Placement/zh-cn

概述
Placement是用户在FreeCAD中指定目标对象在空间中位置与姿态（朝向）的手段. 指定方位属性的方式多种多样，例如通过 脚本、属性面板或Placement对话框（位于Edit菜单中）.

访问定位属性
可通过下列3种方式来调整目标对象的方位Placement属性：







指定方位的方式
方位属性在内部实现会存作位置、旋转（旋转轴与旋转角度会被转换为对应的四元数）两种属性. 指定旋转有若干种方式，例如，若指定了一个旋转中心，这将仅会对旋转计算造成影响，而并不会为后续计算而存储此值. 类似地，如果指定了旋转轴(1,1,1)，可能会在把它保存于一个四元数中的时候将其进行归一化处理，从而在后续浏览此对象时，其值将表现为(0.58, 0.58, 0.58).

Angle，Axis与Position属性
Placement = [Angle, Axis, Position]

这种指定Placement的第一种形式，将以Position来修改对象的空间位置，再以绕Axis的单个旋转操作来描述其朝向. Angle = r为一标量，表示目标对象绕Axis所旋转的角度. 用户输入的是角度，而实际内部存储用的是弧度制.

Axis = (ax,ay,az)是一个向量，描述的是旋转轴（参见关于旋转轴的备注）. 以下为示例： (1,0,0)      ==> 绕X轴旋转 (0,1,0)      ==> 绕Y轴旋转 (0,0,1)      ==> 绕Z轴旋转 (0.71,0.71,0) ==> 绕直线y=x旋转

请注意，也可以令对象沿此旋转轴进行平移（移动，轴向移动），方法是：在Axial框中输入移动距离，再点击Apply axial按钮. （可以这样来想象此轴向移动操作：假设有一附有前置螺旋桨的飞机——飞行时，螺旋桨“绕”旋转轴转动，而飞机整体则“沿”此轴飞行. ）可将此向量中的值看作是应用于对应方向的移动量. 例如，在(0.71,0.71,0)这种y=x的情况下，对象将按Axial框中的值在X与Y方向上进行相同量的移动，且不会在Z方向上移动. Position = (x,y,z)是一个向量，描述目标对象的几何体自此开始计算（事实上，采用的是对象的“局部原点（local origin）”）. 请注意，在脚本里用Placement.Base来表示方位属性中的Position分量. 属性编辑器称此值为"Position"，Placement对话框中则称之为"Translation".

Position与Yaw，Pitch与Roll


Placement = [Position, Yaw-Pitch-Roll]

The second form of Placement fixes an object's location in space with a Position (as in the first form), but describes it's orientation using Yaw, Pitch and Roll angles (Yaw, Pitch, Roll). These angles are sometimes referred to as Euler angles or Tait-Bryan angles (Euler angles). Yaw, Pitch and Roll are common aviation terms for a body's orientation (or attitude).

Position = (x,y,z) is a Vector describing the point from which the object's geometry will be calculated (in effect, a "local origin" for the object).

Yaw-Pitch-Roll = (y,p,r) is a tuple that specifies the attitude of the object. Values for y,p,r  specify degrees of rotation about each of the z,y,x axis (see note).

App.Rotation(10,20,30) = Euler Angle

Yaw = 10 degrees (Z)

Pitch = 20 degrees (Y)

Roll = 30 degrees (X)

Yaw is the rotation about the Z axis, that is to say a rotation from left to right. (The yaw angle is the Psi ψ).

Pitch is rotation about the Y axis, that is to say nose-up and nose-down. (The Pitch angle is the Phi φ).

Roll is rotation about the X axis, that is to say wing up and down. (The Roll angle is the Thêta θ).

Matrix
Placement = Matrix

The third form of Placement describes the object's position and orientation with a 4x4 affine transformation matrix (Affine Transformation).

Matrix =

((r11,r12,r13,t1),   (r21,r22,r23,t2),    (r31,r32,r33,t3),    (0,0,0,1)), with rij specifying rotation and ti specifying translation.

The Placement Dialog
The Placement Dialog is invoked from the Edit menu. It is used to precisely rotate/translate objects. It is also used when we need to create a sketch on a "non standard" plane or change a sketch's orientation to a new plane. The Translation section adjusts the object's location in space. The Center section adjusts the rotational axis to one that does not pass through the object's reference point. The Rotation section adjusts the rotational angle(s) and the method of specifying those angles.

But while the elements within each section generally apply to the purpose of that section there are also some elements in one section that can affect elements in another section. For example, clicking the Selected points button in the Center section with 2 points selected in the 3d view results in not only populating the Center coordinate spinboxes with the coordinates of the midpoint between those 2 selected points, but it also creates a custom axis along the line defined by those 2 selected points in the Rotation section. In another example, placing a value in the Axial spinbox and clicking the Apply axial button in the Translation section translates (moves) the object along the axis defined in the Rotation section. The Apply incremental changes to object placement tick box is useful when translations/rotations are to be made relative the object's current position/attitude, rather than to the original position/attitude. Ticking this box resets the dialogue input fields to zero, but does not change the object's orientation or location. Subsequent entries do change the orientation/location, but are applied from the object's current position. Enabling this checkbox is also useful when using the Selected points button as it can sometimes prevent undesired placement changes.

