Bézier curves are the most commonly used type for designing letters or logos. They are also widely used in animation, both as paths for objects to move along and as IPO curves to change the properties of objects as a function of time.

A control point (vertex) of a Bézier curve consists of a point and two handles. The point, in the middle, is used to move the entire control point; selecting it also selects the other two handles, and allows you to move the complete vertex. Selecting one or two of the other handles allows you to change the shape of the curve by dragging the handles.

A Bézier curve is tangent to the line segment which goes from the point to the handle. The 'steepness' of the curve is controlled by the handle's length.

There are four types of handles (Figure 9.1, “Types of Handles for Bézier curves”):

Figure 9.1. Types of Handles for Bézier curves

Handles can be grabbed, rotated and scaled exactly as ordinary vertices in a mesh would.

As soon as the handles are moved, the type is modified automatically:

Although the Bézier curve is a continuous mathematical object it must nevertheless be represented in discrete form from a rendering point of view.

This is done by setting a resolution property, which defines the number of points which are computed between every pair of control points. A separate resolution can be set for each Bézier curve (Figure 9.2, “Setting Bézier resolution.”).

Figure 9.2. Setting Bézier resolution.

NURBS curves are defined as rational polynomials, and are more general, strictly speaking, than conventional B-Splines and Bézier curves inasmuch they are able to exactly follow any contour. For example a Bézier circle is a polynomial approximation of a circle, and this approximation is noticeable, whereas a NURBS circle is exactly a circle. NURBS curves have a large set of variables, which allow you to create mathematically pure forms (Figure 9.3, “Nurbs Control Buttons.”). However, working with them requires a little more theory:

Figure 9.3. Nurbs Control Buttons.

Figure 9.4. Setting Nurbs Control polygon and weights.

Figure 9.4, “Setting Nurbs Control polygon and weights.” shows the Knot vector settings as well as the effect of varying a single knot weight. As with Béziers, the resolution can be set on a per curve basis.

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 9.5, “The sketched logo” shows the design of the logo we will be building.

Figure 9.5. 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, select the View>>Background Image... menu entry of the 3D Window you are using. A transparent panel will appear, allowing you to select a picture to use as a background. Activate the BackGroundPic button and use the LOAD button to locate the image you want to use as a template (Figure 9.6, “3D window settings.”). You can set the "strength" of the background pic with the Blend slider.

Figure 9.6. 3D window settings.

Get rid of the Panel with ESC or by pressing the X button in the panel header (Figure 9.7, “Logo sketch loaded as background”). You can hide the background image when you are finished using it by returning to the Panel and deselecting the BackGroundPic button.

Figure 9.7. Logo sketch loaded as background

Add a new curve by pressing SPACE>>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 CTRL and clicking 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 9.8, “Bézier handles”).

Figure 9.8. Bézier handles

You can add a new point between two existing points by selecting the two points and pressing WKEY>>Subdivide (Figure 9.9, “Adding a Control Point.”).

Figure 9.9. Adding a Control Point.

Points can be removed by selecting them and pressing XKEY>>Selected. To cut a curve in two, select two adjacent control vertices and press XKEY>>Segment.

To make sharp corners, select a control vertex and press VKEY. You will notice that the color of the handles changes from purple to green (Figure 9.10, “Vector (green) handles.”). At this point, you can move the handles to adjust the way the curve enters and leaves the control vertex (Figure 9.11, “Free (black) handles.”).

Figure 9.10. Vector (green) handles.

Figure 9.11. Free (black) handles.

To close the curve and turn it into a single continuous loop, select at least one of the control vertices on the curve and press CKEY. This will connect the last point in the curve with the first one (Figure 9.12, “The finished outline.”). You may need to manipulate additional handles to get the shape you want.

Figure 9.12. The finished outline.

Leaving EditMode with TAB and entering shaded mode with ZKEY should reveal that the curve renders as a solid shape (Figure 9.13, “Shaded logo.”). We want to cut some holes into this shape to represent the eyes and wing details of the dragon.

Figure 9.13. Shaded logo.

Return to wireframe mode with ZKEY and enter EditMode again with TAB. While still in EditMode, add a circle curve with SPACE>>Curve>>Bezier Circle (Figure 9.14, “Adding a circle.”). Scale the circle down to an appropriate size with SKEY and move it with GKEY.

Figure 9.14. Adding a circle.

Shape the circle using the techniques we have learned (Figure 9.15, “Defining the eye.”). Remember to add vertices to the circle with WKEY>>Subdivide.

Figure 9.15. Defining the eye.

Create a wing cutout by adding a Bézier 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 so, 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 9.16, “Defining the wings.”). Duplicate the selection with SHIFT-D and move the new points into position.

Figure 9.16. Defining the wings.

To add more geometry that is not connected to the main body (placing an orb in the dragon's curved tail for example), use the SHIFT-A menu to add more curves as shown in Figure 9.17, “Orb placement within the tail.”.

Figure 9.17. 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) and locate the Curves and Surface panel. 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 9.18, “Bevel settings” shows the settings used to extrude this curve.

Figure 9.18. Bevel settings

When your logo model is complete, you can add materials and lights and make a nice rendering (Figure 9.19, “Final rendering.”).

Figure 9.19. Final rendering.