NetPlot User's Guide

About NetPlot

The authors of NetPlot are Ivan Slapnicar and Damir Krstinic.

Navigation

• functions of one variable y=f(x)
• parametric functions of one variable x=f(t), y=g(t)
• functions in polar coordinates r=f(t)
• functions of two variables z=f(x,y)
• parametric functions of two variables x=f(u,v), y=g(u,v), z=h(u,v)

Input Form

In the second row the function is entered. It is possible to enter more functions separated by commas (see Examples below).

For 2D plots (functions of one variable, parametric functions of one variable and functions in polar coordinates) in the third row you can choose default axes, square axes or equal axes, and choose whether to display rectangular grid or not. You can also zoom in or out.

For 3D plots (functions of two variables and parametric functions of two variables) in the third row you can choose whether or not to show hidden surfaces, the number of mesh lines (10, 20, 30 or 40) and whether to dispay contour plot and rectangular grid in the x-y plane. By clicking the red arrows you can rotate the plot.

Constants, Operators and Functions

Operators +,-,* and / have the standard meaning. Power operation, a "to" b, is described by a^b or by a**b (the latter is the Gnuplot default). a! stands for 'a factoriels'.

Brief description of some functions is given in the following table:

Function	Argument	Description
abs(x)	complex	absolute value of x, |x|
acos(x)	real	inverse cosine (cos-1x) in radians
asin(x)	real	inverse sine (sin-1x) in radians
atan(x)	real	inverse tangent (tan-1x) in radians
besj0(x)	radians	J0 Bessel function of x
besj1(x)	radians	J1 Bessel function of x
besy0(x)	radians	Y0 Bessel function of x
besy1(x)	radians	Y1 Bessel function of x
ceil(x)	real	least whole number larger than x
cos(x)	radians	cosine of x
cosh(x)	radians	hyperbolic cosine of x
erf(x)	complex	error function
erfc(x)	complex	1-erf(x)
exp(x)	real	ex, exponential function of x
floor(x)	real	largest whole number less than x
gamma(x)	complex	gamma function of real(x)
ibeta(p,q,x)	complex	incomplete beta function of real(p,q,x)
igamma(a,x)	complex	incomplete gamma function of real(a,x)
imag(x)	complex	imaginary part of x
int(x)	real	integer part of x truncated towards 0
inverf(x)	complex	inverse error function of real(x)
invnorm(x)	complex	inverse normal distribution of the real part of x
lgamma	complex	natural log of the gamma function of real(x)
log(x)	real	logex, natural logarithm (base e) of x
log10(x)	real	log10x, logarithm (base 10) of x
norm(x)	complex	normal (Gauss) distribution of real(x)
rand(x)	complex	pseudo-random number generator with seed=real(x)
real(x)	complex	real part of x
sgn(x)	real	1 if x>0, -1 if x<0, 0 if x=0
sin(x)	radians	sine of x
sinh(x)	real	hyperbolic sine of x
sqrt(x)	real	square root of x
tan(x)	radians	tangent of x
tanh(x)	real	hyperbolic tangent of x

Examples

• Sine function
  y=f(x): 
  
  
• Sine function and semi-circle
  y=f(x): 
  
  
• Parametrical circle
  x=f(t),y=g(t): 
  
  The circle does not look round, unless you choose "Equal Axes".
  
  
• Parametrical circle and ellipse
  x=f(t),y=g(t): ,
  
  
• Archimedes' spiral and circle in polar coordinates
  r=f(t): 
  
  
• Hyperbolic paraboloid and the plane
  z=f(x,y): 
  
  
• Parametric sphere
  x=f(u,v),...: 
  
  
• Parametric spiral
  x=f(u,v),...: 
  
  
• Various styles and colors
  For example,
  
  y=f(x): 
  
  plots the first function with magenta impulses, while the second function is ploted with the blue step function.

  After enterning the function, you can write "w" or "with", followed by one of the options: "l" (lines), "i" (impulses), "d" (dots), "p" (points), "boxes" or "steps". After the option you can enter the number of the color ( 1, 2, 3, 4, 5, ...).
  
  

• Functions with parameter(s)
  You can first define function which dependins on some parameter(s), and then plot this function for several values of parameter(s). Here are some examples:
  
  y=f(x): 
  
  y=f(x): 
  
  y=f(x): 
  
  
• Piece-wise defined functions
  y=f(x): 
  
  This function is equal to x^2 for x from [-3:1], x/3 for x from [5:7], and sin(x) otherwise. Note that the definition formally needs to cover the entire real line.
  
  
• Periodic functions
  Useful periodic functions can be obtained by using floor, ceil and int, e.g.
  
  y=f(x): 
  
  By using this or similar functions and the piece-wise definition of functions, we can define periodic functions like:
  
  y=f(x): 
  
  
• Intersections of surfaces
  Consider the body which is bounded by the upper semi-sphere
  
  cos(u)*cos(v),sin(u)*cos(v),sin(v), half od the cylinder 0.5*cos(u)+0.5,0.5*sin(u),v for y<0 and the plane u,0,v (that is, y=0),
  
  

  Ranges:	u :    v :    x :    y :
  x=f(u,v),...:

  
  
  The surface of this body is obtained as follows:
  
  

  Ranges:	u :    v :    x :    y :
  x=f(u,v),...:

  
  
  N.B. The entire function input in the second example reads (only part can be seen in the input window):

  0.5*cos(u)+0.5,
0.5*sin(u),
v*sqrt(1-(0.5*cos(u)+0.5)^2-(0.5*sin(u))^2),

0.5*cos(u)+0.5,
v*0.5*sin(u),
sqrt(1-(0.5*cos(u)+0.5)^2-(v*0.5*sin(u))^2)