Creating NURBS Curves

Every curve has a certain degree; the higher the degree, the smoother the curve. A curve can have a degree of 1, 2, 3, 5, or 7. The degree represents the complexity of the curve between CVs. A curve with a degree of 1 is a linear curve and requires only two points to define it (Figure 7.9). Linear curves and surfaces are characterized by straight lines and sharp corners. A curve degree of 3 produces a smooth curve without using an excessive number of CVs to describe it (Figure 7.10). A curve with a degree of 3 is the most common and versatile curve because it requires only four points and is smooth enough to create a high-quality surface. A higher-degree curve holds closer to the CVs, resulting in a smoother, more accurate interpolation. Because of the accuracy needed for manufacturing, car designers often use degrees higher than 5. For animation, however, a degree of 3 is usually enough.

Figure 7.9. A curve degree of 1 creates a linear curve and a linear surface (if a surface is created from the curve).

Figure 7.10. A curve degree of 3 produces a smooth curve without using an excessive number of CVs.

Each curve requires CVs that total one more than its degree. For example, a curve with a degree of 3 requires four CVs (Figure 7.10); a 7-degree curve requires eight CVs, thereby creating a heavier surface (Figure 7.11). For this reason, a degree of 3 or 5 is usually ideal.

Figure 7.11. This is a 7-degree curve, which means it requires eight CVs.

Typically, you create a curve in one of three ways: with the CV Curve tool, the EP Curve tool, or the Pencil Curve tool.

To create a curve with the CV Curve tool:

1.	Choose Create > CV Curve Tool.
2.	In the Top view, click in several places. A CV appears with each mouse click, and a curve appears on the fourth click (Figure 7.12) Figure 7.12. This curve was created by placing points using the CV Curve tool.
3.	Press to complete the creation of the curve. The curve becomes highlighted to indicate that it's selected.

To create a curve with the EP Curve tool:

1.	Choose Create > EP Curve Tool.
2.	In the Top view, click in several places. A curve is created once the second edit point is placed, and it continues to take shape with each subsequent point (Figure 7.13). Figure 7.13. This curve was created using the EP Curve tool.
3.	Press to finish creating the curve.

Tip

• The EP tool is better suited when you want precise control over exactly where your curve passes. Use the CV tool for tasks like ensuring tangency, when you care more about the CV placement than the curve location.

To create a curve with the Pencil Curve tool:

1.	Choose Create > Pencil Curve Tool.
2.	Click and drag in the Top view to draw a line. The curve is completed once you release the mouse. The Pencil Curve tool tends to be a less efficient way of creating a curve because you end up with more points than you need to describe the shape (Figure 7.14). Figure 7.14. The bottom curve was created using the Pencil Curve tool.