Design and analysis of Bezier curves

Bezier curve is generated by a set of control points. The degree of the Bezier curve is one less than the number of control points. The entire Bezier curve lies within the convex hull of the control polygon. It is challenging for students to understand all the properties of a Bezier curve. This is a GUI which simulates the behavior of this Bezier curve using NX API, C++ and Ufuncs. This enables students to interact with GUI by providing various control points and visualize their effect on the shape of curve.

Installation Manual

  1. Download and extract the contents of the .zip file named Design & Analysis of Bezier
  2. Open the extracted folder named Design & Analysis of Bezier Curves.
  3. Open the folder named ug_customization. Right click on the Windows Batch File named nx and open with Notepad/Notepad++.
  4. Find the current file path of the nx file in your computer (Right click >> Properties). Copy the file path and paste it in the first line (the highlighted portion in the notepad as shown below).    
  5. Change the version of Siemens NX to the one you are using (module works for Siemens NX 10.0, 11.0, and 12.0) in the third line of the notepad file (as highlighted below).
  6. Once these steps are carried out, you have completed the installation procedures before launching the application.
Support Accessibility Output Window
Support Accessibility Output Window

Instruction Manual

NX API based GUI

NX API based GUI

  1. Now, double-click nx to launch the Windows Batch File. This will launch the Siemens NX window and a terminal window (you can minimize it or close it – it contains the information you input in steps 4 and 5). You may notice the UC Geometric Modeling Modules tab in the top toolbar. Click on it. The Design & Analysis of Bezier Curves module will be visible.
  2. To create a Bezier Curve, the user is supposed to specify the control points based on the degree of curve to be generated.
  3. Once Siemens NX is launched, you can click on the Design & Analysis of Bezier Curves button on the Command Ribbon. 
  4. The Design & Analysis of Bezier Curves GUI is shown in the figure below. The detailed explanation of each option in the GUI is given below.
    1. Tangent at U
      The parametric space ‘u’ between 0 and 1 at which the tangent to the Bezier curve is to be calculated.
    2. Specify Point
      Specify the control point of the Bezier curve using the point dialog or the cursor.
    3. Add Control Points
      Click on add control points before adding any control point of the Bezier curve and then use specify point to add the control point.  
    4. Use ‘OK’ or ‘Apply’ to plot the Bezier curve on the NX window. To undo the plot of the Bezier curve use ‘ctlr+Z’.1.    
  5. The output window of the Design & Analysis of Bezier Curves module is shown below. The result consists of the Bezier curve, convex hull, control polygon, degree of the curve and the tangent at specified ‘u’. 
Bezier curve of degree 7 with a convex hull and a control polygon

Bezier curve of degree 7 with a convex hull and a control polygon

Please watch the video tutorial of the module for an example included with the zip file of the module.    

Output from the GUI

Example Problem

Try out the following to learn the impact of change in control points on the shape of Bezier curve and visualizing the properties of the curve.

  1. Generate a Bezier curve with the control points A (0, 100, 0), B (100, 100, 0), C (100, 0, 0), D (200, 0, 0). Calculate the value of the tangent vector for the curve at u = 0.5
  2. Change the value of the control point B from [100, 100, 0] to [150, 150, 0]. find the new coordinates of the Bezier curve and plot this curve. Explain whether this changes the shape of the curve locally or globally
  3. To the generated curve, add an additional control point [125, 125, 0] between B & C and plot the new curve.