Topological data scripting/zh-cn

本页描述了几种利用python来创建与修改零件形状（Part shapes）的方法. 如果您是python新手，请在阅读本页之前，先去浏览python脚本与如何在FreeCAD中运行python脚本.

概述
我们将在本文中向您解释如何直接用FreeCAD的Python解释器来控制零件模块，或者从任意外部脚本来实现这一点. 关于拓扑数据脚本的基本描述位于零件模块的概念介绍. 如果您需要了解关于FreeCAD中python脚本工作原理的更多信息，请一定阅读脚本一节与FreeCAD脚本基础页面.

类图
这是零件模块中最关键类的 统一建模语言（Unified Modeling Language (UML)）概述：

几何图形
这些几何图形对象是一切拓扑对象的基石：
 * Geom 几何图形对象的基类
 * Line 3D空间中的直线段，由起始点与终点定义而成
 * Circle 由中心点、起始点与终点定义的圆形或部分圆环段（circle segment）
 * ...... 以及后续更多的几何图形

拓扑
FreeCAD中有下列可用的拓扑数据类型：
 * 复合（Compound）对象 一组任意类型的拓扑对象.
 * 组合实体（Compsolid） 一个复合实体是一组由其面连接起来的实体. 它会将连线（WIRE）与壳（SHELL）扩展为实体.
 * 实体（Solid） 由壳界定的部分空间. 实体是3D对象.
 * 壳（Shell） 一组由其边连接起来的面. 一个壳可以是开放或闭合的.
 * 面（Face） 在2D空间中，它是部分平面；而在3D空间中，它是部分表面. 面的几何图形由轮廓来约束（调整）. 面是2D对象.
 * 连线（Wire） 一组由其顶点连接起来的边. 连线可以是开放或闭合的轮廓，这取决于其中的边是否互连.
 * 边（Edge） 一种对应于约束曲线的拓扑元素. 一条边通常受其顶点限制. 边是一种1D对象.
 * 顶点（Vertex） 一种对应于点的拓扑元素. 顶点是零维对象.
 * 几何形状（Shape） 一种涵盖上述所有对象的通称.

简易示例 ：创建简单拓扑结构


现在，我们将通过构造简单的几何图形来创建对应的拓扑. 就用我们在图中看到的零件为例，它由4个顶点，2个半圆以及2条线段构成.

创建几何图形
首先，我们必须创建此连线中的不同几何图形部分. 而且，还要小心处理几何图形中位于相同位置的不同顶点. 否则，我们随后可能无法将这些几何图形连接为一个拓扑结构.

因此，我们先来创建其中的点：

弧


为了创建圆周上的弧，我们要做一个辅助点，并通过圆周上的3个点来创建对应的弧：

线段


众所周知，两点定一线段：

请注意：在FreeCAD 0.16版中使用的是Part.Line，而对于FreeCAD 0.17版则必须使用Part.LineSegment

合而为一
最后一步就是将上述基本几何元素放在一起，并烘焙出一个拓扑形状：

制作一个外框
现在令连线在同一方向上挤压成型，构造一个实际的3D图形：

创建基本的几何形状
您可以利用零件模块中的"make..."方法来轻松地创建一个基础的拓扑对象.

其他可用的make...方法： 请参考Part API页来查阅零件模块中的完整可用方法列表.
 * makeBox(l,w,h): 在点p（？）处创建一个维数为(l,w,h)且指向方向d（？）的立方体
 * makeCircle(radius): 以指定的半径创建一个圆形
 * makeCone(radius1,radius2,height): 以指定的两个半径与高度创建一个圆锥体（圆台）
 * makeCylinder(radius,height): 以指定的半径与高度创建一个圆柱体
 * makeLine((x1,y1,z1),(x2,y2,z2)): 根据两点创建一条线段
 * makePlane(length,width): 利用指定的长度与宽度创建一个平面
 * makePolygon(list): 根据指定的点集创建一个多边形
 * makeSphere(radius): 利用指定的半径创建一个球体
 * makeTorus(radius1,radius2): 利用指定的两个半径创建一个圆环体

