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Manual - Blender 2.40

[edit] Curves

Curves and Surfaces are objects just as meshes are objects except they are expressed in terms of mathematical functions, rather than as series of points.

Blender implements both Bézier curves and Non Uniform Rational B-Splines (NURBS) curves and surfaces. Both are defined in terms of a set of “control vertices” which define a “control polygon”, though each follow a different set of mathematical laws. The way the curve and the surface are interpolated might seem similar, at first glance, to Catmull-Clark subdivision surfaces. The curve is interpolated while the surface is attracted.

When compared to meshes, curves and surfaces have both advantages and disadvantages. Because curves are defined by less data, they produce nice results using less memory at modelling time, whereas the demands increase at rendering time.

Some modelling techniques, such as extruding a profile along a path, are only possible with curves. But the very fine control available on a per-vertex basis on a mesh, is not possible with curves.

There are times when curves and surfaces are more advantageous than meshes, and times when meshes are more useful. If you have read the pages on Basic Mesh Modelling and Advanced Mesh Modelling, and after you read this part, you will be able to choose whether to use meshes or curves.

Logo Thumbnail.

Working with curves in Blender is fairly simple and surprisingly there are very few HotKeys when creating curves. It is what you do with those curves that really makes the difference. A curve by itself is just that, a curve. But a curve applied to another curve can create very complex objects.

When you have finished reading and learning about Bézier and NURBS curves there are several more advanced examples on the application of curves in the tutorials section for modelling complex objects.

There is a Working example that shows how to create an interesting bird-like logo, (Logo Thumbnail). The tutorial covers most aspects of working with Bézier curves including: adding curves, setting up a background image as a template guide and bevelling the final curve.

In addition, the Tutorial section has examples on both Skinning and Curve deform techniques.

[edit] Béziers

Bézier curves are the most commonly used curve 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.

There are three panels designed to assist in working with and modifying curves: Curve and Surface, Curve Tools and Curve Tools1. Each panel has buttons that change the characteristics of curves.

Curve example.

(Curve example) is the most basic curve you can create. It consists of two control points or vertices, labelled “C”, the curve “B”, handles “H” and an object centre “O”.

Selecting the control point also selects the handles, and allows you to move the complete vertex. Selecting one or more handles allows you to change the shape of the curve by dragging the handles.

To create a curve use the toolbox’s Add → Curve → Bezier Curve menu entry to add a new curve, (Curve example). By default the new curve exists only in 2D. For example, if you created the curve in the Top view, the shape of the curve can only be change in the XY Plane. You can apply transforms to the curve but you can’t change its shape in 3D.

3D Curve - a Path.

To work with the curve in 3D you need to turn on the 3D property of the curve using the 3D button in the Curve and Surface panel. You can visually see that a curve is in 3D by noticing the curve has railroad tracks or marks. (3D Curve - a Path) is a 3D curve and (Curve example) is a 2D curve.

A handle is always tangent to the curve. The “steepness” of the curve is controlled by the handle’s length, any “H” to a “C”. The longer a handle is the steeper the curve (i.e. the more curve wants to hug the handle).

There are four types of handles (Types of Handles for Bézier curves):

• Free Handle (black). The handles are independent of each other. To convert to Free handles use H. H also toggles between Free and Aligned.
• Aligned Handle (purple). These handles always lie in a straight line. Hotkey: H (toggles between Free and Aligned).
• Vector Handle (green). Both parts of a handle always point to the previous handle or the next handle. Hotkey: V.
• Auto Handle (yellow). This handle has a completely automatic length and direction, set by Blender to ensure the smoothest result. Hotkey: ⇧ ShiftH.

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 handle type is modified automatically:

• Auto Handles becomes Aligned;
• Vector Handles becomes Free.

[edit] Curve resolution

Although the Bézier curve is a continuous mathematical object it must nevertheless be represented in discrete form (set of small segments) 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.

Resolution example.

A separate resolution can be set for each Bézier curve by adjusting the DefResolU field. The default is 6. (Resolution example) is an example of the same curve, superimposed, with the aid of Gimp, showing two different resolution settings. The lighter shaded curve has a low resolution of 4; the curve begins to look linear. The darker curve has a resolution of 12 and is very smooth. Note that high resolutions may look nicer but they can slow down interactive rendering if there is a large number of curves (et/or if these ones have a large amount of control points).

[edit] Bevel and Taper Objects

3D Curve modified by Bevel and Taper curves.

A Bevel object, applied to a Curve object, forms a skin for the curve. Where the curve is the path or length of a pipe, the Bevel Object, extruded along that path, defines the outside shape, like the outside of a cord, or hose pipe. Normally the Bevel is a simple round circle, and thus makes the curve into a pipe or soda can. The Bevel shape must be two-dimensional, and it can be rectangular for simulating wrought iron or flat steel, oval (with a crease) for a power cord, star-shaped for a shooting star illustration; anything that can be physically formed by extrusion (extruded).

