Timeline for Plotting implicitly-defined space curves
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Nov 9, 2017 at 11:01 | answer | added | matrix42 | timeline score: 16 | |
| Nov 5, 2014 at 5:14 | answer | added | Michael E2 | timeline score: 35 | |
| Sep 17, 2012 at 4:47 | comment | added | user2316 | In line with other functions (Solve, Reduce,...) it would be nice to go: ContourPlot3D[ (x^2 + y^2 + z^2 + 8)^2 - 36 (x^2 + y^2) && y^2 + (z - 2)^2 - 4,{x, -4, 4}, {y, -4, 4}, {z, -2, 2}] (I don't know how to put a comment in..) | |
| May 25, 2012 at 4:29 | vote | accept | J. M.'s missing motivation♦ | ||
| May 24, 2012 at 3:44 | comment | added | rcollyer | @Jens if comment upvotes counted ... the term "just" made me laugh. :) | |
| May 24, 2012 at 3:36 | comment | added | Jens | I was debating whether I should write an answer based on that, but it would be less efficient. If someone wants to try it anyway, you could perhaps directly use the field line plotter in this answer. | |
| May 24, 2012 at 3:26 | comment | added | Jens |
@rcollyer Regarding the equation: if you accept a differential equation then it's easy: take the cross product of the gradients of the implicit functions, and perhaps normalize it (call it t[r], where r is a 3D point). Then the curve is described by D[r[u],u] == t[r[u]] for curve parameter u. This is because t must be tangent to both surfaces for all points r on the intersection curve. You "just" have to integrate that equation with a starting point r0 on the intersection.
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| May 24, 2012 at 3:00 | comment | added | rcollyer | There is of course a followup to this: how does one get the equation (algebraic preferred, numerical acceptable) of those intersections? :) | |
| May 23, 2012 at 21:36 | comment | added | J. M.'s missing motivation♦ |
@Plato: that might be best done as a separate question... (that would be covered by the "two parametrically-defined surfaces" case, as BSplineSurface[] objects can be transformed into BSplineFunction[]s).
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| May 23, 2012 at 21:28 | comment | added | PlatoManiac |
@J. M.♦ Can we extend the question a bit by considering intersection of two BSpline surfaces that has no explicit analytical form? This will be very effective for 3D modeling.
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| May 23, 2012 at 20:47 | answer | added | Daniel Lichtblau | timeline score: 75 | |
| May 23, 2012 at 20:25 | comment | added | J. M.'s missing motivation♦ | @R.M, Funny, I thought getting the intersection of two parametrically-defined surfaces was an even tougher problem... so I decided not to ask for it in the question. :) That would be nice, though. | |
| May 23, 2012 at 20:21 | answer | added | Szabolcs | timeline score: 40 | |
| May 23, 2012 at 20:18 | comment | added | rm -rf♦ | Finally, I'll be able to properly intersect the columns with the roof | |
| May 23, 2012 at 20:16 | history | tweeted | twitter.com/#!/StackMma/status/205391675177185280 | ||
| May 23, 2012 at 20:05 | history | asked | J. M.'s missing motivation♦ | CC BY-SA 3.0 |