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2.10 Curvature Radius App

Contents

This Curvature Radius App can be used to calculate the radius of curvature at a specified point. After install this app, there should be an app icon named Curvature Radius in Apps panel.

Examples

  1. Make an empty worksheet active, then select menu item File: Import: Single ASCII... to import the Gaussian.dat file, which is under <Origin Installation Directory>\Samples\Curve Fitting\, using the default settings.
  2. Select column B, then choose menu item Plot: Symbol: Scatter to make a graph one plot.
    Curvature Radius Graph Create.png
  3. Make this graph to be the active window, Click Curvature Radius icon from Apps panel to bring up the Curvature Radius app.
  4. Use the default settings and click OK button to add ROI to graph.
    Curvature Radius Graph Add ROI.png
  5. Move the vertical line to the highest point, and then you can see the corresponding curvature radius is shown on the top of the vertical line.
    Curvature Radius Graph Move Line.png
  6. Click the ROI menu.png button, and then select New Output (O), then the result will be printed to Script Window.
    Curvature Radius New Output.png

Dialog Settings

ROI Box Tab

Curvature Radius ROI Box Dialog.png
Show Tool Name Specify whether to show the tool's name near the top of the layer.
Show on Graph Specify what to show on the graph.
  • XY Coordinate
    Specify whether to show the XY coordinate of the point on the graph.
  • Radius of Curvature
    Specify whether to show the radius of curvature on the graph.
Color Setting Specify the displaying color.
  • Vertical Line Color
    Specify the color of the vertical line, which is used to select a point.

Output Tab

Curvature Radius Output Dialog.png
Output Quantities To Customize the output results
  • Script Window
    Specify whether to output the results to Script Window.
  • Results Log
    Specify whether to output the results to Results Log.
  • Append to Worksheet
    Specify whether to append the results to a worksheet.
  • Result Worksheet Name
    This is only available when Append to Worksheet is checked. It is used to specify the name of the worksheet.
Quantities Specify the quantities to be outputted.
  • Dataset Identifier
    Specify dataset identifier for the output quantities.
  • XY Coordinate of Current
    Specify whether to output the XY coordinate of the specified point.
  • Current Radius of Curvature
    Specify whether to output the radius of curvature of the specified point.
  • XY Coordinate of Minimum Radius
    Specify whether to output the XY Coordinate of the minimum radius point.
  • Minimum Radius of Curvature
    Specify whether to output the minimum radius.
  • X Coordinate of All Radius
    Specify whether to output the X Coordinate of all radius.
  • All Radius of Curvature
    Specify whether to output all radius.

Fly-out Menu

Click the button ROI menu.png at the upper-right corner of the layer to expand the fly-out menu, which includes the following options.

Curvature Radius Flyout menu.png
New Output (O) Output the results to the specified windows (Script Window or Results Log), and the specified worksheet (if not empty, append the results).
Go to Report Worksheet Activate the report worksheet.
Go to Source Worksheet Activate the source data worksheet.
Find Minimum Radius Find the minimum radius in a specified x range and move the vertical line to that place.
Change Data Select the source data set. This is applicable only when there are multiple curves on the graph.
Save Theme Save the settings as a theme.
Save as <default> Save the settings as default theme.
Load Theme Load theme settings.
Preferences Open the Curvature Radius Preferences dialog.

Algorithm

In this gadget, the calculation for radius of curvature is assuming the curve is written in the form \(y = f(x)\), and then the radius of curvature is given by:

\[ R = \frac{(1+(\frac{dy}{dx})^2)^{3/2}}{|\frac{d^2y}{dx^2}|} \]

If the first order derivative or the second order derivative does not exist, the radius of curvature at that point does also not exist.