A Taper object is an open curve with control points above its object centre. When applied to a Bevelled Curve, it changes the diameter of the Bevel along the length of the curve, like a python just having eaten a rat, or like a hose bulging up under pressure, or a vine growing.

For adjusting proper size of Bevel effect for individual curve’s segment use Set Radius option accessible through W-4. Default value is 1.0.

Caution: no Bevel Effect if bevel Radius parameter set to 0.0.

[edit] NURBS

NURBS curves are defined as rational polynomials and are more general, strictly speaking, than conventional B-Splines and Bézier curves inasmuch as 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 require a little bit more understanding of the underlying components that make up a NURBS curve in order to get full use of them. They have a large set of variables, which allow you to create mathematically pure forms. However, working with them requires a little more discussion on the various parts of a NURBS curve.

[edit] Uniform-Endpoints

We start with Knots. NURBS curves have a knot vector, a row of numbers that specifies the parametric definition of the curve (i.e. they describe the range of influence for each of the control-points). Remember the control-points from Bézier curves, NURBS have them too and each control-point affects some part of the curve along that range. The control-points appear as purple vertices.

Default Uniform curve.

(Default Uniform curve) is the default NURBS curve created using the NURBS Curve menu item from the toolbox’s Add menu and is an example of a Uniform curve. The curve itself is drawn in black, labelled “C” and the control-points are drawn in purple; one out of the 4 is labelled “P”.

You can’t manipulate the Knot vector directly but you can configure it using two presets: Uniform and Endpoint.

The Uniform button produces a uniform division for closed curves, but when used with open curves you will get “free” ends, which are difficult to locate precisely.

Endpoint curve.

The Endpoint button sets the Knot vector in such a way that the first and last vertices are always part of the curve, which makes them much easier to place. (Endpoint curve) is an example of applying the Endpoint button to the (Default Uniform curve). You can see that the curve has now been pulled to the end control-points labelled “A” and “B”.

[edit] Order

The Order field is the “depth” or degree of the curve (i.e. you are specifying how much the control-points are taken into account for calculating the curve shape).

Order 1 is a point and is not an available depth setting, Order 2 is linear (Order 2 curve), Order 3 is quadratic (Order 3 curve), (Order 4 curve) is cubic, and so on. The valid range is 2 to 6. Notice that as the Order rises the curve moves away from the control-points.

Order 2 curve.

Order 3 curve.

Order 4 curve.

If your curve has 6 or more control-points the Order can not be set higher than 6. 6 is the highest Order allowable. If you have less than 6 control-points then the highest Order is limited by the number of control-points. For example, if your curve has 5 control-points then the highest Order allowable is 5.

Always use an order of 5, if possible, for curve paths because it behaves fluidly under all circumstances, without producing irritating discontinuities in the movement. For example, if you have a cube assigned to travel along a NURBS path with an Order of say 2 then the cube will appear to move roughly (or jerky) along the path.

[edit] Weight

NURBS curves have a Weight assigned to each control-point that controls how much each “pulls” on the curve. Think of it as if each control-point has an arm that reaches out and grabs hold of the curve and tries to pull on it. The larger the Weight the more the control-point pulls on the curve, see (Weight of 5) and (Weight of 20). The valid range of Weight settings are 0.1 to 100.0.

Weight of 5.

Weight of 20.

The larger Weight of 20 pulls the curve towards the control-point labelled “C”. Each control-point can have a different Weight setting. As the Weight for a control-point increases the curve will hug the control-points closer. If the Weights are large enough the curve will almost follow the control-points, see (Weight of 100).

Weight of 100.

The control-points can effectively compete with each other. For example, the control-point with the largest Weight will pull the curve towards it and away from the others. If all the control-points have the same Weight then the Weight is effectively cancelled, as if none had Weights.

In (Weight of 100) the top two control-points have their Weight set at 100.0, labelled “A” and “B”. The opposite control-points have their Weight at 1.0. You can see that the curve is “pulled” toward control-points “A” and “B”. And at such a high Weight the curve almost follows the control-points.

In the Curve Tools panel there are four preset Weights that provide typical Weight settings for certain kinds of control-point arrangements. Some generate Weight settings that are used for control-points that form circles.

To see the Weight value of a control-point, select it, open the Transform Properties panel using N and look at the Vertex W field. The Weight field doesn’t show the Weight!

[edit] Resolution

As with Béziers curves NURBS curves’ Resolution can be controlled from the Curve Tools panel.

[edit] Opening, Closing, Deleting, Joining, Bevel, Taper

As with Béziers curves, Opening, Closing, Deleting and Joining NURBS curves is performed using the same Hotkeys and same Curve Tools, with the same rules applying, see the Béziers curves section above, as well as the next page.

Manual

[edit] Subpages

1. .see also
2. Curve Deform
3. Curve Taper
4. Editing