# 3D wish list for 5.2

themadmathematician shared this idea 8 years ago

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...

-

1

Hi,

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 ;)

Cheers,

Mathieu

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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?

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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

Thanks :-)

1

Hi,

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 = ?

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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

Will be in next release :)

(5.0.22.0)

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Michael,

good news :D

Awaiting for Curvature and CurvatureVector for curves in 3D

(and GaussianCurvature for surfaces :D :D :D )

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Awaiting for Curvature and CurvatureVector for curves in 3D

Do you have a reference for what CurvatureVector should do for a 3D curve?

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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.

https://ggbm.at/568889

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How do you calculate it in 3D?

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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)

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OK, please try these in 5.0.23.0:

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)

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Any plans for spherical trigonometry capability?

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Michael,

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).

https://ggbm.at/568969