Cerca SurfX3D in rete e scaricalo (il programma opera in ambiente Windows).
[una versione è presente anche qui]
Se, scaricato il programma, non funziona l'help devi caricare i file di Windows come ti apparirà suggerito.
Altrimenti usa il presente file, che se vuoi puoi memorizzare sul tuo computer.

Il programma è di uso semplicissimo. Per elaborazioni grafiche più sofisticate puoi ricorrere ad R (gratuito ed operante su tutte le piattaforme, ma in cui il movimento delle figure non è guidabile col mouse).

Help in formato Html.
Per cercare le occorrenze di una parola chiave usa il comando Trova.
Qui qualche immagine. Qui trovi degli esempi da caricare.

I grafici tracciati possono essere ruotati col mouse. Cliccando le icone "lucchetto", a destra (sotto il menu Help), puoi limitare le direzioni delle rotazioni.
Per copiare/incollare le definzioni usa i comandi azionabili col pulsante destro del mouse.

SurfX3D HELP

SurfX3D Overview
Built-in Math Functions
Parametric Surfaces
    Parametric Surface Plot Parameters
Explicit Surfaces
    Explicit Surface Plot Parameters
Implicit Surfaces
    Implicit Surface Plot Parameters
Menus
    File menu commands
    Edit menu commands
    View menu commands
    Plot menu commands
    Export menu commands
    Help menu commands

SurfX3D Overview

Surface Explorer 3D allows defining mathematical surfaces and plotting those surface equations in 3D.

Three types of surface definitions are supported:
1)    Parametric    X,Y,Z(u,v)
2)    Explicit        Z=F(X,Y)
3)    Implicit        F(X,Y,Z)=0

Surface equations are entered in a ‘Basic-like’ syntax such as:
    Z = sin ( ( X * Y ) / 5 )

A user definable colorizing function provides the ability to show the surface in varying degrees of color (0 ≤ R,G,B ≤ 100).

Various plot parameters can be specified:

   The viewing angles that the surface will be drawn from
   Viewable ranges of independent axis variables
   Number of contour lines to be drawn
   Drawing scale
   Hidden line removal
   Displaying coordinate axis
   Background color
   Line color

There are a number of built-in math functions including trigonometric functions, logarithm functions, absolute values, and others that can be used to define surface equations and colorizing functions.


Built-in Math Functions

The following mathematical operators are available:

Operator  Purpose
 ( )     grouping
  +      addition
  -      subtraction
  *      multiplication
  /      division
  ^      power

The following built-in math functions are available:

Function Syntax     Purpose
  min(v1,v2)     min of two values
  max(v1,v2)     max of two values
  abs(v)         absolute value
  sqrt(v)        square root
  exp(v)         e ^ v
  ln(v)          natural logarithm
  log10(v)       base 10 logarithm
  ceil(v)        next higher integer
  floor(v)       next lower integer
  rand()         random number
  hypot(x,y)     hypotenuse: sides x,y
  sin(radians)   trig sine
  cos(radians)   trig cosine
  tan(radians)   trig tangent
  asin(v)        arc sine
  acos(v)        arc cosine
  atan(v)        arc tangent
  sinh(v)        hyperbolic sine
  cosh(v)        hyperbolic cosine
  tanh(v)        hyperbolic tangent
  atan2(y,x)     arc tangent ( y / x )
  sign(x)        -1 if x < 0 else 1

Parametric Surfaces    X,Y,Z(u,v)

A parametric surface is defined using two independent parameters u and v.
X, Y, and Z are then defined using u and v. Thus, the surface is defined as:
    X = X(u,v)     Y = Y(u,v)     Z = Z(u,v)

The color of the surface can also be defined using u and v as follows (0 ≤ R,G,B ≤ 100):
   R = R(u,v)   // red component    (es:.: (sin(u)+1)*50 o (u+1)*50 se -1≤u≤1 o …)
   G = G(u,v)   // green component  (es:.: (cos(u)+1)*50 o (v+1)*50 se -1≤v≤1 o …)
   B = B(u,v)   // blue component   (es:.: 0 o ... )

Parametric Surface Plot Parameters    X,Y,Z(u,v)

Surface Description
    Description of the surface

Parametric Surface Equation Definition:
    The equations of the surface can use:
•  u, v values
•  Built-in math functions
•  Sub-expressions (C1-C8)
    Provide the defining surface equations
X(u,v) = [ X defining surface equation ]
Y(u,v) = [ Y defining surface equation ]
Z(u,v) = [ Z defining surface equation ]

