Using the box and cylinder that we created in AutoCAD, we will explore the effects of the various controls Rhino provides for meshing. These are the detailed controls. To reach the detailed control box from the "Create Polygon Mesh from NURBS Object" window (which pops up when you select Tools->Polygon Mesh->Mesh from NURBS Object), hit the Detailed Controls button. The detailed controls window is shown at left.
We will discuss each of these six controls and illustrate their influence on the box-cylinder mesh. At the end of this document, we will explain the purpose of each of the four check boxes. We will begin with a summary of our recommendations for setting the mesh controls.
Recommendations: Check Refine and Weld. Do not check Jagged Seams nor Simple Planes. Set Max Angle = 20. Set Max Aspect Ratio = 1. Preview the mesh. If there are too many polygons and/or some of the polygons are too small, try and preview various increasing values for Min Edge Length. If after you have optimized the Min Edge Length parameter there are overly large triangles, try and preview various values of Max Edge Length. We have found that setting the Max Edge Length = twice the value of Min Edge Length often generates the optimal setting. Note that the proper values for the Edge Length parameters depend on the numerical dimensions of your geometry—so you may need to use different values for different geometries.
Max Angle: We will begin with Max Angle = 20 and Max Aspect Ratio = 1. You must input a value for both of these quantities every time you mesh. The resulting mesh is very detailed, especially near the cylinder edges and the box-cylinder intersection. This mesh contains 1437 vertices and 1792 polygons:
Decreasing the Max Angle to 10 resulted in producing, as you might expect, an even more detailed mesh (4070 vertices and 4803 polygons). Increasing the Max Angle to 30 results in a more uniform distribution of polygons (no bunching near cylinder edges and box-cylinder intersection). This mesh contains 577 vertices and 730 polygons:
To assess the effects of the other controls, we will set Max Angle = 20 for the rest of this study.
Max Aspect Ratio: We took the original mesh and set the Max Aspect Ratio to 2 (Max Angle = 20 and Max Aspect Ratio = 2). This change reduced the mesh size slightly (1253 vertices and 1604 polygons). The main effect can be seen in the box which now contains higher aspect triangles:
We recommend setting the Max Aspect Ratio = 1 since that is ideal for thermal analysis.
Min Edge Length: We took the original mesh and added a Min Edge Length requirement of 1 (Max Angle = 20, Max Aspect Ratio = 1 and Min Edge Length = 1). The resulting mesh is too small to model the cylinder shape accurately. There is also a great variance in polygon size and aspect ratio; such variances are not good for thermal meshes. This mesh contains 137 vertices and 149 polygons:
Reducing the Min Edge Length to 0.5 improves the accuracy of the cylinder shape. This mesh, which contains 243 vertices and 262 polygons, suffers from overly large polygons on the box—especially when compared with the size of the polygons on the cylinder. The ready solution to this sort of problem is to use the Max Side Length control.
Max Side Length: We tested using the Max Side Length without setting a value for the Min Side Length. Compared with the original mesh (Max Angle = 20 and Max Aspect Ratio = 1), setting the Max Side Length to a value equal to or greater than 4 resulted in no change. A value of 2 or 3 for the Max Side Length did not reduce the size of the mesh; such settings only shifted the triangles on the box. Setting the Max Side Length to 1 increased the size of the mesh to 1529 vertices and 1897 polygons.
For the rest of our trials, we set the Min Edge Length = 0.4. We ran a series of trials at this condition (Max Angle = 20, Max Aspect Ratio = 1, Min Side Length = 0.4, and Max Side Length = varying).
