Plotting Graphs from Mathematical Expressions

In RINEARN Graph 2D, you can not only plot graphs from data files but also generate graphs directly from mathematical expressions. This feature is referred to as "Math Plotting". This section provides an explanation of how to use this feature.

Additionally, this section explains the syntax used to write expressions for the math plotting tool.

Math Plotting Tools

The tools used for math plotting are developed using the VCSSL programming language, which is natively supported by RINEARN Graph 2D (For details, refer to "Control and Automation with VCSSL"). These tools can be launched from the "Program" menu at the top of the graph screen.

There are several tools available depending on the form of the mathematical expressions. These tools are also released as standalone applications, and detailed usage instructions are available on their respective web pages. Below is a list of the tools and an overview of each.

Plotting 2D Graphs in the y(x) Format

Plotting Animated 2D Graphs in the y(x,t) Format

Plotting Animated 2D Graphs in the x(t), y(t) Format

Legacy Math Plotting Tool

If needed, you can also use the legacy formula plotting tool from before RINEARN Graph 2D supported VCSSL. It is accessible from the menu at the top of the graph screen under "Tools" > "(Legacy) Math Plot".

This legacy tool only supports z(x,y) format graphs, and you must write variables like <x> and <y> surrounded by angle brackets. Despite its limitations, it is still available for long-time users accustomed to its functionality.

Please note that in this legacy tool, the "log" function represents the common logarithm (log10) rather than the natural logarithm (ln). (In the new tools, "log10" is explicitly used for common logarithms.)

Writing Math Expressions and List of Functions

In each math plotting tool, you can input formulas in the designated field, such as "z(x,y) =", using standard mathematical notation.

Examples of Math Expressions

Math expressions can be written as shown in the following examples:

To plot y = x + 1:

To plot y = x^2:

or

To plot y = sin(2x) + cos(3x):

Order of Operations

As shown in the examples above, multiplication is denoted by the "*" symbol, and division is denoted by the "/" symbol. Multiplication and division are calculated before addition and subtraction. If you want to prioritize addition or subtraction, enclose the desired part in parentheses, like (y + 2) * 3.

Mathematical Functions

In math expressions, you can use common mathematical functions, such as sin(2 * x) from the earlier examples. Examples of supported functions include the following:

sqrt( )

Square root

exp( )

Exponential function

log10( )

Base-10 logarithm
* Note: In the legacy formula plotting tool under the "Tools" menu, "log" is equivalent to "log10". However, in the new formula plotting tools under the "Program" menu (following the VCSSL specification), "log" is equivalent to "ln". To avoid confusion, it is recommended to use log10 or ln explicitly.

ln( )

Natural logarithm (base-e)

abs( )

Absolute value

fac( )

Factorial
* Note: In the legacy math plotting tool under the "Tools" menu, use "!( )" for factorials.

pow( )

Exponentiation
* Example: pow(2,3) for 2^3, or pow(-2,-3) for -2^-3.
* Note: In the legacy formula plotting tool under the "Tools" menu, use 2^3 instead.

sin( )

Sine (trigonometric function)

cos( )

Cosine (trigonometric function)

tan( )

Tangent (trigonometric function)

asin( )

Arcsine (inverse trigonometric function)

acos( )

Arccosine (inverse trigonometric function)

atan( )

Arctangent (inverse trigonometric function)

Additionally, many other mathematical functions are supported. For a complete list and details, refer to the VCSSL Math Library documentation.