wiki>Kesten: minor changes

2012-01-08T23:32:37Z

minor changes

新規ページ

{{Page/Header|2.6x|Doc:2.6/Manual/Modeling/Meshes/Sculpting|Doc:2.6/Manual/Modeling/Curves/Editing}}

= Curves =
To create a curve, go to {{Literal|Add }} {{Literal|Curve}} and select from the options. In Object Mode with the curve selected you can Scale {{Literal| s }}, Move ("Grab) {{Literal|g}} or rotate {{Literal|r}} the entire curve.
To edit a curve, switch to Edit Mode and click the {{Literal|Curves}} menu option.

Curves and [[Doc:2.6/Manual/Modeling/Surfaces|Surfaces]] are objects just as meshes are objects except they are expressed in terms of mathematical functions, rather than as a series of points.

<push to Referenece>
Blender implements both [[#Béziers|Bézier]] curves and Non-Uniform Rational B-Splines ([[#NURBS|NURBS]]) curves and surfaces. Both are defined in terms of a set of “control vertices” (or “control points”) 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''.
TDOD find wiki or other references to explain interpolated vs attracted.

== Compared to Polygonal Mesh ==
TODO add picture of polygonal mesh
One main advantage to curves over polygonal meshes is that curves are defined by less data, so can produce excellent results using less memory and storage space at modeling time. However, this procedural approach to surfaces can increase demands at render time.

</push to Reference>

Some modeling techniques like [[Doc:2.6/Manual/Modeling/Curves/Editing/Advanced|extruding]] a profile along a path are only possible using curves. At the same time, vertex-level control is more difficult when using curves.

<push to Reference>
There are times when curves and surfaces are more advantageous than meshes, and times when meshes are more useful. It is recommended you read the section on [[Doc:2.6/Manual/Modeling/Meshes/Editing|mesh editing]], which should help you decide whether to use meshes or curves in your project.

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 [[Doc:Tutorials#Modeling|tutorials]] section for modeling complex objects.
</push to Reference>

<update to 2.6>
[[File:Manual-Part-II-LogoFinal.png|thumb|right|Logo Thumbnail.]]
There is a [[Doc:2.4/Tutorials/Modeling/Curves/Bézier|Working example]] that shows how to create an interesting bird-like logo. The tutorial covers most aspects of working with Bézier curves including: adding curves, setting up a background image as a template guide and beveling the final curve.

In addition, the Tutorial section has examples on both [[Doc:2.4/Tutorials/Modeling/Surfaces/Skinning|Skinning]] and [[Doc:2.4/Tutorials/Modeling/Curves/Curve Deform|Curve deform]] techniques.
{{clr}}
</update to 2.6>

= Finding Curve Tools =
You can browse by menu options by selecting {{Literal|Curves}} in Edit Mode.
You can learn about the python calls by lowering the Info Window and by opening a python console and typing bpy.ops.curve followed by {{Literal|Ctrl Spacebar}

The {{Literal|Select}} menu is customized to curves if the curve is selected in Edit mode of the 3D view. Further options can be found in the {{Literal|Specials}} menu ({{Shortcut|W}}).
{{clr}}

= Visualization =

In {{Literal|Edit}} mode, the curve is drawn as a black line, and in {{Literal|Solid}} shading (or {{Literal|Shaded}}, …), the closed curves are filled with a flat surface. {{Literal|3D}} curves have additional “arrows” all along the curve, illustrating both the direction and the ''relative'' speed of the movement objects will have when following them as path (unless a custom {{Literal|Speed}} Ipo is defined…).

<verify for windows and mac><br>
Each control point is drawn in orange. Bézier “vectors” are materialized with salmon-pink lines, whereas NURBS vertices are linked by yellow lines. As with meshes, selected vertices are highlighted in yellow (with a lighter shade for the active element).
{{clr}}

== Control Points and Segments ==
Curves are mainly defined by their control points, as described below in their respective section. However, you will sometimes encounter another concept, the “segment” of curve. A segment is defined implicitly by its two adjacent control-points. Unlike with meshes, you can’t explicitly select a segment – you must select its two adjacent control-points.

