Second Phase of the Honda Grant:

Title :: Constrained Scaling of Trimmed, Multi-Patch NURBS Surfaces

PI : Dr. Fuhua (Frank) Cheng
Co-PI : Dr. Caiming Zhang, Dr. Pifu Zhang

Goal :

To Provide the design industry with the capability of globally or locally

modifying (scaling) an existing model (such as a vehicle) in length, heigth,

or width without affecting certain significant features (trimming curves) on

the original model and, consequently, avoiding expensive re-desiogn process.

Current Achievement :

Two techniques have been developed by our research group for the second

phase. They are the attach-and-deform based approach and the fix-and-

stretch based approach. The first result was published in the ASME DTM

Conference:

  "Constrained Shape Scaling of Trimmed NURBS Surfaces"
   (with P.  Zhang and C. Zhang), Proc. 1999 ASME Design
   Theory and Methodology Conference (ASME DTM-99),
   September 12-15, 1999, Las Vegas, NV.

The second result will appear in the Computer-Aided Design journal:

  "Constrained Shape Scaling of Trimmed NURBS Surfaces using
   Fix-and-Stretch Approach" (with P. Zhang and C. Zhang), to
   appear in Computer-Aided Design.

A brief description and analysis of these techniques are given below.

First technique : the attach-and-deform based approach

The new surface is formed by scaling the given (multi-patch) NURBS surface
according to the scaling requirement first.  The (original) features are then
attached to the scaled NURBS surface at appropriate locations. Because of the
difference between the curvature of the scaled surface and the original features,
a deformation of the scaled surface is needed to guarantee complete attachment
of the features to the scaled surface.

The deformation process of the scaled surface should not change the boundary
curves of the scaled surface (to avoid violating boundary condition with adjacent
surfaces).  It should also reflect the shape and curvature distribution of the
scaled surface. This is achieved by minimizing a shape-preserving objective
function which covers all the factors in the deformation process such as bending,
stretching and spring effects.

The resulting surface maintains a NURBS representation and, hence, is compatible
with most of the current data-exchange standards.

This process can be illustrated as follows :

• Stage 1 : Scale the given NURB surface

  

• Stage 2 : Remove the scaled feature

  

• Stage 3 : relocate the original feature (attach the original feature to the scaled

  surface)

  

• Stage 4 : Deform the Scaled surface so it would contain the relocated feature and, in the

  mean while, reflect the shape and curvature distribution of the original surface

  

  ---

  Examples of the first technique :

  Two surfaces taken from the following Honda truck body model

  have been used in the test cases

  

  • Example 1 : A 54-patch surface of the front hood (the green surface with two trimming curves)

    Before Scaling (with highlight lines)

    

    Before Scaling (without highlight lines but showing all the patches)

    

    After scaling (with highlight lines)

    using the attach-and-deform approach (scaling factors: 1.2, 1.2, 1.2)

    

    After scaling (with highlight lines)

    using the attach-and-deform approach (scaling factors: 1.5, 1.5, 1.5)

    

  • Example 2: A 42-patch surface of the side (the blue surface with two trimming curves)

    Before Scaling (with highlight lines)

    

    Before Scaling (without highlight lines but showing all the patches)

    

    After scaling (with highlight lines)

    using the attach-and-deform approach (scaling factors: 1.2, 1.2, 1.2)

    

    After scaling (with highlight lines)

    using the attach-and-deform approach (scaling factors: 1.5, 1.5, 1.5)

    

  • Example 3: An 8-patch hood surface with 3 trimming curves

    Before Scaling (with highlight lines)

    

    Before Scaling (without highlight lines but showing all the patches)

    

    After scaling (with highlight lines)

    using the attach-and-deform approach (scaling factors: 1.15, 1.2, 1.3)

    

  • Example 4: An 36-patch trunk hood surface with 2 trimming curves

    Before Scaling (with highlight lines)

    

    Before Scaling (without highlight lines but showing all the patches)

    

    After scaling (with highlight lines)

    using the attach-and-deform approach (scaling factors: 1.15, 1.2, 1.3)

    

  • Example 5: An 36-patch door panel surface with 2 trimming curves

    Before Scaling (with highlight lines)

    

    Before Scaling (without highlight lines but showing all the patches)

    

    After scaling (with highlight lines)

    using the attach-and-deform approach (scaling factors: 1.15, 1.2, 1.3)

    

    After scaling (with highlight lines)

    using the fix-and-stretch approach (scaling factors: 1.3, 1.3, 1.3)

    

    ---

    ---

    Second technique : the fix-and-stretch based approach

    
    
    The basic idea of the second technique is to hold selected regions that
    contain the features unchanged while stretch the remaining part of the
    surface until certain boundary condition is reached.
    
