Updated 10 Aug 2003

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Rhino has a number of tools for creating and editing meshes. We looked at ‘Mesh from NURBS object’ on the previous page. Here we will try out the ‘Apply Mesh to NURBS Surface’ tool and then look at how UV coordinates can help us orientate a mesh correctly.

2.   We will use the ‘Mesh from NURBS’ tool we encountered in the previous tutorial, and we will use the ‘Detailed Controls...’ to set the size of the polygons from which our mesh will be made. Click the ‘Mesh from NURBS’ tool’ and select the rectangular plane. Set the Maximum edge length  to 1 unit. This will force the mesh to be made of  polygons no bigger than 1 unit square. You can of course pick any figure to suit your application and scale. Hit the OK button and a mesh will be created. Remember that the mesh is an additional part, and your original rectangular NURBS surface remains,  covered exactly by the mesh. You can move one to reveal the other.

1.   First step, make a rectangular surface to act as a master part for our mesh. Here we have a surface 5 units high, 10 wide. The size and proportions will have some bearing on the mesh we generate from it. This may be important if we know already how many polygons we want to use on our model part.

3.   Here we can see the mesh created is made from 66 points and 50 polygons, and the original surface is selected, highlighted in yellow. The mesh is 10 polygons wide and 5 high, the same number of units as the original surface. To make a mesh of a different number of polygons, we could change either the size of the original surface, or the Maximum edge length.

4.   Now we need a surface to which we will apply our mesh. Here we have created a simple wing upper surface from two curves, and used two straight lines joining the ends of the curves. These construction lines are highlighted in yellow. We used a 2-rail sweep, but a loft or surface from edges would work just as well. The wing surface is indicated in black, and it is this surface to which we will apply our mesh.

5.   Here we can see the ‘Apply Mesh to NURBS Surface’ tool in use,  the mesh is selected and highlighted and the command line is requesting the surface to which the mesh is to be applied should be selected. We will now click on the wing surface and the mesh will be fitted over it. When this is done, we can select either mesh or surface as seperate parts.

6.   This view shows the original wing surface and the mesh we created, moved back to seperate them. Note that we would not usually move meshes away from their original NURBS surface locations because we want to retain the accuracy of the original surface geometry. It would be sensible to place the NURBS items on seperate layers so they could be viewed or turned off with the layers dialogue.

7.   So far, this tutorial has shown the sequence of operations to use the ‘Apply Mesh to NURBS Surface’ tool. It has not yet produced an ideal mesh for this wing, however. For example, the shape would be better represented if the ‘10’ side of our mesh was along the wing root rather than the leading edge. Also while the mesh we have created would certainly render very well, the polygon count is high for this particular shape. As the leading and trailing edges of this particular wing are straight, we could have polygons running all the way from from root to tip. Even with 10 edges along the root, this would mean the wing surface would have only 10 polygons; a significant saving.

9.   In this view we created a mesh 1 x 10 polygons; it is highlighted in yellow. When we apply this to the wing surface we find it is orientated so the short side ( 1 unit long) is mapped from front to back, rather than root to tip. This is shown in red. Not what we want at all! Somehow we need to reorientate the mesh through 90 degrees when it is applied to the wing surface.

10.  Clicking on the ‘Direction’ button then selecting a NURBS surface will show us several things about it. White arrows will give a ‘facing direction’,and if we place the cursor over the surface two small arrows, one green and one red, will indicate the orientation of the U and V coordinates of the surface. Here we are examining the wing surface and we can see the red arrow points from tip to root, while the green arrow points forwards to the leading edge. Doing the same examination of the original rectangle used to make our mesh, the red arrow points towards the 1 unit edge, while the green arrow points to the 10 unit edge.

Notice we are looking at the NURBS surfaces, and NOT the mesh made from these surfaces. The UV directions are inherited by the meshes produced, but Rhino cannot display these on a mesh object.

However, when a mesh is applied to a NURBS surface the UV directions are aligned. Therefore we need to somehow change the direction of either the wing surface or the surface making the mesh so that both red arrows point the way we want, and the mesh gets applied in the right direction.

11.  In this view, the ‘Direction’ button has been clicked and the wing surface selected. The Command History shows a list of possible commands that can then be applied and we have typed in ‘swapuv’ and hit the Enter key. Now the red arrow points forwards, the green one spanwise. Hitting the Enter key will finish the command, and now when we apply the mesh the polygons will align themselves so that the 10 unit edge will be along the root, and the single polygon side will run along the leading edge of the wing. Just what we wanted!

12.  Here is the final mesh in front of the original NURBS surface. 10 polygons only, and when rendered in the flight sim it will be appear indistinguishable from a wing with hundreds of polygons.

The next tutorial will show how we can edit a mesh by manipulating the vertices, adding and deleting polygons and joining meshes produced from different original NURBS surfaces.

Any comments or suggestions, feel free to E-mail Tim or James here.