== Adding Points ==
===Extrude===
You can add new points by clicking {{Literal|Curves | Extrude}}. This only works if you have selected the first or last points on the curve.
===Subdivide===
You can add points to the middle of a curve by selecting two consecutive points followed by {{Literal|Curves | Segment | Subdivide}}. After this operation, the entire segment made of the three points is selected. You must select only the newly created point to move it independently.

== Multiple Curves ==
If you have more than one curve in the 3D View, you may need to switch to Object Mode and select the other curve, the switch back to Edit Mode, if you wish to change which curve is being edited. You may join curves of the same type in Object Mode with {{Button|J}} and separate them in Edit Mode with {{Button|P}}. If you separate two objects, you may need to reset the origin (axes for the object) by selecting in Object Mode, Object -> Origin to Object.

== Closed Curves ==
Curves may be closed and opened in Edit Mode by pressing the Curve -> Toggle Cyclic, or pressing {{Button|Alt}} {{Button|C}}

== Nurbs ==
=== Curve Structure ===
{{Note|1=About U and V coordinates|2=U and V are the conventional names of parametric “coordinates” components (note that these are the same names as texture ones…). They are used to define the resolution, the “knots” for NURBS, etc., along given “axis”. For curves, only the U component is relevant (as they have only one dimension, they are lines). The V component is used by NURBS surfaces.}}
{{clr}}

{{clr}}
== Hiding Elements ==
As in {{Literal|Object}} mode, you can hide what is selected, and then reveal what was hidden. This is very handy to clean up a bit your views, when you are working on a complex model with thousands of vertices…

To hide, use {{Shortcut|ctrl|alt|H}}, the {{Literal|Hide}} button of the {{Literal|Curve Tools1}} panel, or use the {{Menu|Curve|Show/Hide Control Points|Hide Selected}} menu option.

To reveal what was hidden, use {{Shortcut|alt|H}}, the {{Literal|Reveal}} button of the {{Literal|Curve Tools1}} panel, or the relevant option in the same {{Menu|Curve|Show/Hide Control Points}} menu.
{{clr}}

<TODO: Add sections for other menu subitems like segment and control points>

<update to 2.6 | "I don't know the equivalent in 2.6">
== Curve Resolution ==
Although these curves are continuous mathematical objects, they 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. Note that this applies only to Bézier curves, and is different for NURBS.

You have in fact three resolution settings, two in the {{Literal|Curve and Surface}} panel, and one in the {{Literal|Curve Tools}} panel:
*{{Literal|DefResolU}}: The resolution applied by default to all curves of the object, both in the 3D views and at render time.
*{{Literal|RenResolU}}: The resolution applied by default to all curves of the object when rendering, if not set to zero (else {{Literal|DefResolU}} is used).
*{{Literal|Resol U}}: This setting is only available in {{Literal|Edit}} mode, it will modify the resolution of the curves (partly) selected currently. Note that it is reset to the {{Literal|DefResolU}} value each time you modify this setting.

[[File:Manual-Part-II-Curves-Bezier-Resolution-Ex1.png|frame|right|Bézier resolution example.]]
A separate ''resolution'' can be set for each curve by adjusting the {{Literal|DefResolU}} field of the [[Doc:2.4/Reference/Panels/Editing/Curves/Curve and Surface|{{Literal|Curve and Surface}} panel]]. The default is '''6'''. (''Bézier 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 (and/or if these ones have a large amount of control points).
{{clr}}

</update to 2.6>

== 2D and 3D Curves ==
By default, (except for the {{Literal|Path}} primitive), new curves are 2-dimensional, meaning all control points lie in the same plane (X-Y in {{Literal|Local}} space). This allows automatic filling of closed curves.