导入所需的模块
首先，我们需要导入零件（Part）模块，继而通过python使用其中提供的内容. 另外，我们也将从FreeCAD模块中导入基础（Base）模块：

创建一个向量
在构建几何图形的过程中， 向量 是提供最关键信息的对象类型之一. 向量属性中通常都有3个数字（但并非总是如此）：即直角坐标系中的3种坐标分量：x、y、z. 您可以按下列方式来创建一个向量：

我们刚刚在x=3, y=2, z=0坐标处创建了一个向量. 在零件模块中，到处都能看到向量的身影. 构建零件形状的过程中，也会用到另一种名为顶点的点表示法，它是一种向量的简易容器. 您可像下面那样来访问一个点的向量：

创建一条边
一条边不过是具有两个顶点的线段：

请注意，您也可以通过输入两个向量来创建一条边：

您能通过下列方式来查看一条边的长度与中点：

将图形显示在屏幕上
到目前为止，我们已经创建了一个边对象，但是它却并没有出现在屏幕上. 这是因为：只有在您告诉FreeCAD要呈现什么内容之后，它才会显示出对应的3D场景. 为此，我们要通过下列简单函数来实现这一点：

此show函数在我们当前的FreeCAD文档中创建了一个对象，并为之赋予此前创建的"edge"几何形状. 每当需要在屏幕上显示您所创建的对象们时，使用此函数即可.

创建一个连线
一条连线（wire）由多条边构成. 创建连线需要指定一个边列表，或者甚至是一个连线列表：

Part.show(wire3)命令将显示构成我们所创连线的4条边. 而其他有用的信息可通过下列方式方便地检索：

创建一个面
只有根据闭合连线创建的面才是有效的. 在本示例中，wire3是一个闭合的连线，而wire2却不是一个闭合的连线（参见此前的代码）

只有面才具有自己的面积，而连线与边却没有.

创建一个圆形
我们可以按下列方式简单地创建一个圆形：

如果您想以特定的位置与方向来创建它，则可：

所创的圆形ccircle将位于x轴上距原点10个单位处，并沿轴方向面向外侧. 请注意：makeCircle仅接收Base.Vector作为其位置以及方向参数，而非元组（tuples）. 您也可以通过指定起始角度与结束角度来创建部分圆：

arc1与arc2拼接起来即是一个圆. 角度参数使用的是角度制；如果您采用的是弧度制，可简单的通过下列公式进行转换：角度 = 弧度 * 180/PI，或借助python的数学模块（当然啦，要在导入数学模块后才能使用）：

沿多个点创建一条弧
可惜的是，FreeCAD并没有提供makeArc函数，但是我们有Part.Arc函数可通过3个点来创建一条弧. 它经过起始点、中点以及两者间的一个中间点来创建一个弧对象. 另外，必须调用弧对象的.toShape函数来得到一个边对象，与Arc用法相同的是Part.LineSegment而非Part.makeLine.

Arc函数仅接受Base.Vector作为绘弧所用的点，而非元组（tuples）. arc_edge就是我们要借助Part.show(arc_edge)语句所显示的边. 您也通过截取部分圆来获得一条弧：

弧都是像线条那样的有效边，因此也可将其用作连线.

创建一个多边形
多边形是利用多条直边连接而成的简易连线. makePolygon函数将获取一个点列表，并通过其中的多个点来创建一条连线：

创建一条贝塞尔曲线
贝塞尔曲线常用于模拟平滑的曲线，绘制贝塞尔曲线要借助一系列极点（poles）以及权值. 下列函数根据一组FreeCAD.Vector点来创建一条Part.BezierCurve. (请注意：当“获取”或“设置”单个极点或权值时，起始索引为1而非0. )

创建一个平面
平面就是一个简单的矩形平面. makePlane(length,width,[start_pnt,dir_normal])方法可用于创建一个平面. 默认值为 start_pnt = Vector(0,0,0)与dir_normal = Vector(0,0,1). 通过dir_normal = Vector(0,0,1)将创建一个面向z轴正方向的平面，而dir_normal = Vector(1,0,0)将创建一个面向x轴正方向的平面：

其中的包围盒BoundBox是一个包围目标平面的长方体，它有一条自(3,0,0)始至(5,0,2)终的对角线. 可以看出，BoundBox的厚度在y轴上为0，这是因为被包围的对象是一个平面.

