Cardinal Spline

A Cardinal Spline is a series of individual curves between points joined to form a larger curve. The spline is specified by an array of points and a tension parameter. A Cardinal Spline passes smoothly through each point in the array; there are no sharp corners and no abrupt changes in the tightness of the curve. By passing through every point, there are no missed points that can cause errors when fitting a surface over the splines.

The tension of a Cardinal Spline determines the fitting of each curve section in regards to the data points. The range for the tension value is 0.0 to 1.0 where 1.0 would deliver straight lines between the data points and 0.0 would produce the most flexible curves fitted through each data point.

figure 1, Activating

The Cardinal Spline feature works on data clouds captured through the various scanning methods available in Geomet. To activate the feature, locate a data cloud feature in the inspection report and highlight it through the left click of the mouse. Then right click to bring up the sub menu. Locate [Cardinal Spline], see figure 1.

When activating the Cardinal Spline tool, Geomet will locate all data cloud features in you current inspection and display them in the tool. The Cardinal Spline tool will update all features that you select in one operation. In figure 2, we show that two features, number 4 and 6, will be updated.

figure 2, Cardinal Spline Setup Tool

There are three parameters used to tune the fitting process for splines. These are: Tension, Grid Distance and Location Filter. Understanding these parameters will greatly enhance your success in creating splines from data points.

Tension Parameter

This value controls how the spline is fitted between the data points. The valid range is 0.0 to 1.0 where 0.0 produces the largest radius between data points and 1.0 will produce straight lines between data points. We recommend that 0.0 be used as a default.

Grid Distance

This is the setting used when the original data points were scanned. Geomet carries it over from the scanning operation. However, on earlier Geomet systems, this value was not included in the original scan features and should be entered manually.

When applying Cardinal Splines to data clouds that do not conform to a uniform row / column configuration, undesirable results may occur. In this condition, Geomet allows the selection of "Create Single Curve" and "Force Fit" which is explained later in this document.

Location Filter

Geomet starts building rows and columns first by sorting the data points into row and column order. The location filter is applied when Geomet moves down a column and ‘looks’ for the next data point. For example: if the column has a start point with a "Y" value of 1.000", it would look down the column and expect to find the next point also with a "Y" value near 1.000". Since scanning operations do not deliver exact position, the data point under the start point might have a "Y" value of 1.012". The Location Filter is a factor of the grid distance where 0.15 would yield a search zone of 0.15 * Grid Distance (0.15 * 0.05 = .0075). This value determines the zone around the original "Y" value of 1.000" and the column sorting would not include the next point at 1.012.

In data clouds that have well-defined row and column structures, the Location Filter can be low, such as 0.25. In poorly defined patterns, use a value between 0.5 and 0.9.

When the value is set too high, the splines created can "jump" to neighboring points from other columns.

Under the group designated as "Spline Fitting and Display Options", you can establish the spline methodology and fitting behaviors.

Create Single Curve

This option will take all your data points without regard to rows and columns and fit the curves through each point in the same order as the points were captured. This option is designed to work with data point gathering options such as GeoTracer where you capture data points in a line with distinct start and finish end points. When this option is checked, the display and export of one spline for this feature will occur.

Rows / Columns

These selections are available when "Create Single Curve" is not chosen. They are designed to work with data points gathered under automatic scanning options in Geomet. These scanning options capture the data points in organized Row and Column formations that can be extracted to deliver uniform splines. When selecting Row and/or Columns, Geomet will attempt to build straight lines in the XY plane of the captured data points. Then rows and columns are extracted and used to form the splines. It is important that these rows and columns are organized in controlled positions. See Setup Parameters above.

Force Fit

This option is used with Rows and Columns. When calculating the rows and columns, some data points might be skipped if they do not fall within the parameter settings. This can cause a row to contain 2 or more splines. When selecting Force Fit, all data points identified in the row or column will be used to fit one spline. Another use for Force Fit is when there were exclusion zones used in data point scanning. This will fit the spline over the exclusion zone.

Closed Path

When this option is checked, Geomet will attempt to close the path from the last data point to the first.

Data Point

When selected, this option will display the complete set of data points in addition to any splines selected for showing.

Export Options

These options, combined with Spline Fitting and Display Options control the export characteristics. The selections of Row and Column for export are available when Create Single Curve is NOT selected.

NOTE: selecting Row and Columns in the Display group does not automatically create exported rows and columns!

NOTE: Cardinal Splines is exported in the IGES format only!

Rows

This selection will create and export splines derived from the data points that conform to rows. The rows exported are controlled by the selections of Force Fit and Closed Path.

Columns

This selection will create and export splines derived from the data points that conform to columns. The columns exported are controlled by the selections of Force Fit and Closed Path.

Data Points

This selection will export the data cloud in addition to any row and column selection already made.

Once the settings have all been established, select <Ok> to commence building the Cardinal Splines. Geomet will build rows and/or columns of data points and then perform the fitting of the Cardinal Spline. In figure 3, a raw set of data points that have been captured with Radial Boundary Contour using a grid spacing of 0.020" is shown. Figure 4 shows the application of Cardinal Spline.

figure 3, Raw Data Points	figure 4, Applied Cardinal Splines

To remove a Cardinal Spline from the data cloud, select <Remove> and the display will only show the data points.

Related Procedures:

Reverse Engineering Tools, Select Scan Method, GeoTracer, Radial Boundary Scan, 4-Point Boundary Scan, Line Scan, Export Tool