<TODO: delete this. no longer relevant. Or replace with section on how to restrict to 2D>
However, you might want to be able to place your control points freely in 3D space. To do so, enable the {{Literal|3D}} button of the {{Literal|Object Data}} panel. Note that you will lose the closed curves filling, and arrows will be displayed as per the [[#Visualization|Visualization]] section above.
{{clr}}

== Closed and Open Curves ==
Curves (Bézier or NURBS) are mono-dimensional: they are lines, that never crosses themselves (i.e. control points are only linked to at most two others, forming a continuous line, without any fork…). However, curves can be open (i.e. they start and end points are not linked by a curve segment) or closed. Closed curves are solid, inasmuch that Blender adds a solid flat face inside them (unless they are made {{Literal|3D}}).
{{clr}}

<push to Reference>
== Béziers ==
Bézier curves are the most commonly used curves 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.

[[File:Manual-Part-II-Curves-Bezier-Ex1.png|frame|right|Curve example.]]
(''Curve example'') is the most basic Bézier curve you can create. It consists of two control points or vertices, labeled “<code>C</code>”, the curve “<code>B</code>”, handles “<code>H</code>” and an object center “<code>O</code>”.

A handle “<code>H</code>” defines the tangent vector to the curve in point “<code>C</code>” (on its side). The “steepness” of the curve is controlled by the handle’s length (“<code>H</code>” to a “<code>C</code>”). 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''):
*{{Literal|Free}} Handle (black). The handles are independent of each other. To convert to {{Literal|Free}} handles use {{Shortcut|H}}. {{Shortcut|H}} also toggles between {{Literal|Free}} and {{Literal|Aligned}}.
*{{Literal|Aligned}} Handle (purple). These handles always lie in a straight line, and give a continuous curve (without sharp angles…). Hotkey: {{Shortcut|H}} (toggles between {{Literal|Free}} and {{Literal|Aligned}}).
*{{Literal|Vector}} Handle (green). Both parts of a handle always point to the previous handle or the next handle (this allows you to create curves made of straight lines!). Hotkey: {{Shortcut|V}}.
*{{Literal|Auto}} Handle (yellow). This handle has a completely automatic length and direction, set by Blender to ensure the smoothest result. Hotkey: {{Shortcut|shift|H}}.

{|align=center
|[[File:Manual-Part-II-BezierHandles.png|frame|none|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:
*{{Literal|Auto}} Handles becomes {{Literal|Aligned}};
*{{Literal|Vector}} Handles becomes {{Literal|Free}}.
{{clr}}

== NURBS ==
NURBS curves are defined as rational polynomials and are more general, strictly speaking, than conventional B-Splines and [[#Béziers|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. However, a NURBS cannot have real sharp angles in it, unlike a Bézier curve…

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.

{{Note|1=Note|2=NURBS are a ''very'' complicated topic, I think they might be a good subject for a “Theory” article – written by someone knowing them deeply! (For a start, here's the [http://en.wikipedia.org/wiki/Nurbs Wikipedia page.])}}
{{clr}}

=== Knots ===
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.

'''Note that ''knots'' setting concerns only ''open'' NURBS''', not closed ones.

[[File:Manual-Part-II-Curves-Nurbs-Basic-Ex1.png|frame|right|Default Uniform curve.]]
(''Default Uniform curve'') is the default NURBS curve created using the {{Literal|NURBS Curve}} menu item from the toolbox’s [[Doc:Reference/Menus/Toolbox#Add Sub-menu|{{Literal|Add}} menu]] and is an example of a {{Literal|Uniform}} curve. The curve itself is drawn in black, labeled “<code>C</code>” and the control-points are drawn in purple; one out of the 4 is labeled “<code>P</code>”.

You can’t manipulate the ''Knot'' vector directly but you can configure it using three presets: {{Literal|Uniform}}, {{Literal|Endpoint}} and {{Literal|Bezier}}.