请注意，makePlane仅接收Base.Vector作为其start_pnt与dir_normal参数，而非元组（tuples）.

创建一个椭圆
有多种方法可以创建椭圆：

创建一个长半轴为2、短半轴为1，且中点位于(0,0,0)处的椭圆.

创建一个指定椭圆的副本.

创建一个以点Center为中心的椭圆，所在平面由Center、S1与S2定义，长轴由Center与S1定义，长半轴为Center与S1间的距离，而短半轴则是S2与长轴间的距离.

以长半轴MajorRadius与短半轴MinorRadius创建一个椭圆，其所在平面由Center与法线(0,0,1)定义.

在上面的代码中，我们分别传入了S1、S2与中心位置. 与Arc函数类似，Ellipse函数创建了一个椭圆对象而非边，所以我们需要用toShape将其转换为一条边，以便显示.

请注意：Arc仅接收Base.Vector作为其输入点，而非元组.

针对上述Ellipse函数的构造函数，我们为之传入了中心位置，MajorRadius与MinorRadius.

创建一个环面
利用makeTorus(radius1,radius2,[pnt,dir,angle1,angle2,angle])来创建环面. 其默认值为：pnt=Vector(0,0,0), dir=Vector(0,0,1), angle1=0, angle2=360与angle=360. 可以将环面想象为：一个小圆沿着一个大圆扫过的图形. Radius1为大圆的半径，radius2为小圆的半径，pnt为环面的中心，而dir则为法线方向. angle1与angle2都是针对小圆的以弧度制（？）表示的角度；最后一个参数angle描述的是截取的部分环面：

以上代码将场景一个直径为20（半径为10）且厚度为4（小圆半径为2）的环面.

The above code will create a slice of the torus.

The above code will create a semi torus; only the last parameter is changed. i.e the angle and remaining angles are defaults. Giving the angle 180 will create the torus from 0 to 180, that is, a half torus.

Creating a box or cuboid
Using makeBox(length,width,height,[pnt,dir]). By default pnt=Vector(0,0,0) and dir=Vector(0,0,1).

Creating a Sphere
Using makeSphere(radius,[pnt, dir, angle1,angle2,angle3]). By default pnt=Vector(0,0,0), dir=Vector(0,0,1), angle1=-90, angle2=90 and angle3=360. angle1 and angle2 are the vertical minimum and maximum of the sphere, angle3 is the sphere diameter.

Creating a Cylinder
Using makeCylinder(radius,height,[pnt,dir,angle]). By default pnt=Vector(0,0,0),dir=Vector(0,0,1) and angle=360.

Creating a Cone
Using makeCone(radius1,radius2,height,[pnt,dir,angle]). By default pnt=Vector(0,0,0), dir=Vector(0,0,1) and angle=360.

Modifying shapes
There are several ways to modify shapes. Some are simple transformation operations such as moving or rotating shapes, others are more complex, such as unioning and subtracting one shape from another.

Translating a shape
Translating is the act of moving a shape from one place to another. Any shape (edge, face, cube, etc...) can be translated the same way:

This will move our shape "myShape" 2 units in the x direction.

Rotating a shape
To rotate a shape, you need to specify the rotation center, the axis, and the rotation angle:

The above code will rotate the shape 180 degrees around the Z Axis.

Generic transformations with matrixes
A matrix is a very convenient way to store transformations in the 3D world. In a single matrix, you can set translation, rotation and scaling values to be applied to an object. For example:

Note: FreeCAD matrixes work in radians. Also, almost all matrix operations that take a vector can also take three numbers, so these two lines do the same thing:

Once our matrix is set, we can apply it to our shape. FreeCAD provides two methods for doing that: transformShape and transformGeometry. The difference is that with the first one, you are sure that no deformations will occur (see "scaling a shape" below). We can apply our transformation like this:

or

Scaling a shape
Scaling a shape is a more dangerous operation because, unlike translation or rotation, scaling non-uniformly (with different values for x, y and z) can modify the structure of the shape. For example, scaling a circle with a higher value horizontally than vertically will transform it into an ellipse, which behaves mathematically very differently. For scaling, we can't use the transformShape, we must use transformGeometry:

Subtraction
Subtracting a shape from another one is called "cut" in OCC/FreeCAD jargon and is done like this:

Intersection
The same way, the intersection between two shapes is called "common" and is done this way:

Union
Union is called "fuse" and works the same way:

Section
A Section is the intersection between a solid shape and a plane shape. It will return an intersection curve, a compound curve composed of edges.