Sub-Expressions (C1 – C8)
    Sub-Expressions can be used for defining parametric constants, repeated expressions, or just simplifying equations.
    They can use:
•  u, v values
•  Built-in math expressions.
•  Higher number expressions can use lower number expressions ie C6 can use C5,C4,C3,C2,C1
Example:    C2=C1*sin(u)*cos(v)   is valid     C3=3*C4   not valid

Surface Colorizing:
    Enable Color Surface - must be checked to perform surface colorization.
    The equations of the surface color can use:
•  u, v values
•  Built-in math functions
•  Sub-expressions (C1-C8)
    Note that these functions must produce a value between 0=off and 100=on
    Each video pixel consists of a red, green, and blue component (0 ≤ R,G,B ≤ 100):
R(u,v) = [ Red defining surface color equation ]
G(u,v) = [ Green defining surface color equation ]
B(u,v) = [ Blue defining surface color equation ]

Ranges
    Specify the minimum and maximum values for u and v for the viewable region of the surface.
    Min value must be less than max value.
    Also specify the number of u and v contour lines to draw.

Mesh Size
    U,V - specify the number of intervals in each independent variable for surface resolution
    Note: Larger values will take more rendering time (50-100 typical).

Viewing Angles (Degrees)
XY Tilt - angle of x-y plane and a plane perpendicular to line of view
A value of zero is looking at the surface as a top view. (typical 60)
Z Rotate - rotation angle about the z-axis. (typical 50)

Overall:
Scale % - used to reduce the image size (100=full scale)
Back Color - background screen color (use color selection button)
Show Axis - if checked, will draw the X, Y, Z coordinate axis.

Line Control
Draw U Lines – if checked, will draw the u contour lines
Draw V Lines – if checked, will draw the v contour lines
Line Color - the color used for drawing contour lines (use color selection button)

Explicit Surfaces    Z = F(x,y)

An explicit surface is one of the simplest ways of defining a surface.
The Z value is defined as a function of X and Y. Thus, the surface equation is:
    Z = F(x,y)
The surface is restricted to having one Z value for a given X and Y combination.
Not every surface can be defined explicitly.

The color of the surface can also be defined using x, y and z as follows (0 ≤ R,G,B ≤ 100):
   R = R(x,y,z)   // red component
   G = G(x,y,z)   // green component
   B = B(x,y,z)   // blue component

Explicit Surface Plot Parameters    Z = F(x,y)

Surface Description
Description of the surface

Explicit Surface Equation Definition:
The equation of the surface can use:
•  x, y values
•  Built-in math functions
•  Sub-expressions (C1-C8)
Provide the defining surface equation
Z(x,y) = [ Z defining equation ]

Sub-Expressions (C1 – C8)
Sub-Expressions can be used for defining parametric constants, repeated expressions, or just simplifying equations.
They can use:
•  x, y values
•  Built-in math expressions.
•  Higher number expressions can use lower number expressions ie C6 can use C5,C4,C3,C2,C1
Example:   C2=C1*sin(x)*cos(y)   is valid
           C3=3*C4    not valid

Surface Colorizing:
Enable Color Surface - must be checked to perform surface colorization.
The equations of the surface color can use:
•  x, y, z values
•  Built-in math functions
•  Sub-expressions (C1-C8)

Note that these functions must produce a value between 0=off and 100=on
Each video pixel consists of a red, green, and blue component (0 ≤ R,G,B ≤ 100).
R(x,y,z) = [ Red defining surface color equation ]
G(x,y,z) = [ Green defining surface color equation ]
B(x,y,z) = [ Blue defining surface color equation ]

Ranges
Specify the minimum and maximum values for X,Y,Z for the viewable region of the surface.
Min value must be less than max value.
Limit Z – if checked, will limit z-values to specified

Mesh Size
X,Y - specify the number of intervals in each axis for surface resolution
Note: Larger values will take more rendering time (50-100 typical).

Viewing Angles (Degrees)
XY Tilt - angle of x-y plane and a plane perpendicular to line of view
A value of zero is looking at the surface as a top view. (typical 60)
Z Rotate - rotation angle about the z-axis. (typical 50)

Overall:
Scale % - used to reduce the image size (100=full scale)
Back Color - background screen color (use color selection button)
Show Axis - if checked, will draw the X, Y, Z coordinate axis.

