Topological data scripting/cn
- 1 简介
- 2 创建基本图形
- 3 修改形状
- 4 探索形状
- 5 完整例子：OCC 瓶
- 6 载入和保存
This is a Unified Modeling Language (UML) overview of the most important classes of the Part module:
The geometric objects are the building block of all topological objects:
- Geom Base class of the geometric objects
- Line A straight line in 3D, defined by starting point and and point
- Circle Circle or circle segment defined by a center point and start and end point
- ...... And soon some more ;-)
The following topological data types are available:
- Compound A group of any type of topological object.
- Compsolid A composite solid is a set of solids connected by their faces. It expands the notions of WIRE and SHELL to solids.
- Solid A part of space limited by shells. It is three dimensional.
- Shell A set of faces connected by their edges. A shell can be open or closed.
- Face In 2D it is part of a plane; in 3D it is part of a surface. Its geometry is constrained (trimmed) by contours. It is two dimensional.
- Wire A set of edges connected by their vertices. It can be an open or closed contour depending on whether the edges are linked or not.
- Edge A topological element corresponding to a restrained curve. An edge is generally limited by vertices. It has one dimension.
- Vertex A topological element corresponding to a point. It has zero dimension.
- Shape A generic term covering all of the above.
We will now create a topology by constructing it out of simpler geometry. As a case study we use a part as seen in the picture which consists of four vertexes, two circles and two lines.
First we have to create the distinct geometric parts of this wire. And we have to take care that the vertexes of the geometric parts are at the same position. Otherwise later on we might not be able to connect the geometric parts to a topology!
So we create first the points:
from FreeCAD import Base V1 = Base.Vector(0,10,0) V2 = Base.Vector(30,10,0) V3 = Base.Vector(30,-10,0) V4 = Base.Vector(0,-10,0)
To create an arc of circle we make a helper point and create the arc of circle through three points:
VC1 = Base.Vector(-10,0,0) C1 = Part.Arc(V1,VC1,V4) # and the second one VC2 = Base.Vector(40,0,0) C2 = Part.Arc(V2,VC2,V3)
The line can be created very simple out of the points:
L1 = Part.Line(V1,V2) # and the second one L2 = Part.Line(V4,V3)
The last step is to put the geometric base elements together and bake a topological shape:
S1 = Part.Shape([C1,C2,L1,L2])
Now extrude the wire in a direction and make an actual 3D shape:
W = Part.Wire(S1.Edges) P = W.extrude(Base.Vector(0,0,10))
You can easily create basic topological objects with the "make...()" methods from the Part Module:
b = Part.makeBox(100,100,100) Part.show(b)
A couple of other make...() methods available:
- makeBox(l,w,h): Makes a box located in p and pointing into the direction d with the dimensions (l,w,h)
- makeCircle(radius): Makes a circle with a given radius
- makeCone(radius1,radius2,height): Makes a cone with a given radii and height
- makeCylinder(radius,height): Makes a cylinder with a given radius and height.
- makeLine((x1,y1,z1),(x2,y2,z2)): Makes a line of two points
- makePlane(length,width): Makes a plane with length and width
- makePolygon(list): Makes a polygon of a list of points
- makeSphere(radius): Make a sphere with a given radius
- makeTorus(radius1,radius2): Makes a torus with a given radii
See the Part API page for a complete list of available methods of the Part module.
First we need to import the Part module so we can use its contents in python. We'll also import the Base module from inside the FreeCAD module:
import Part from FreeCAD import Base
Vectors are one of the most important pieces of information when building shapes. They contain a 3 numbers usually (but not necessarily always) the x, y and z cartesian coordinates. You create a vector like this:
myVector = Base.Vector(3,2,0)
We just created a vector at coordinates x=3, y=2, z=0. In the Part module, vectors are used everywhere. Part shapes also use another kind of point representation, called Vertex, which is acually nothing else than a container for a vector. You access the vector of a vertex like this:
myVertex = myShape.Vertexes print myVertex.Point > Vector (3, 2, 0)
An edge is nothing but a line with two vertexes:
edge = Part.makeLine((0,0,0), (10,0,0)) edge.Vertexes > [<Vertex object at 01877430>, <Vertex object at 014888E0>]
Note: You can also create an edge by passing two vectors:
vec1 = Base.Vector(0,0,0) vec2 = Base.Vector(10,0,0) line = Part.Line(vec1,vec2) edge = line.toShape()
You can find the length and center of an edge like this:
edge.Length > 10.0 edge.CenterOfMass > Vector (5, 0, 0)
So far we created an edge object, but it doesn't appear anywhere on screen. This is because we just manipulated python objects here. The FreeCAD 3D scene only displays what you tell it to display. To do that, we use this simple method:
An object will be created in our FreeCAD document, and our "edge" shape will be attributed to it. Use this whenever it's time to display your creation on screen.
