3D wish list for 5.2
So I played around a little and there are frustratingly many things I cannot do. I look forward to 5.2 :wink:
- I realize it is difficult, but finding a numeric curve or area like a locus without an equation is much much better than nothing. Then you could intersect cylinders with eath other and other things.
- Defining unions to create more complex 3D-bodies, like conglomerates of cubes, intersections of polyhedra etc...
- Creating Archmedean, Catalan and Johnson solids.
- Creating solids defined from centers and in- or outradius rather than points on surface (which makes them very difficult to co-centre).
- 3D-scatterplots and other 3D statistics.
- A plane can intersect a cone but not the reflection of a cone... (why is the reflection of a cone not a cone?)
- If you stellate a polyhedra, the net applies only to the original polyhedra or the pyramid on one face at a time, not to the stellated polyhedra.
- I miss the command Intersect[plane, plane, plane] to produce a point (OR line OR plane) immediately.
- I'm sure teachers all over the world would love you if you could make UpperSum and LowerSum equivalents for 3D rotational volumes. Not to say anything about RotationalVolume[ <function>, <direction>, <from>, <to> ]...
Just think what you could do with 3D-differential equation commands...
It also seems to hang every so often...
Thanks for your message, many of these features are planned for 5.2.
About Intersect[plane, plane, plane], I think that Intersect[plane, Intersect[plane, plane]] should work ;)
Good news, then :-)
About Intersect[ plane, Intersect[plane, plane]]: Yes it works, and it may even be pedagogical to show each of the three intersecting lines and how they in turn intersect each other, but I think Intersect[plane, plane, plane] is a logical, intuitive command syntax that one would expect to be there without reading the manual, no?
I'll add my wishes ... christmas is not far away ;-)
- in- and output of planes via parameter or normal form
- possibilty to define cones and cylinders that are not perpedacular to the ground/end-circle
- use Latex again
- automatic usage of vector arrows in names of vectors for 2D and 3D
Here are my wishes :laughing:
1. the icons for new tools created in 3D should appear in 3D toolbar window rather then in 2D.
2. f(t_0) should work for parametric curves in 3D just like it works in 2D.
f=Curve[t,t^2,t,0,2] , f(1) - works
g=Curve[t,t^2,t^3,t,0,2] , g(1) - does not work
3. CAS should use the special command for limits of sequences (n=integer or something like this).
In consequence Limit[sin(n*Pi),n=integer,infinity] = 0 instead of = ?
Will be in next release :)
good news :D
Awaiting for Curvature and CurvatureVector for curves in 3D
(and GaussianCurvature for surfaces :D :D :D )
Curvature works already :)
Do you have a reference for what CurvatureVector should do for a 3D curve?
The field of inverted CurvatureVector is so called "porcupine plot". You can see if the joint of two curves is C^2 . C^2 = curvature continuity = centrifugal force for constant speed continuity. Any point on a highway should be C^2. This works in any dimention.
How do you calculate it in 3D?
For any parametrized curve f:t->f(t) in 3D if you already calculated curvature
CurvatureVector = curvature.((f'xf'')xf')/|(f'xf'')xf'|
i.e. CurvatureVector = curvature.(UnitNormalVector of Frenet's frame)
OK, please try these in 18.104.22.168:
CurvatureVector[A, a] for 3D curve, eg a = Curve[t,t^2,t^3,t,0,1]
Curvature[param1, param2, surface], eg surface = Surface[cos(u) cos(v), sin(u) cos(v), u + sin(v), u, 0, 6.28319, v, 0, 6.28319]
Curvature[A,f(x,y)], eg f(x,y) = sin(x) + sin(y)
Any plans for spherical trigonometry capability?
A=f(t) works fine for parametrized curves in 3D.
I am awaiting for A=f(u,v) for parametrized surfaces in 3D and for the domain different from rectangle Surface[...,...,...,u,0,1,v,0,-u+1] (useful when no transformation of the rectangle domain is allowed).
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