## TableCurve 3D Model Complex Data Sets Fast and Easy

#### Eliminate Tedious Data Analysis Chores with TableCurve 3D

TableCurve 3D is the first and only program that combines a powerful surface fitter with the ability to find the ideal equation to describe three dimensional empirical data.

TableCurve 3D uses a selective subset procedure to fit 36,000 of its 453,697,387 built-in equations from all disciplines to find the one that provides the ideal fit – instantly!

## Overview

Model Complex Data Sets Fast and Easy

What once could take days of tedious work now takes minutes, with a much more powerful result.

Find Optimum Equations to Describe Empirical Data

TableCurve 3D® gives scientists and engineers the power to find the ideal model for even the most complex data, including equations that might never have been considered. TableCurve 3D’s built-in equation set includes a wide array of linear and nonlinear models for any application:

• Linear equations
• Polynominal and rational functions
• Logrithmic and exponential functions
• Nonlinear peak functions
• Nonlinear transition functions
• Nonlinear exponential and power equations
• User-defined functions (up to 15)

TableCurve 3D’s state-of-the-art surface fitting includes capabilities not found in other software packages:

• In addition to standard least squares minimization, TableCurve 3D’s non-linear engine is capable of three different robust estimations: least absolute deviation, Lorentzian minimization and Pearson VII Limit minimization.
• Option to change the maximum number of terms permitted when fitting linear equations (minimum 3; maximum 11)
• On systems that support multi-threading, TableCurve 3D’s Background Thread Processing option allows fitting to occur without any form of user input
• Option to set the default term significance anywhere from 1 to 15.

Automation Takes The Trial And Error Out Of Curve Fitting

Using its selective subset procedure, TableCurve 3D will fit 36,000 of the over 450 million built-in equations or just the ones you need – instantly. With TableCurve 3D, a single mouse click is all it takes to start the automated curve fitting process – there is no set up required! You can even enter your own specialty models to be fit and ranked along with the built-in equations. TableCurve saves you precious time because it takes the endless trial and error out of curve fitting.

User-Defined Fit Functions

Up to 15 user-defined equations can be entered and ranked along with the built-in equations. These specialized models can contain most mathematical constructs, including special functions, series convergence and conditional statements, differentiations, integrations and parameter constraints. TableCurve 3D even offers the option of graphically adjusting equation parameters to assure convergence for the fit of user-defined models. Unlike most surface fitting programs, TableCurve 3D’s user-defined functions are compiled so they can be fitted at nearly the speed of the built-in equations. For maximum flexibility, TableCurve 3D gives you the option to save your functions as individual files, in libraries or both.

Visually Discover the Best Equation to Model your Data: Graphically Review Surface Fit Results

Once your XYZ data have been fit, TableCurve 3D automatically sorts and plots the fitted equations by the statistical criteria you select (r2, DOF adjusted r2, Fit Standard Error or the F Statistic). Graphically review the fitted results as you scroll through the equation list. A 3D residuals graph as well as parameter output are generated for each fitted equation. Add confidence or prediction intervals to the graph to detect outliers in your data. You can also automatically display a 2D contour plot on the top and bottom of the surface fit graph to get another view of your data. Data, statistical and numeric summaries are also available from within the Review Surface Fit window so you can further analyze fit results.

The Best Fit

Viewing a surface fit from all angles is imperative in determining whether or not a given fit is accurate. Using a simple interface, TableCurve 3D lets you view a graph from any angle. It will even animate the graph automatically in a specified XY and/or Z angle sequence. Just sit back and observe every nuance within the fit. TableCurve 3D gives you all of the tools you need to discover the model that best meets your requirements for the ideal fit.

Flexible Output Options

Output TableCurve 3D’s publication-quality graphs in black and white or color, portrait or landscape. You can also produce files containing data and equations in Lotus, Excel, ASCII, Quattro Pro and SigmaPlot formats. TableCurve 3D can speed up your programming by generating actual function code and test routines for all fitted equations in FORTRAN, C, Basic and Pascal.

All This Power – and Still Easy to Use!

TableCurve 3D takes full advantage of the Windows graphical user interface to simplify every aspect of operation – from data import to output of results. Import data from many popular file formats including SigmaPlot, Excel, Lotus, SPSS and ASCII. Once your data are in the TableCurve editor, start the automatic fitting process with a single mouse click. Choose to fit all equations, select a group of equations or create a custom equation set. All equations are readily available from the Toolbar or TableCurve’s Process Menu. You can even set up TableCurve 3D to begin fitting the moment data are imported or modified with Background Thread Processing Fitting. Users consistently comment that – out of the box, without reading the instructions – TableCurve is highly intuitive, easy-to-use and remarkably simple to learn.

