Surface Plotter - Syntax Reference

A function definition is made up of operators and operands, no matter how complex it is.

Operands

Operands are divided into two main categories: numerical operands and boolean operands.
Boolean operands are the result of applying relational operator to two numerical operands. (i.e: 2 < 3 results true, which is boolean type).
Numerical operands are constants, variables, and result of internal function calls.

Here are the details of numerical operands:

Constants

Surface Plotter defines two constants: 

  e             natural number                    value = 2.7182818..
  pi            area of circle with radius 1      value = 3.14159265..

Variables

Valid variables are x and y.
To set the minimum value and maximum value of these variables, use the setting panel at the right side.
For more information, see: settings

Internal Functions

  abs(x)        returns the absolute value of x
  acos(x)       returns the arc cosine of x
  acosh(x)      returns the inverse hyperbolic cosine of x
  asin(x)       returns the arc sine of x
  asinh(x)      returns the inverse hyperbolic sine of x
  atan(x)       returns the arc tangent of x
  atanh(x)      returns the inverse hyperbolic tangent of x     
  ceil(x)       rounds x up to the nearest integer
  cos(x)        returns the cosine of x
  cosh(x)       returns the hyperbolic cosine of x
  exp(x)        returns the exponential of x 
  floor(x)      rounds x down to the nearest integer
  frac(x)       returns the fraction part of x
  int(x)        returns the integer part of x
  ln(x)         returns the natural logarithm of x
  log(x)        returns the base-10 logarithm of x
  round(x)      rounds x to the nearest integer 
  sign(x)       returns -1 if x < 0, 1 if x > 0, and 0 if x = 0
  sin(x)        returns the sine of x
  sinh(x)       returns the hyperbolic sine of x
  sqr(x)        returns x * x
  sqrt(x)       returns the square root of x
  tan(x)        returns the tangent of x
  tanh(x)       returns the hyperbolic tangent of x

  Surface Plotter version 1.20 or newer:
  
  min(a,b)      returns the smaller value of a and b
  max(a,b)      returns the greater value of a and b
  atan2(a,b)    computes the phase theta by computing an arc tangent of b/a in
                the range -pi to pi
  mod(a,b)      returns the remainder of a divided by b as defined by IEEE 754
Note:

Operators

Surface Plotter recognizes three kinds of operators: arithmetic operators, relational operators, and boolean operators.
Relational operators and Boolean operators are used only in conjuction with "if" function.
Arithmetic operators are operators for manipulating numbers. They are the same with those BASIC programming language uses.
Here is the list of all valid arithmetic operators and their precedence.

Precedence of Operators

 
  ------------------------------------------------------------------------------
   Operator    Precedence      Operation         Category         Associativity
  ------------------------------------------------------------------------------
      +        First (high)    sign identity     unary            right to left
      -                        sign negation
  ------------------------------------------------------------------------------
      ^        Second          power             power            right to left
  ------------------------------------------------------------------------------
      *        Third           multiplication    multiplication   left to right
      /                        division                         
  ------------------------------------------------------------------------------
      +        Fourth          addition          addition         left to right
      -                        substraction
  ------------------------------------------------------------------------------
Note: Expressions within parentheses are evaluated before being treated as a single operand.

Relational operators and Boolean operators

Since version 1.10, Surface Plotter's function parser recognizes relational operators and boolean operators.
Here is the list of valid relational operators and boolean operators: 

  ------------------------------------------------------------------------------
   Operator    Operation                 Category         Operand Type(s)
  ------------------------------------------------------------------------------
      <        less than                 relational       numerical expression
      >        greater than              relational       numerical expression
      <=       less than or equal        relational       numerical expression
      >=       greater than or equal     relational       numerical expression
      =        equal                     relational       numerical expression
      <>       not equal                 relational       numerical expression
      &        logical and               boolean          boolean expression
      |        logical or                boolean          boolean expression
      !        logical inversion         boolean          boolean expression
  ------------------------------------------------------------------------------
Note: All operators listed above produce boolean type result. The result can only be used as the conditional statement for "if" function.

The "if" function

The "if" function has the following syntax:

if(conditional statement, expression1, expression2)

Surface Plotter will evaluate expression1 if conditional statement is evaluated to true and expression2 otherwise.
For example, the result of the following statement

if(x < 0, -x, x)

is -x if x is less than zero and x otherwise (absolute of x)
The following expressions are also valid:

z = (fx,y) = sin(if(x < 0; 2*x, 3*x))
z = f(x,y) = if(x = 0,0,sin(x)/x) - 2

And for the last, you can nest "if" functions. For example, you can write sign(x) as:

z = f(x,y) = if(x <= 0, if(x = 0, 0, -1), 1)

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