A wire is a multi-edge line and can be created from a list of edges or even a list of wires:
edge1 = Part.makeLine((0,0,0), (10,0,0)) edge2 = Part.makeLine((10,0,0), (10,10,0)) wire1 = Part.Wire([edge1,edge2]) edge3 = Part.makeLine((10,10,0), (0,10,0)) edge4 = Part.makeLine((0,10,0), (0,0,0)) wire2 = Part.Wire([edge3,edge4]) wire3 = Part.Wire([wire1,wire2]) wire3.Edges > [<Edge object at 016695F8>, <Edge object at 0197AED8>, <Edge object at 01828B20>, <Edge object at 0190A788>] Part.show(wire3)
Part.show(wire3) will display the 4 edges that compose our wire. Other useful information can be easily retrieved:
wire3.Length > 40.0 wire3.CenterOfMass > Vector (5, 5, 0) wire3.isClosed() > True wire2.isClosed() > False
Only faces created from closed wires will be valid. In this example, wire3 is a closed wire but wire2 is not a closed wire (see above)
face = Part.Face(wire3) face.Area > 99.999999999999972 face.CenterOfMass > Vector (5, 5, 0) face.Length > 40.0 face.isValid() > True sface = Part.Face(wire2) face.isValid() > False
Only faces will have an area, not wires nor edges.
A circle can be created as simply as this:
circle = Part.makeCircle(10) circle.Curve > Circle (Radius : 10, Position : (0, 0, 0), Direction : (0, 0, 1))
If you want to create it at certain position and with certain direction:
ccircle = Part.makeCircle(10, Base.Vector(10,0,0), Base.Vector(1,0,0)) ccircle.Curve > Circle (Radius : 10, Position : (10, 0, 0), Direction : (1, 0, 0))
ccircle will be created at distance 10 from origin on x and will be facing towards x axis. Note: makeCircle only accepts Base.Vector() for position and normal but not tuples. You can also create part of the circle by giving start angle and end angle as:
from math import pi arc1 = Part.makeCircle(10, Base.Vector(0,0,0), Base.Vector(0,0,1), 0, 180) arc2 = Part.makeCircle(10, Base.Vector(0,0,0), Base.Vector(0,0,1), 180, 360)
Both arc1 and arc2 jointly will make a circle. Angles should be provided in degrees, if you have radians simply convert them using formula: degrees = radians * 180/PI or using python's math module (after doing import math, of course):
degrees = math.degrees(radians)
Unfortunately there is no makeArc function but we have Part.Arc function to create an arc along three points. Basically it can be supposed as an arc joining start point and end point along the middle point. Part.Arc creates an arc object on which .toShape() has to be called to get the edge object, the same way as when using Part.Line instead of Part.makeLine.
arc = Part.Arc(Base.Vector(0,0,0),Base.Vector(0,5,0),Base.Vector(5,5,0)) arc > <Arc object> arc_edge = arc.toShape()
Arc only accepts Base.Vector() for points but not tuples. arc_edge is what we want which we can display using Part.show(arc_edge). You can also obtain an arc by using a portion of a circle:
from math import pi circle = Part.Circle(Base.Vector(0,0,0),Base.Vector(0,0,1),10) arc = Part.Arc(c,0,pi)
Arcs are valid edges, like lines. So they can be used in wires too.
A polygon is simply a wire with multiple straight edges. The makePolygon function takes a list of points and creates a wire along those points:
lshape_wire = Part.makePolygon([Base.Vector(0,5,0),Base.Vector(0,0,0),Base.Vector(5,0,0)])
A Plane is simply a flat rectangular surface. The method used to create one is this: makePlane(length,width,[start_pnt,dir_normal]). By default start_pnt = Vector(0,0,0) and dir_normal = Vector(0,0,1). Using dir_normal = Vector(0,0,1) will create the plane facing z axis, while dir_normal = Vector(1,0,0) will create the plane facing x axis:
plane = Part.makePlane(2,2) plane ><Face object at 028AF990> plane = Part.makePlane(2,2, Base.Vector(3,0,0), Base.Vector(0,1,0)) plane.BoundBox > BoundBox (3, 0, 0, 5, 0, 2)
BoundBox is a cuboid enclosing the plane with a diagonal starting at (3,0,0) and ending at (5,0,2). Here the BoundBox thickness in y axis is zero, since our shape is totally flat.
