Timeline for Interior of simple closed curve
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 8, 2023 at 17:05 | vote | accept | Daniel Castro | ||
| Dec 27, 2022 at 1:02 | answer | added | cvgmt | timeline score: 4 | |
| Dec 26, 2022 at 19:26 | answer | added | lericr | timeline score: 3 | |
| Dec 26, 2022 at 18:58 | comment | added | lericr | Oh, sorry, I overlooked your last comment...so you DO want a discretized region. I'll put together an answer... | |
| Dec 26, 2022 at 18:54 | comment | added | lericr | To go the discretization route, you don't need splines. Your function can generate a parametric plot on which you can use DiscretizeGraphics. You can control the refinement of the discretiztion. Then you'll have a boundary made up of 1-D sub-regions. Extract these and create a FilledCurve and discretize the results. That seems like more steps than necessary, so maybe someone else has a more direct route. But the main point is that I don't think there is a built in function that creates interior regions bounded by parameterized functions defining the boundary. | |
| Dec 26, 2022 at 18:41 | comment | added | lericr |
If you don't want any discretization, then I think you're going to need to use the implicit region functionality. We could "regionize" your example with ParametricRegion[{x[t], y[t]}, {{t, 0, 8}}], but that just gets us a 1-D region. To get a 2-D region, I think you're going to need to provide the 2-D parameterization. You could do this by adding a second parameter and filling out the interior with vectors from {0,0} to {x[t],y[t]}. I'm not aware of a built-in function that automatically creates "interior" regions from non-mesh boundary regions in the general case.
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| Dec 26, 2022 at 15:47 | comment | added | Daniel Castro | @Syed True. But as I mentioned, it doesn't make too much sense to discretize a continuous closed curve whose analytic expression is known. | |
| Dec 26, 2022 at 15:45 | comment | added | Syed |
poly = Polygon@Table[{x[t], y[t]}, {t, 1, 8, 1}] ?
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| Dec 26, 2022 at 15:16 | history | asked | Daniel Castro | CC BY-SA 4.0 |