Blender Documentation: Last modified July 30 2003 s68
<<< Previous | Curves and Surfaces | Next >>>

## NURBS

NURBS curves are defined as rational polinomyals, and are more general, strictly speaching, than conventional B-Splines and Beziér curves. They have a large set of variables, which allow you to create mathematically pure forms. However working with them requires a little more intuition:

- Knots. Nurbs curves have a knot vector, a row of numbers that specify the parametric definition of the curve. Two pre-sets are important for this. "Uniform" produces a uniform division, for closed curves, but for open one you will end with "free" ends, difficult to locate precisely. "Endpoint" sets the knots in such a way that the first and last vertexes are always part of the curve, hence much easier to place;

- Order. The order is the 'depth' of the curve calculation. Order '1' is a point, order '2' is linear, order '3' is quadratic, etc. Always use order '5' for Curve paths; this behaves fluidly under all circumstances, without irritating discontinuities in the movement. Mathematically speaking this is the order of both the Numerator and the Denominator of the rational polynomial defining the NURBS;

- Weight. Nurbs curves have a 'weight' per vertex - the extent to which a vertex participates in the "pulling" of the curve.

Figure 3. Setting Nurbs Control polygon and weights.

Figure 3 Shows the Knot vector settings as well as the effect of varying a single knot weight. Just as with Beziers, the resolution can be set per curve.

###

Working example

Blender's curve tools provide a quick and easy way to build great looking extruded text and logos. We will use these tools to turn a rough sketch of a logo into a finished 3D object.

Figure 4 shows the design of the logo we will be building.

Figure 4. The sketched logo

First, we will import our original sketch so that we can use it as a template. Blender supports TGA, PNG and JPG format images. To load the image, move the cursor over a 3D window and press SHIFT+F7 to get to the view settings for that window. Activate the BackGroundPic button and use the "LOAD" button to locate the image you want to use as a template (Figure 5).

Figure 5. 3D window settings.

Return to the 3D view by pressing SHIFT+F5 (Figure 6). You can hide the background image when you are finished using it by returning to the SHIFT+F7 window and deselecting the BackGroundPic button.

Figure 6. Logo sketch loaded as background

Add a new curve by pressing SHIFT+A->CURVE->BEZIER CURVE. A curved segment will appear and Blender will enter EditMode. We will move and add points to make a closed shape that describes the logo you are trying to trace.

You can add points to the curve by selecting one of the two endpoints, then holding CONTROL and LMB. Note that the new point will be connected to the previously selected point. Once a point has been added, it can be moved by selecting the control vertex and pressing GKEY. You can change the angle of the curve by grabbing and moving the handles associated with each vertex (Figure 7).

Figure 7. Beziér handles

You can add a new point between two existing points by selecting the two points and pressing WKEY>>SUBDIVIDE (Figure 8).

Figure 8. Adding a Contrl Point.

Points can be removed by selecting them and pressing XKEY->SELECTED. You cut a curve into two curves by selecting two adjacent control vertices and pressing XKEY->SEGMENT.

To make sharp corners, you can select a control vertex and press CTRL+V. You will notice the colour of the handles change from purple to green (Figure 9). At this point, you can adjust the handles to adjust the way the curve enters and leaves the control vertex (Figure 10).

Figure 9. Vector (green) handles.

Figure 10. Free (black) handles.

To close the curve and make it into a single continuous loop, select at least one of the of the control vertices on the curve and press CKEY. This will connect the last point in the curve with the first one (Figure 11). You may need to manipulate some more handles to get the shape you want.

Figure 11. Figure Figure 8

Leaving editmode with TAB and entering shaded mode with ZKEY should reveal that the curve renders as a solid shape (Figure 12). We want to cut some holes into this shape to represent the eyes and wing details of the dragon. When working with curves, Blender automatically detects holes in the surface and handles them accordingly. Return to wireframe mode with ZKEY and enter editmode again with TAB.

Figure 12. Shaded logo.

While still in editmode, add a circle curve with SHIFT+A->CURVE->BEZIER CIRCLE (Figure 13). Scale the circle down to an appropriate size with SKEY and move it with GKEY.

Figure 13. Adding a circle.

Shape the circle using the techniques we have learned (Figure 14). Remember that you can add vertices to the circle with WKEY->SUBDIVIDE.

Figure 14. Defining the eye.

Create a wing cutout by adding a Bezier circle, converting all of the points to sharp corners, and then adjusting as necessary. You can duplicate this outline to save time when creating the second wing cutout. To do this, make sure no points are selected, then move the cursor over one of the vertices in the first wing cutout and select all linked points with LKEY (Figure 15). Duplicate the selection with SHIFT+D and move the new points into position.

Figure 15. Defining the wings.

If you want to add more geometry that is not connected to the main body (placing an orb in the dragon's curved tail for example), you can do this by using the SHIFT+A menu to add more curves as shown in Figure 16

Figure 16. Orb placement within the tail.

Now that we have the curve, we need to set its thickness and beveling options. With the curve selected, go to the EditButtons (F9). The "Ext1" parameter sets the thickness of the extrusion while "Ext2" sets the size of the bevel. BevResol sets how sharp or curved the bevel will be.

Figure 17 shows the settings used to extrude this curve.

Figure 17. Bevel settings

| From Curves to Meshes
| If want to perform more complex modeling operations, you can convert the curve to a mesh with ALT+C->MESH. Note that this is a one-way operation: you cannot convert a mesh back into a curve.

When your logo model is complete, you can add materials and lights and make a nice rendering (Figure 18).

Figure 18. Final rendering.

<<< Previous | Home | Next >>>
| Up | Curves