PS: since version 0.17 introduce new object Part, this object have his placement, and the Placement object created in the Part object is incremented with the Part Placement. For obtain the Part Placement use this code

Selected points button is used to populate the coordinates in the Center coordinates spinboxes and (when 2 or 3 points are selected) additionally to create a custom (user-defined) axis of rotation in the Rotation section. A point can be a vertex, but it can also be any point along an edge or on a face. When you select an edge or face the entire edge or face is selected, but FreeCAD also remembers which point on that face or edge the mouse pointer was hovering over when that edge or face was selected. It is this point's coordinates that get used in the Placement dialog when the Selected points button is clicked. You might be thinking this isn't a very precise way of selecting a point, and you are correct, but in many cases it is sufficient that the point selected is guaranteed to be on that edge or face. In cases where you need to precisely designate a point to be used you should select a vertex. When there is no vertex in the desired location consider creating one, perhaps in a temporary sketch attached to that face or edge, perhaps using a Draft workbench object, such as a line or point, etc.

Let us first consider the simple case of selecting 1 point. The workflow is to first select the desired point, then click the Selected points button. The coordinates of the selected point will be used to populate the X, Y, and Z spinboxes within the Center section. Now any rotation done on the object will about this center of rotation.

Now consider the case of selecting 2 points. You would select the 2 desired points, and then click the Selected points button. The coordinates of the midpoint between the 2 selected points get placed into the X, Y, and Z spinboxes within the Center section. Now any rotation done on the object will be about this center of rotation. But in addition to setting up the Center section coordinates a custom (user-defined) axis is also added to the Axis element within the Rotation section. (Note: if you were in Euler rotation mode, the mode gets switched to Rotation with an axis mode and the new custom axis is selected as the current axis of rotation.) Now any rotation done using the new custom axis will be about this axis of rotation. As an added bonus, the distance is measured between the 2 selected points, and this information is given in the Report View. (Note: Hold down the Shift key while clicking the Selected points button to copy the distance measurement to the clipboard.) By entering this distance into the Axial spinbox in the Translation section and clicking the Apply axial button you can translate (move) the object so that the first selected point now occupies the coordinates occupied by the second selected point (at the time the Selected points button was clicked).

Now consider the case of selecting 3 points. You would select the 3 desired points, and then click the Selected points button. The coordinates of the first selected point (order of selection is very important here) get placed into the X, Y, and Z spinboxes within the Center section. Since 3 points define a plane FreeCAD is able to take advantage of that and use those 3 points to create a new custom (user-defined) axis of rotation that is normal (perpendicular) to that defined plane. As with 2 selected points, the distance between points is also shown in the Report View, but this time it is the distance between the 2nd and 3rd selected points. (Note: Hold down the Shift key while clicking Selected points button -- Shift + Click -- to copy the angle measurement to the clipboard.) Additionally, the angle between the 2nd and 3rd points is also measured and displayed in the Report View. By entering this angle into the Angle spinbox within the Rotation section we can very precisely rotate the object such that now the 2nd selected point is in alignment with the coordinates occupied by the 3rd selected point. (Note: you might want to increase the number of digits used within the Edit menu -> Preferences -> General -> Units -> Number of decimals spinbox if you desire more precision.)

Examples
Rotations about a single axis:

Before Rotation (top view)

After Rotation about Z (top view)

After Rotation about y=x (right view)

Rotation with offset centre point:

Before Rotation (top view)

After Rotation about Z (top view)

Rotation using Euler angles:

Before Rotation

After Rotation

Placement.Base vs Shape Definition
Placement is not the only way to position a shape in space. Note the Python console in this image:



Both cubes have the same value for Placement, but are in different locations! This is because the 2 shapes are defined by different vertices (curves in more complex shapes). For the 2 shapes in the above illustration:

>>> ev = App.ActiveDocument.Extrude.Shape.Vertexes >>> for v in ev: print v.X,",",v.Y,",",v.Z ...   30.0,30.0,0.0 30.0,30.0,10.0 40.0,30.0,0.0  40.0,30.0,10.0  40.0,40.0,0.0  40.0,40.0,10.0  30.0,40.0,0.0  30.0,40.0,10.0  >>> e1v = App.ActiveDocument.Extrude001.Shape.Vertexes >>> for v in e1v: print v.X,",",v.Y,",",v.Z ...   0.0,10.0,0.0 0.0,10.0,10.0 10.0,10.0,0.0  10.0,10.0,10.0  10.0,0.0,0.0  10.0,0.0,10.0  0.0,0.0,0.0  0.0,0.0,10.0  >>> The Vertices (or Vectors) that define the shape use the Placement.Base attribute as their origin. So if you want to move a shape 10 units along the X axis, you could add 10 to the X coordinates of all the Vertices or you could set Placement.Base to (10,0,0).

Using "Center" to Control Axis of Rotation
By default, the axis of rotation isn't really the x/y/z axis. It is a line parallel to the selected axis, but passing through the reference point (Placement.Base) of the object to be rotated. This can be changed by using the Center fields in the Placement dialog or, in scripts, by using the Center parameter of the FreeCAD.Placement constructor.

For example, suppose we have a box (below) positioned at (20,20,10).

We wish to spin the box around it's own vertical centre line (ie local Z), while keeping it the same position. We can easily achieve this by specifying a Center value equal to the coordinates of the box's central point (25,25,15).

In a script, we would do: Same script with the file example RotateCoG2.fcstd (discussion on the forum)

Issues

 * As of version 0.13, update of Placement properties in the Data tab has been disabled for objects created with PartDesign, except for the initial sketch from which the solid will be created. Therefore the Placement of a solid created in PartDesign from a sketch can only be altered by adjusting Placement parameters of the initial construction sketch (the first sketch) from which the solid was created.
 * Placement functionality will eventually be handled in the Assembly workbench.

More

 * This tutorial: Aeroplane covers the mechanics of changing an object's Placement extensively.
 * A step-by-step explanation of the Placement Dialog can be found here Tasks_Placement.