The {{Literal|Uniform}} button of the [[Doc:2.4/Reference/Panels/Editing/Curves/Curve Tools|{{Literal|Curve Tools}} panel]] produces a uniform division for closed curves, but when used with open curves you will get “free” ends, which are difficult to locate precisely.

[[File:Manual-Part-II-Curves-Nurbs-EndPoint-Ex1.png|frame|right|Endpoint curve.]]
The {{Literal|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 {{Literal|Endpoint}} button to the (''Default Uniform curve''). You can see that the curve has now been pulled to the ''end'' control-points labeled “<code>A</code>” and “<code>B</code>”.
{{clr}}

{|align=right
|[[File:Manual-Curves-Nurbs-Bezier-Order3.png|frame|right|{{Literal|Bezier}} NURBS, Order 3.]]
|-
|[[File:Manual-Curves-Nurbs-Bezier-Order4.png|frame|right|{{Literal|Bezier}} NURBS, Order 4.]]
|}
Finally, {{Literal|Bezier}} “''Knot'' vector” (I’m not really sure this remains a real knot, in fact…) make the NURBS control points mimic the Bézier control points behavior. This works only with two orders value (see below): '''3''' and '''4'''.
*With an {{Literal|Order}} of '''3''', all odd points act as a center of a Bézier control point, and all even points act as a Bézier handle. So vertices (1,2,3) define a first Bézier segment, (3,4,5) a second one, and so on…
*With an {{Literal|Order}} of '''4''', all four groups of control points define a Bézier segment, i.e. vertices (2,3,4,5) define a first segment, (5,6,7,8) a second one, etc. Note that here, the first vertice is for some reasons unused…
{{clr}}

=== Order ===
The {{Literal|Order}} field of the [[Doc:2.4/Reference/Panels/Editing/Curves/Curve Tools|{{Literal|Curve Tools}} panel]] 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).

{{Literal|Order}} '''1''' is a point and is not an available depth setting, {{Literal|Order}} '''2''' is linear (''Order 2 curve''), {{Literal|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 {{Literal|Order}} rises the curve moves away from the control-points.

{|align=center
|[[File:Manual-Part-II-Curves-Nurbs-Order2.png|frame|none|Order 2 curve.]]
|[[File:Manual-Part-II-Curves-Nurbs-Order3.png|frame|none|Order 3 curve.]]
|[[File:Manual-Part-II-Curves-Nurbs-Order4.png|frame|none|Order 4 curve.]]
|}
If your curve has '''6''' or more control-points the {{Literal|Order}} can not be set higher than '''6'''. '''6''' is the highest {{Literal|Order}} allowable. If you have less than '''6''' control-points then the highest {{Literal|Order}} is limited by the number of control-points. For example, if your curve has '''5''' control-points then the highest {{Literal|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 {{Literal|Order}} of say '''2''' then the cube will appear to move roughly (or jerky) along the path.

{{Note|1=Math Note|2=Mathematically speaking the {{Literal|Order}} is the order of both the Numerator and the Denominator of the rational polynomial defining the NURBS curve.}}
{{clr}}

=== Weight ===
NURBS curves have a {{Literal|Weight}} ([[Doc:2.4/Reference/Panels/Editing/Curves/Curve Tools|{{Literal|Curve Tools}} panel]]) 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 {{Literal|Weight}} the more the control-point pulls on the curve, see (''Weight of 5'') and (''Weight of 20''). The valid range of {{Literal|Weight}} settings are '''0.1''' to '''100.0'''.

{|align=center
|[[File:Manual-Part-II-Curves-Nurbs-Weight5.png|frame|none|Weight of 5.]]
|[[File:Manual-Part-II-Curves-Nurbs-Weight20.png|frame|none|Weight of 20.]]
|}
The larger {{Literal|Weight}} of 20 pulls the curve towards the control-point labeled “<code>C</code>”. Each control-point can have a different {{Literal|Weight}} setting. As the {{Literal|Weight}} for a control-point increases the curve will hug the control-points closer. If the {{Literal|Weight}}s are large enough the curve will almost follow the control-points, see (''Weight of 100'').