## Product Features

The product features for PeakFit are detailed below in the following categories:

Data Input

• ASCII
• Excel®
• Lotus 123®
• Quattro Pro®Windows®
• SigmaPlot®
• AIA Chromatography
• dBase ® III+, IV
• DIF
• ASCII and Spreadsheet – like Editors
• Averaging Digital Filter

Data Preparation

• Gaussian Deconvolution to remove Spectrophotometer Instrument Response smearing
• Exponential Deconvolution to remove Chromatographic Detector Response smearing
• Smoothing (Savitsky Golay, FFT Filter, Loess, Gaussian Convolution)
• Real – time FFT/Time Domain Graphical Editor
• Dual Graph Data Sectioning with Graphical data point exclusion
• Non – Parametric Digital Filter to Filter or augment data
• Compare with Reference
• Subtract Baseline Imported from File
• Data Transforms
• Area Normalization
• Inspect Second and Fourth Derivatives
• Data Weighting

Peak Autoplacement

• Automatic by Local Maxima and Residuals
• Automatic by Second Derivatives
• Automatic by Deconvolved Local Maxima
• Share and Lock Parameters
• Constant or V ariable Widths and/or Shape in a single step

Non-Linear Curve Fitting

• Marquardt – Levenburg Algorithm
• 83 built-in nonlinear peak models
• Least – Squares and 3 Robust (Maximum Likelihood) methods
• Up to 100 Peaks and 1000 Parameters
• Intelligent Constraints to insure Fit Integrity
• Sparse Curvature Matrix for Faster Fitting
• Both Numeric and Graphical Fitting Options
• Zoom – in or Toggle Points during Fitting

Output and Export Options

• File Export with full Generated Data: Lotus 123, Excel, Quattro Pro Windows, SigmaPlot, and ASCII
• Graphs to clipboard or file in BMP or WMF formats
• All Numeric data in Graph to Clipboard in Spreadsheet Format

## Automation

#### Automation Code Generation

• FORTRAN 77, FORTRAN 90, C, C-80 bit, QBasic and Pascal
• Function code or function code with full test routines
• Available for all built-in equations

## TableCurve 3D Surface Fitting Features

3D surface fitting features in TableCurve 3D are listed below:

Technical Specifications

• 453,697,490 built-in equations
• 243 polynomials, including 18 Taylor series polynomials, 36 Chebyshev polynomials, 13 Fourier simple and true bivariate models, 9 Cosine Series models, 9 Sigmoid Series models
• 260 rationals, including 4 rationals with Taylor series numerators and denominators and 40 Chebyshev rationals
• 453,696,714 selective subset mixed basis function linear equations, of which up to 36,582 will be selected within a given fit
• 72 3D nonlinear peak equations
• 72 3D nonlinear transition equations
• 24 3D nonlinear exponential and power equations
• 4 robust plane equations
• Rapid searching, sorting, and filtering of equations
• User customizable equation sets
• Full control of fit process, including goodness of fit criteria, minimization and other options
• Robust plane fitting option
• Three robust fitting methods available for all nonlinear equations and user functions

#### User-Defined Functions (UDFs)

• UDF editor with push-button help for inserting functions
• UDFs automatically compiled for speed
• Up to 15 UDFs can be fit at one time, each with up to 10 adjustable parameters
• Graphical UDF adjustment procedure for refining starting estimates
• UDFs can be saved as libraries

#### Non-Parametric Fitting

• Algorithms for gridded data include B-Spline, Bicubic+Akima, Akima III, B-Spl Var knots, NURBS
• Algorithms for scattered data include Akima I, Akima II, Preusser, Renka I,Renka II, Renka III, Watson, Loess
• Fill Sparse Grid option that uses scattered data interpolation algorithms to complete a sparse or incomplete grid
• Interpolate Uniform grid option that uses scattered data algorithms to generate a uniform grid of estimated values

#### Surface-Fit Analysis and Output Numerical

• Evaluation option with automated table generation, includes function, derivatives, roots and cumulative volume
• Full numeric and statistical summary, including coefficients, standard error, confidence limits, ANOVA, goodness of fit, measured function minima and maxima
• Data summary with predicted values, residuals and confidence/prediction limits
• Precision summary and term significance analysis
• Quick Evaluation option for estimation at a point, minimum, maximum
• Save Quick Evaluation and Evaluation across all sessions
• Five levels of perspective for 3D viewing with full angular control of light source illumination
• Confidence/prediction intervals (90%, 95%, 99%, 99.9%, 99.99%)
• Intellimouse rotation of 3D view angles
• Inspect any of the five first or second order partial derivatives

