While the Action menu differs radically from one Category to the next, it always begins with the same three items below.
Basic Action Menu
Action
About This Object...
About This Category
Create
The second item is always enabled, and brings up a window that describes the current Category in some detail. The first and third items are enabled as soon as an object has been selected from the Main menu (except that About This Object... is never enabled for a user defined object). Create, as its name implies, redraws the current object with all the current settings. About This Object... brings up a window which in principle should contain all kinds of interesting descriptive material concerning the current object. Unfortunately, that requires a lot of work, and as yet many objects have only the barest minimum description, e.g., giving the formulas that describe the object. But this will at least let you see how the object depends on the global parameters, aa,bb,...,ii, the information required for creating interesting morphs..
Below, for each Category, we list the items in the Action menu that are appended to the above Basic Action menu. (Depending on the particular object, certain items may be missing.)
Action
Parameterize by Arclength
Show Generalized Cycloids
Show Osculating Circles
Show Osculating Circles With Normals
Action
Show as Curve
Show as Tube
Show Tangent Developable
Show Repère Mobile
Show Projection on Osculating Plane
Show Projection on Normal Plane
Show All Three Projection
Frenet Frame
Parallel Frame
Parameterize by Arclength
Action
Show Parallel Surfaces
Surface Coloration
Hue = v/2 pi
Hue = v/2 pi
Hue = u^2 + v^2
White Paint
User Paint...
Distinguish Sides By Color
Set Surface Front Color...
Set Surface Back Color...
Default Front and Back Colors
User Coloration...
Stereo
Show All Gridlines
Show Alternate Gridlines
Show Every Third Gridlines
Show No Gridlines
Show Original Surface
Show Conjugate Surface
Set Associate Family Parameter...
Don't Show Reflections
The Show All Gridlines, Show Alternate Gridlines, Show Every Third
Gridline, and Show No Gridlines items allrefer only to the Surface
category and behave just as you expect. In particular the Show No
Gridlines item will turn off the display of the u,v coordinate curves
entirely when a surface is redrawn (except, of course, in wire-frame
mode). While this option is available in monochrome and stereo
display modes, it is rarely if ever advisable in these situations,
and should be reserved for (occassional) use when displaying a
surface in color, where it can improve the aesthetics.
The group of items, Show Original Surface, Show Conjugate Surface,
Set Associate Family Parameter..., Show Reflections, and Don't Show
Reflections, refer only to minimal surfaces given by Weierstrass
Enneper data (those at the bottom of the minimal surface submenu) and
are dimmed unless one of these is selected.
Action
Choose Line By Mouse
Choose Interval By Mouse
Choose Circle By Mouse
Cartesian Grid
Polar Grid
Polar Conformal Grid
Cartesian Morphing
Polar Morphing
Color Code Gridlines
Action
Create Truncated
Create Subdivided
Create Stellated
Action
IC By Mouse
Continue
Erase
Hide Direction Fields
SHide ODE Controls
ODE(1D)-2nd Order ODE(2D)-1st Order
Action
IC By Mouse
Continue
Erase
Project ODE Orbits
Hide Direction Fields
Hide ODE Controls
ODE(2D)-2nd Order ODE(3D)-1st Order ODE(3D)-2nd Order
Action
IC By Mouse [Drag]
Continue
Erase
Project ODE Orbits
Hide ODE Controls
Action
IC By Mouse [Drag]
Continue
Erase
Action
Continue
Set Lattice Parameters...
The Action menu for the Wave Category depends on which wave equation is under consideration. It also has somewhat different items when an initial value problem is being solved numerically.
Continue Display
As Graph Evolve
Profile Display
Time Slices Continue Display
As Graph Evolve
Profile Display
As Graph Display
Wave Form Only Display
Fourier Transform Only Display
Both Continue Display
As Graph Evolve
Profile Display
Time Slices Continue Display
As Graph Evolve
Profile Display
Time Slices Show
Modulus and Phase Show
Modulus Only Continue Display
As Graph Evolve
Profile Display
Time Slices Display
Wave Form Only Display
Fourier Transform Only Display
Both Show
Modulus and Phase Show
Modulus Only
KDV
Action
KDV
IVP
Action
Sine
Gordon
Action
Cubic
Schroedinger
Action
Cubic Schroedinger
IVP
Action