Extrusion
Extrusion is the act of "pushing" a flat shape in a certain direction, resulting in a solid body. Think of a circle becoming a tube by "pushing it out":

If your circle is hollow, you will obtain a hollow tube. If your circle is actually a disc with a filled face, you will obtain a solid cylinder:

Exploring shapes
You can easily explore the topological data structure:

By typing the lines above in the python interpreter, you will gain a good understanding of the structure of Part objects. Here, our makeBox command created a solid shape. This solid, like all Part solids, contains faces. Faces always contain wires, which are lists of edges that border the face. Each face has at least one closed wire (it can have more if the face has a hole). In the wire, we can look at each edge separately, and inside each edge, we can see the vertexes. Straight edges have only two vertexes, obviously.

Edge analysis
In case of an edge, which is an arbitrary curve, it's most likely you want to do a discretization. In FreeCAD the edges are parametrized by their lengths. That means you can walk an edge/curve by its length:

Now you can access a lot of properties of the edge by using the length as a position. That means if the edge is 100mm long the start position is 0 and the end position 100.

Using the selection
Here we see now how we can use the selection the user did in the viewer. First of all we create a box and show it in the viewer.

Now select some faces or edges. With this script you can iterate over all selected objects and their sub elements:

Select some edges and this script will calculate the length:

Complete example: The OCC bottle
A typical example found in the OpenCasCade Technology Tutorial is how to build a bottle. This is a good exercise for FreeCAD too. In fact, if you follow our example below and the OCC page simultaneously, you will see how well OCC structures are implemented in FreeCAD. The complete script below is also included in the FreeCAD installation (inside the Mod/Part folder) and can be called from the python interpreter by typing:

The complete script
Here is the complete MakeBottle script:

Detailed explanation
We will need, of course, the Part module, but also the FreeCAD.Base module, which contains basic FreeCAD structures like vectors and matrixes.

Here we define our makeBottle function. This function can be called without arguments, like we did above, in which case default values for width, height, and thickness will be used. Then, we define a couple of points that will be used for building our base profile.

Here we actually define the geometry: an arc, made of three points, and two line segments, made of two points.

Remember the difference between geometry and shapes? Here we build shapes out of our construction geometry. Three edges (edges can be straight or curved), then a wire made of those three edges.

So far we have built only a half profile. Instead of building the whole profile the same way, we can just mirror what we did and glue both halves together. We first create a matrix. A matrix is a very common way to apply transformations to objects in the 3D world, since it can contain in one structure all basic transformations that 3D objects can undergo (move, rotate and scale). After we create the matrix we mirror it, then we create a copy of our wire with that transformation matrix applied to it. We now have two wires, and we can make a third wire out of them, since wires are actually lists of edges.

Now that we have a closed wire, it can be turned into a face. Once we have a face, we can extrude it. In doing so, we make a solid. Then we apply a nice little fillet to our object because we care about good design, don't we?

At this point, the body of our bottle is made, but we still need to create a neck. So we make a new solid, with a cylinder.

The fuse operation, which in other applications is sometimes called a union, is very powerful. It will take care of gluing what needs to be glued and remove parts that need to be removed.

Then, we return our Part solid as the result of our function.

Finally, we call the function to actually create the part, then make it visible.

Box pierced
Here is a complete example of building a pierced box.

The construction is done one side at a time; when the cube is finished, it is hollowed out by cutting a cylinder through it.

Loading and Saving
There are several ways to save your work in the Part module. You can of course save your FreeCAD document, but you can also save Part objects directly to common CAD formats, such as BREP, IGS, STEP and STL.

Saving a shape to a file is easy. There are exportBrep, exportIges, exportStl and exportStep methods available for all shape objects. So, doing:

will save our box into a STEP file. To load a BREP, IGES or STEP file:

To convert an .stp file to an .igs file:

Note that importing or opening BREP, IGES or STEP files can also be done directly from the File → Open or File → Import menu, while exporting can be done with File → Export.