Introduction

igp.net supports the following data types:

• Point Set
• Function
• Polynomial
• Label
• Integral

Details

Point Set

This data type consists of a sequence of 2D points. They can be represented by four basic shapes: square, circle, cross and triangle. By default, points are connected with lines. You can enable/disable the lines as well as the points. You can also choose sizes, line colors, fill colors, etc. All ordinary stuff is possible here.

Each point set might have a function driver assigned. This means that y coordinate of each added/moved point will be sampled from a selected function. You can use both custom functions and polynomials - just choose a desired base function from a combo box it the point set edit page.

You can use custom transformations to modify coordinates. Just enter an expression with x representing old values. For instance, to flip all points horizontally. Enter -x as a formula, specify to affect y coordinates and click apply.

A Point Set can be used as a basis for constructing more sophisticated functions:

• approximation using linear regression,
• interpolation using a single Lagrange polynomial,
• interpolation using B-Splines.

By default, all of these trendlines are updated in real time while the pointset changes. To prevent this from happening, use the unbind function from the polynomials edit page to freeze a trendline in it's current shape.

You can copy/paste point coordinates in an Excel-friendly format (2 columns, each point corresponds to a row):

X<tab>Y
...
X<tab>Y

To display points' coordinates on the graph, just choose a desired location from a combobox: none, top, bottom, left, right. To specify what should be displayed use the coordinates pattern. x and y will be replaced by the x or y coordinate respectively. The default pattern is x ; y .

Function

This data type is defined by an arbitrary expression. It provides an ability to calculate accurate values of the function. Derivative values are approximated. See NumericGuide for more details.

igp.net also supports function series. Just enter an expression with a n parameter and enable series support for a specific function.

CAUTION Series support is an experimental feature. Use it with caution. Note that high number of needed iterations will significantly deteriorate the performance. Also note that you might disable function visibility to speed up graph refreshing. You can insert pointsets to capture current function shape with no performance cost.

Polynomial

Polynomials are defined by a set of pairs (m,e) where m is a multiplier and e is an exponent. This specific subclass of function allows to calculate accurate values of derivatives and intergals. Polynomials are intended primarily to be used for interpolation, but feel free to use them any way you like.

Label

Labels are simple text elements that might be placed within the graph with either graph-based on screen-based coordinates. They are used to display results of finding functions' roots and extrema.

Axes labels are constructed in the same manner as any other ones. Feel free to customize them to fit your needs.

Integrals

Integrals allow calculation of definite intergals, average values and curve lengths. Two calculation methods are supported (see NumericGuide for details):

• accurate - for polynomials only
• numeric - for both polynomials and arbitrary functions

You can specify a top and a bottom function. As the latter, the OX axis can be chosen.