[[File:Manual-Part-II-Curves-Nurbs-Weight100.png|frame|right|Weight of 100.]]
The control-points can effectively compete with each other. For example, the control-point with the largest {{Literal|Weight}} will pull the curve towards it and away from the others. If all the control-points have the same {{Literal|Weight}} then the {{Literal|Weight}} is effectively canceled, as if none had {{Literal|Weight}}s.

In (''Weight of 100'') the top two control-points have their {{Literal|Weight}} set at '''100.0''', labeled “<code>A</code>” and “<code>B</code>”. The opposite control-points have their {{Literal|Weight}} at '''1.0'''. You can see that the curve is “pulled” toward control-points “<code>A</code>” and “<code>B</code>”. And at such a high {{Literal|Weight}} the curve almost follows the control-points.

To see the {{Literal|Weight}} value of a control-point, select it, open the [[Doc:2.4/Reference/Panels/Transform Properties/Curve mode|{{Literal|Transform Properties}} panel]] using {{Shortcut|N}}, and look at the {{Literal|Vertex W}} field. The {{Literal|Weight}} field doesn’t show the {{Literal|Weight}}!
{{clr}}

=== Preset Weights ===
[[File:Manual-Curves-Nurbs-CircleWeights.png|thumb|250px|right|A circle NURBS curve.]]
NURBS curves can create pure shapes such as circles (note that a Bézier circle is not a pure circle). To create pure circles, you must set to specific values the weights of the control-points – some of which are provided as presets in the {{Literal|Curve Tools}} panel (lower right corner). This is not intuitive, and you should read more on NURBS before trying this.

Basically, to produce a circular arc from a curve with three control-points, the end points must have a unitary weight, while the weight of the central control point must be equal to one-half the cosine of half the angle between the segments joining the points. Lets take an example: if you have three control-points creating a right angle, to get a quadrant, you would set the center point’s weight to <code>cos(90/2)/2 = cos(45)/2 = sqrt(2)/4 = 2**-1.5 ≃ 0.354</code> (these settings are valid with an order of '''4'''… so you must have at least four control points, as with three points – and hence an order of '''3''' –, you won’t get a “circular” quadrant!).

The other presets are more useful for [[Doc:2.4/Manual/Modeling/Surfaces|NURBS surfaces]] (to create spheres, cylinders, …).
{{clr}}

== Primitives ==
Blender can add five different curve primitives, two Bézier and three NURBS:
*{{Literal|Bezier Curve}} adds an open 2D Bézier curve with two control points.
*{{Literal|Bezier Circle}} adds a closed, circle-shaped 2D Bézier curve (made of four control points).
*{{Literal|NURBS Curve}} adds an open 2D NURBS curve, with four control points, with {{Literal|Uniform}} knots.
*{{Literal|NURBS Circle}} adds a closed, circle-shaped 2D NURBS curve (made of height control points).
*{{Literal|Path}} adds a NURBS open 3D curve made of five aligned control points, and with {{Literal|Endpoint}} knots and the {{Literal|CurvePath}} setting enabled.
{{clr}}

{{Page/Footer|Doc:2.5/Manual/Modeling/Meshes/Sculpting|Doc:2.5/Manual/Modeling/Curves/Editing}}

[[Category:Curves]]

利用者:Kesten/Projects/CurvesWiki Proposal - 版の履歴

Yamyam: 1版をインポートしました

wiki>Kesten: minor changes

← 古い版	2018年6月28日 (木) 20:45時点における版
(相違点なし)

利用者:Kesten/Projects/CurvesWiki Proposal - 版の履歴

Yamyam: 1版 をインポートしました

wiki>Kesten: minor changes

Yamyam: 1版をインポートしました