Line Control:
X Lines – checkmark to draw constant X lines, specify number of lines
Y Lines – checkmark to draw constant Y lines, specify number of lines
Line Color - the color used for drawing contour lines (use color selection button)

Implicit Surfaces    F(x,y,z) = 0

An implicit surface is expressed as a function of X, Y, Z equal to zero.
Thus, the equation of an implicit surface is:
    F(x,y,z) = 0
The plotting algorithm uses an error function F(x,y,z) = Err.
In order for the plotting algorithm to work, Err must produce a sign change.
Otherwise, the root searching algorithm will not find a zero root.

The color of the surface can also be defined using X, Y, and Z as follows (0 ≤ R,G,B ≤ 100):
    R = R(x,y,z)    // red component
    G = G(x,y,z)    // green component
    B = B(x,y,z)    // blue component
Suggestion:
The plotting can be much slower than Parametric or Explicit surfaces.
Reduce the size of the plot window to speed up drawing time.
Once you are satisfied with the plot parameters, increase the drawing window size, redraw the plot and wait, wait, wait.

Implicit Surface Plot Parameters    F(x,y,z) = 0

Surface Description
Description of the surface

Implicit Surface Equation Definition:
The equation of the surface can use:
•  x, y, z values
•  Built-in math functions
•  Sub-expressions (C1-C8)
Provide the defining surface equation
F(x,y,z) = [ defining surface equation ]

Sub-Expressions (C1 – C8)
Sub-Expressions can be used for defining parametric constants, repeated expressions, or just simplifying equations.
They can use:
•  x, y, z values
•  Built-in math expressions.
•  Higher number expressions can use lower number expressions ie C6 can use C5,C4,C3,C2,C1
Example:   C2=C1*sin(x)*cos(y)   is valid
           C3=3*C4     not valid

Surface Colorizing:
Enable Color Surface - must be checked to perform surface colorization.
The equations of the surface color can use:
•  x, y, z values
•  Built-in math functions
•  Sub-expressions (C1-C8)

Note that these functions must produce a value between 0=off and 100=on
Each video pixel consists of a red, green, and blue component (0 ≤ R,G,B ≤ 100).
R(x,y,z) = [ Red defining surface color equation ]
G(x,y,z) = [ Green defining surface color equation ]
B(x,y,z) = [ Blue defining surface color equation ]

Ranges
Viewing range can be specified in one of two ways
Specify the minimum and maximum values for X,Y,Z for the viewable region of the surface.
Min value must be less than max value.

Mesh Size
X,Y,Z - specify the number of search intervals in each axis for surface resolution
Note: Larger values will take more rendering time (50-100 typical).

Viewing Angles (Degrees)
XY Tilt - angle of x-y plane and a plane perpendicular to line of view
A value of zero is looking at the surface as a top view. (typical 60)
Z Rotate - rotation angle about the z-axis. (typical 50)

Overall:
Scale % - used to reduce the image size (100=full scale)
Back Color - background screen color (use color selection button)
Show Axis - if checked, will draw the X, Y, Z coordinate axis.

Line Control:
X,Y,Z–if checked, will draw the specified section cut lines
Line Color - the color used for drawing contour lines (use color selection button)

File menu commands
The File menu offers the following commands:
New           – Creates a new document  Ctrl+N  (attivabile anche da icona)
Open          – Opens an existing document  Ctrl+O  (attivabile anche da icona)
Save          – Saves an opened document using the same file name  Ctrl+S  (attivabile anche da icona)
Save As       – Saves an opened document to a specified file name.
Print         – Prints a document. Ctrl+P
Print Preview – Displays the document on the screen as it would appear printed.
Print Setup   – Selects a printer and printer connection.
Exit          – Exits SurfX3D. Alt+F4

Edit menu commands
The Edit menu offers the following commands:
Copy – Copies data from the document to the clipboard  Ctrl+C  (attivabile anche da icona)

View menu commands
The View menu offers the following commands:
Toolbar – Shows or hides the toolbar.
Status Bar – Shows or hides the status bar.

Plot menu commands
The Plot menu offers the following commands:
Auto Draw – Automatically draw when plot file is opened.
Draw Plot – Draws the plot. Use the Plot icon to perform the same.
Cancel    – Cancel a plot that is in the process of rendering.

Export menu commands
The Export menu allows exporting to other file formats:
VRML – Export to Virtual Reality Modeling Language file
POV  – Export to Persistence of Vision file
DXF  – Export to CAD Drawing Exchange File

Help menu commands
The Help menu offers the following commands, which provide you assistance with this application:
Help Topics – Offers you an index to topics on which you can get help.
About – Displays the version number of this application.