    More specifically, the new surface is formed by fixing selected regions
    of the given trimmed NURBS surface that contain the trimming curves and
    stretching the remaining part of the surface to reach certain boundary
    condition. The stretching process is performed using an optimization
    process to ensure that the resulting surface reflects the shape and
    curvature distribution of the scaled version of the given surface.
    The resulting surface maintains a NURBS representation and, hence,
    is compatible with most of the current data-exchange standards.
    
    The idea can be illustrated as follows :
    
    

    ---

  • Stage 1 : Identify regions to be held unchanged during the stretching process

    

  • Stage 2 : Stretch the remaining part until certain boundary condition is reached

    

    ---

    Examples of the second technique:

    The surfaces used here are the same as the ones used in Approach 1.

    • Example 1 : A 54-patch surface of the front hood (the green surface with two trimming curves)

      Before Scaling (with highlight lines)

      

      Before Scaling (without highlight lines but showing all the patches)

      

      After scaling (with highlight lines)

      using the fix-and-stretch approach (scaling factors: 1.2, 1.2, 1.2)

      

      After scaling (with highlight lines)

      using the fix-and-stretch approach (scaling factors: 1.5, 1.5, 1.5)

      

    • Example 2 : A 42-patch surface of the side (the blue surface with two trimming curves)

      Before Scaling (with highlight lines)

      

      Before Scaling (without highlight lines but showing all the patches)

      

      After scaling (with highlight lines)

      using the fix-and-stretch approach (scaling factors: 1.2, 1.2, 1.2)

      

      After scaling (with highlight lines)

      using the fix-and-stretch approach (scaling factors: 1.5, 1.5, 1.5)

      

    • Example 3: An 8-patch hood surface with 1 trimming curve

      Before Scaling (with highlight lines)

      

      Before Scaling (without highlight lines but showing all the patches)

      

      After scaling (with highlight lines)

      using the fix-and-stretch approach (scaling factors: 1.1, 1.2, 1.25)

      

    • Example 4: An 36-patch trunk hood surface with 2 trimming curves

      Before Scaling (with highlight lines)

      

      Before Scaling (without highlight lines but showing all the patches)

      

      After scaling (with highlight lines)

      using the fix-and-stretch approach (scaling factors: 1.1, 1.2, 1.25)

      

    • Example 5: An 36-patch door panel surface with 2 trimming curves

      Before Scaling (with highlight lines)

      

      Before Scaling (without highlight lines but showing all the patches)

      

      After scaling (with highlight lines)

      using the fix-and-stretch approach (scaling factors: 1.1, 1.2, 1.25)

      

      After scaling (with highlight lines)

      using the fix-and-stretch approach (scaling factors: 2.0, 2.0, 2.0)

      

      ---

      ---

      Comparison :

      
      
      The second approach is more robust than the first one in that it can
      tolerate scaling factors of bigger values (up to 2 in some cases, see
      Examples 1, 2, and 5 for approach 2), while the first approach would
      generate abnormal curvature distribution for scaling factors as low as
      1.3 (see Examples 1, 2, and 5 for approach 1).
      The second approach also guarantees that the features (trimming curves)
      remain exactly the same after scaling.
      
      The disadvantage of the second approach is that it needs more memory
      than the first approach in some cases. Hence, it can not handle as
      many trimming curves as the first approach does on a machine with
      small internal memory. For instance, the first approach can handle
      three trimming curves for Example 3 while the second approach can
      only handle one trimming curve for that example on our machine.
      
      
      

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      Comments

      Fuhua (Frank) Cheng / cheng@cs.engr.uky.edu