#### Graphical

• Surface-fit graph with customizable layout, backplanes, labels, grids, scaling, points, font, titles and resolution
• All customizations rendered in real time
• Fourteen types of gradient plots, including one each for Excel, Lotus and Quattro palettes
• Four types of shaded plots with full angular control of light source illumination
• Mesh resolution up to 120×120
• Contour plots can be added automatically
• Full animation of fitted surfaces
• Adjustable cache size and compression method for surface-fit graphs
• 3D Residuals graphs

## Applications

Quite often, substantial cost savings can be realized by optimizing process control parameters. Since TableCurve 3D automatically reports the XYZ locations for the surface’s minimum and maximum, process optimization is often a simple matter of using a single number within a TableCurve 3D report.

TableCurve is an excellent tool for examining response surfaces from designed experiments.

Create Black Box Models

At times, engineers and scientists may be faced with a highly complex process, such as human biochemistry, where underlying models are poorly defined. For such instances, TableCurve 3D can provide important insights into the subtle mechanisms in play. A successful model may suggest further experiments in synergistic pharmaco-kinetics, high energy physics or reaction chemistry.

Generate Calibration Curves

TableCurve 3D excels for those applications in the field of calibration science where an additional variable, such as temperature, influences the calibration. Whether you need to calibrate a sensor, a flow meter, wind tunnel measurements or satellite instrumentation signals, TableCurve 3D can furnish the ideal approximating function.

Produce Equations for Complex Modeling or Monte-Carlo Simulations

TableCurve 3D can be used to convert empirical data from hundreds of sources into simplified surface equations. These equations can then be input into complex models or Monte-Carlo simulations to simulate the effects of hundreds or even thousands of variables upon a given model.

Fit Tabulated Data

Frequently, scientists and engineers need to convert tables of data found in handbooks or journal publications into a simple equation, often for use in software or microcode. TableCurve 3D is capable of producing equations which preserve all or most of the accuracy present within the tabulated data. TableCurve 3D even furnishes a Precision Summary for instrument designers who must use fixed point math in their microprocessors.

Interpolate Data

There is no simpler, faster or more automated way to interpolate surface data than TableCurve 3D. Data tables or individual points are effortlessly generated for even the most demanding data sets.

## Product Uses

Precisely Characterizing Changes in Surface Condition of Material Combusted in Microgravity Environment Using Ultrasonic Imaging and TableCurve 3D®

Three dimensional TableCurve 3D graphs made before-and-after combustion in Space Shuttle microgravity of a plastic specimen surface height profile that demonstrates the flame spread mechanism at work.

Surface Profiling

Precisely characterizing the changes in surface condition of material combusted in microgravity environment were made using ultrasonic imaging and TableCurve 3D. A comparison was made of the material specimens before and after microgravity combustion experiments. It was important to characterize the changed surface profile after the burn. These experiments were performed to better understand how flames spread in the microgravity environment such as would be present on the International Space Station. This type of information is critical for safety of astronauts on the Space Station.

Ultrasonic imaging technique were used to acquire precise information about the surface profile before and after the burn. This involved acquiring precise ultrasonic wave time-of-flight data across the entire surface. The time-of-flight measurements (x,y position and time-of-flight (msec)) were converted to surface depression (microns). The experiment was done on the Space Shuttle flight# STS-54. The data was then imported into TableCurve 3D for 3D viewing and data manipulation.

The figures below show the surface height in microns of a plastic sample as a function of x and the y position in mm before and after the burn.

Figure 1 above shows a surface map of a material sample before burning in microgravity environment as it appears in TableCurve 3D.

Figure 2. The material sample after burning in microgravity as it appears in TableCurve 3D.

The burn front traveled from right-to-left and caused an ~ 1000 um depression initially, followed by a decreasing (ramping) depression, and finally, an actual increase (hump) in the surface before burning out.

The burn profile is significantly different from that seen in a normal gravity environment.

## System Requirements

Below are the minimum requirements to run TableCurve:

#### Hardware

• 486 Processor or higher
• 16 MB RAM required (32 MB or more recommended)
• 10MB hard disk space

#### Software

Windows 10, 8.x,  7, Windows Vista, 95, 98, NT and XP (32 bit)

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