of the coordinate and adding/subtracting that to the location of the element. self.xcin = self.xc + self.tiny * abs(self.xc) + self.tiny For large values of the coordinate (which to be fair is probably rare for cross sectional models), this causes large distances between the element and its control points inside/outside, which isn't what we want. Proposal is to replace the above by just adding/subtracting a small number. Optionally we can consider exposing the small number as a keyword argument in the elements. self.xcin = self.xc + self.tiny — Reply to this email directly, view it on GitHub <#120>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABFCIYHLUIWKA2OC3LX4TH32ACWO3AVCNFSM6AAAAABRR3HBPOVHI2DSMVQWIX3LMV43ASLTON2WKOZSGY2DSMZVG4YDIOI> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[dbrakenhoff]

For a small number that is just large enough for Python to distinguish the distance, what about using numpy.spacing(n)? Where n is some small number that lets your tests pass.

Interesting, I didn't know about np.spacing. But machine precision is probably a little too small for this, I think.

[panibillo]

Consider this case, I think it may apply in the context of interest, but you can judge: Suppose a world coordinate system with numerically very large numbers. An element with endpoints z1 and z2, and center z0: (conveniently for writing, it's on the real axis) z1 = 1.0e9 + 0j z0 = 1.1e9 + 0j z2 = 1.2e9 + 0j The mapping from z to Z would be Z(z) = (z - z0) * r The element length in Z will be 2, so r = 2/(z2-z1)

>> z1, z0, z2 = 1.0e9, 1.1e9, 1.2e9 >> r = 2 / (z2 - z1)

1e-08 Now, define a control point c1 close to z1, and offset from the boundary in direction 1j.

>> z1

1000000000.0

>> c1 = z1 + 1j * (np.spacing(z1))

(1000000000+2.384185791015625e-07j) Map c1 to the Z-plane: C1 = Z(c1) = (c1 - z0) * r

>> C1 = (c1 - z0) * r

(-1+2.384185791015625e-15j) C1 is measurably off of the real axis.

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On Mon, Nov 11, 2024 at 7:47 AM Davíd Brakenhoff ***@***.***> wrote: For a small number that is just large enough for Python to distinguish the distance, what about using numpy.spacing(n)? Where n is some small number that lets your tests pass. Interesting, I didn't know about np.spacing. But machine precision is probably a little too small for this, I think. — Reply to this email directly, view it on GitHub <#120 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABFCIYBYAJBUDBKTG7JASZD2ACYPJAVCNFSM6AAAAABRR3HBPOVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDINRYGIZDCMRQGM> . You are receiving this because you commented.Message ID: ***@***.***>

[dbrakenhoff]

Hi Bill, thanks for the suggestion and worked example, I'll give it a try! The reason I wasn't sure initially is because so far we've used shifts on the order of ~1e-6, and I wasn't sure if in 2D we wouldn't be running into any floating point precision stuff with some of the methods to determine whether a point is inside or outside a polygon, etc.