Offer to visualize "Variable or Function" definitions

[NeatNit]

I find this recurring pattern of defining a Variable or Function, for example:

f(t) = [t, t^2, t^3]

And then immediately afterwards adding another object to visualize, in this example a Parametric Curve:

f(t)

I've included other examples here:

• Parametric Curve
• Vector or Point
• Parametric Surface

The pattern is always the same - the Variable or Function defines X, then another object is made where the content is just X.

It would be really nice if Math3d offered to "cut out the middle man": when the Variable or Function is defined, it would detect what it might be and add a checkbox to visualize it as such:

• If it's in the form f(t) (or any other variable name, e.g. f(r), f(x)) and returns a 3D vector, offer Parametric Curve visualization.
• If it's in the form f(u,v) (f(x,y), f(j,k), ...) and returns a 3D vector, offer Parametric Surface visualization.
• If it's in the form f(x,y) and returns a number, offer Explicit Surface or Explicit Surface (Polar) visualization
• If it's in the form f(x,y,z) and returns a 3D vector, offer Vector Field visualization.
• (not sure about this one) If it's in the form f(x,y,z) and returns a number, offer Implicit Surface visualization, where f(x,y,z) = 0.
• If it's in the form f (just a variable) and is a 3D vector, offer Vector or Point visualization (generally shouldn't allow both at the same time, though there'd be no harm in that)
• If it's in the form f (just a variable) and is a list of 2 or more 3D vectors, offer Line visualization.

When a visualization is offered and selected, a color selector and a secondary cogwheel would appear (as well as parameter ranges, where applicable) to control the visualization as if it were a separately made object of that type.

[ChristopherChudzicki]

I really like this idea! It would be a big improvement and definitely help improve discoverability of some features.

Thanks again for all the issues you've posted today! I'll definitely be thinking about them.

[kevinkitty7]

A small bug, for "Variable or Function", it does not support the simplest function "max/min".

In "Variable or Function", when I type w(x) = max(x,1) It shows "Eval Error, Depends on undefined symbol(s) max"

max/min functions just works fine in other places, such as "Explicit Surface".

Hope this can be fixed.