How to fill in the area under an IntersectPath in 3D

antoni.parellada shared this question 2 years ago

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I am trying to draw a solid surface like I drew in magenta on the attached drawing. The upper boundary is an IntersectPath.

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mathmagic ● 2 years ago

do you mean c: x² + y² ≤ 0.7^2 ∧ x ≥ -0.6

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antoni.parellada ● 2 years ago

Not really. I'm attaching a new version of the Geogebra file, where I have been able to hack my way through the project enough to see the surface in magenta that I was after (slightly offset, but barely noticeable). This is the idea:

/x8p5rL8ZAfWggAAAABJRU5ErkJggg==

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mathmagic ● 2 years ago

Surface(conditioning, t, b(u, t), t, -3, 3, u, -2, conditioning) equivalent to

Surface((1-v) conditioning+ v (-2), t, b((1-v) conditioning+ v (-2), t), t, -3, 3, v, 0,1) for variable conditioning

I used this fact in https://www.geogebra.org/m/...

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antoni.parellada ● 2 years ago

Thank you, but my issue still remains unsolved: u, -2, conditioning in the span of the parameter u is a hack I just used in desperation because I can figure out how to "close" the open boundary of the umbrella - it does not translate to a valid solution on other quadrants, and it doesn't even do more than just approximate the issue. If you can figure out how to make it work so that that parameter u goes away completely, I would really appreciate it.

In fact, this is my main problem: I don't know what to parameterize with u, and it ends up getting in the way. I don't know if there is a way to parameterize a surface in 3D with just one parameter.

Thank you.

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antoni.parellada ● 2 years ago

I got it! Thank you very much! Attached.

/EuTz4zxXIAADwwj?format=png&name=900x900

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