Max Edge Length = 2
# Vertices = 334
# Polygons = 371
Max Edge Length = 1.5
# Vertices = 342
# Polygons = 381
Max Edge Length = 1
# Vertices = 417
# Polygons = 483
Max Edge Length = 0.8
# Vertices = 357
# Polygons = 397
Max Edge Length = 0.6
# Vertices = 451
# Polygons = 511
Max Edge Length = 0.4
# Vertices = 678
# Polygons = 763
In general, the smaller the value for Max Edge Length, the more vertices and polygons Rhino created. There is, however, an important transition between Max Edge Length values of 1.0 and 0.8. With this decrease in Max Edge Length, the mesh becomes smaller. When Max Edge Length is set below 1 (we did not check to see if this transition occurred exactly at 1.0; it did occur somewhere between 1.0 and 0.8), Rhino is "forced" into producing an orderly arrangement of polygons on the box. Whereas the arrangement of polygons for Max Edge Length >= 1.0 is somewhat random, for Max Edge Length <= 0.8 the polygons are arranged within rectangular grids. From this and other studies, we conclude that the best value of Max Edge Length is approximately double the value of Min Edge Length.
Max Distance To Surface: This control sets the maximum distance between the mesh and the surface. For the box-cylinder geometry, this exerted the same effect as Max Angle. Given the original mesh (Max Angle = 20 and Max Aspect Ratio = 1), setting the Max Dist To Surf >= 0.01 had no effect. A value of 0.001 resulted in a mesh with 10666 vertices and 11286 polygons. We recommend not setting this parameter for creating a mesh that will be imported into WinTherm.
Min Initial Grid Quads: Rhino creates a quad mesh on each NURBS surface in the first stage of meshing. While calculating the initial mesh grid, Rhino ignores trim curves. After the initial grid is complete, Rhino meshes all trim edges, connects the initial grid to the trim edges and then refines the mesh if the Refine option is selected. To examine the effect of this parameter, we started with the original mesh (Max Angle = 20 and Max Aspect Ratio = 1). Setting the Min Initial Grid Quads to a value of 1 had no effect. Setting it to a value of 10 resulted in a mesh with 1484 vertices and 1842 polygons, a slight increase in mesh size. The major difference between this and the original mesh is that the box polygons are more orderly. Since this effect can be achieved—with many fewer polygons—with judicious setting of the Min and Max Side Length, we advocate using the Side Length controls and leaving the Min Initial Grid Quad parameter blank.
The Check Boxes
Refine: When Refine is checked, after initial meshing, Rhino uses a recursive process to refine the mesh until it meets the criteria defined by Max Angle, Min edge length and Max edge length and Max dist, and edge to Srf options. Not checking Refine results in faster meshing, less accurate meshes, and lower polygon count. Clearing this check box produces untrimmed individual surfaces and surface areas away from trim edges and joined edges meshed with evenly sized quadrangles. We recommend checking Refine.
Jagged Seams: When Jagged Seams is checked, all surfaces are meshed independently and the meshes of joined surface edges are not stitched together. Cracks will appear between joined surfaces in the rendered image when this option is checked. Do not check Jagged Seams.
Simple Planes: When Simple Planes is checked, all planar surfaces are meshed by meshing the surface edges and then filling the area bounded by the edges with triangles. Selecting this check box results in slower meshing and minimum polygon count on planar surfaces. Meshing can be slower especially for complex trimmed surfaces. We have found no reason to use this option.
Weld: Selecting this check box welds coincident mesh control points that come from seams between tangent surfaces of a polysurface. We recommend using the Weld option.
Learn More About Meshing
There are many codes that will create a polygon mesh. Most of these will not create a mesh suitable for thermal analysis. The following is a review of some of these tools. We do not endorse any specific code; rather, we supply this information as a guide.
by James Truax, ThermoAnalytics, Inc.
Version 1.0
I. Creating Surfaces
From Curve Network – (NetworkSrf ® Surface – From Curve Network)
Usage
This is the newest surface creating command Rhino has implemented. It is available in the latest beta version at www.rhino3d.com. This command uses two series of curves to create a single surface. These sets of curves run along and perpendicular to the surface.
> WATCH THE VIDEO
Rhino is a NURBS modeler produced by Robert McNeel & Associates. A demo of Rhino can be downloaded from their website, http://rhino3d.com. Although Rhino has meshing capability, McNeel does not promote Rhino as a meshing utility. As a result, there is little information about meshing in the Rhino website, manual, or online help. In this document we will illustrate several techniques for creating a mesh using Rhino.