Note: makePlane only accepts Base.Vector() for start_pnt and dir_normal but not tuples
To create an ellipse there are several ways:
Creates an ellipse with major radius 2 and minor radius 1 with the center in (0,0,0)
Create a copy of the given ellipse
Creates an ellipse centered on the point Center, where the plane of the ellipse is defined by Center, S1 and S2, its major axis is defined by Center and S1, its major radius is the distance between Center and S1, and its minor radius is the distance between S2 and the major axis.
Creates an ellipse with major and minor radii MajorRadius and MinorRadius, and located in the plane defined by Center and the normal (0,0,1)
eli = Part.Ellipse(Base.Vector(10,0,0),Base.Vector(0,5,0),Base.Vector(0,0,0)) Part.show(eli.toShape())
In the above code we have passed S1, S2 and center. Similarly to Arc, Ellipse also creates an ellipse object but not edge, so we need to convert it into edge using toShape() to display.
Note: Arc only accepts Base.Vector() for points but not tuples
eli = Part.Ellipse(Base.Vector(0,0,0),10,5) Part.show(eli.toShape())
for the above Ellipse constructor we have passed center, MajorRadius and MinorRadius
Using the method makeTorus(radius1,radius2,[pnt,dir,angle1,angle2,angle]). By default pnt=Vector(0,0,0),dir=Vector(0,0,1),angle1=0,angle2=360 and angle=360. Consider a torus as small circle sweeping along a big circle. Radius1 is the radius of big cirlce, radius2 is the radius of small circle, pnt is the center of torus and dir is the normal direction. angle1 and angle2 are angles in radians for the small circle, the last parameter angle is to make a section of the torus:
torus = Part.makeTorus(10, 2)
The above code will create a torus with diameter 20(radius 10) and thickness 4 (small cirlce radius 2)
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.
Using makeBox(length,width,height,[pnt,dir]). By default pnt=Vector(0,0,0) and dir=Vector(0,0,1)
box = Part.makeBox(10,10,10) len(box.Vertexes) > 8
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 itself.
sphere = Part.makeSphere(10) hemisphere = Part.makeSphere(10,Base.Vector(0,0,0),Base.Vector(0,0,1),-90,90,180)
Using makeCylinder(radius,height,[pnt,dir,angle]). By default pnt=Vector(0,0,0),dir=Vector(0,0,1) and angle=360
cylinder = Part.makeCylinder(5,20) partCylinder = Part.makeCylinder(5,20,Base.Vector(20,0,0),Base.Vector(0,0,1),180)
Using makeCone(radius1,radius2,height,[pnt,dir,angle]). By default pnt=Vector(0,0,0), dir=Vector(0,0,1) and angle=360
cone = Part.makeCone(10,0,20) semicone = Part.makeCone(10,0,20,Base.Vector(20,0,0),Base.Vector(0,0,1),180)
There are several ways to modify shapes. Some are simple transformation operations such as moving or rotating shapes, other are more complex, such as unioning and subtracting one shape from another. Be aware that
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:
myShape = Part.makeBox(2,2,2) myShape.translate(Base.Vector(2,0,0))
This will move our shape "myShape" 2 units in the x direction.
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.
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:
myMat = Base.Matrix() myMat.move(Base.Vector(2,0,0)) myMat.rotateZ(math.pi/2)
Note: FreeCAD matrixes work in radians. Also, almost all matrix operations that take a vector can also take 3 numbers, so those 2 lines do the same thing:
When our matrix is set, we can apply it to our shape. FreeCAD provides 2 methods to do 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). So we can apply our transformation like this:
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 differenty. For scaling, we can't use the transformShape, we must use transformGeometry():
myMat = Base.Matrix() myMat.scale(2,1,1) myShape=myShape.transformGeometry(myMat)
Subtracting a shape from another one is called "cut" in OCC/FreeCAD jargon and is done like this:
cylinder = Part.makeCylinder(3,10,Base.Vector(0,0,0),Base.Vector(1,0,0)) sphere = Part.makeSphere(5,Base.Vector(5,0,0)) diff = cylinder.cut(sphere)
The same way, the intersection between 2 shapes is called "common" and is done this way:
cylinder1 = Part.makeCylinder(3,10,Base.Vector(0,0,0),Base.Vector(1,0,0)) cylinder2 = Part.makeCylinder(3,10,Base.Vector(5,0,-5),Base.Vector(0,0,1)) common = cylinder1.common(cylinder2)
Union is called "fuse" and works the same way:
cylinder1 = Part.makeCylinder(3,10,Base.Vector(0,0,0),Base.Vector(1,0,0)) cylinder2 = Part.makeCylinder(3,10,Base.Vector(5,0,-5),Base.Vector(0,0,1)) fuse = cylinder1.fuse(cylinder2)
交线是固体形体和平面的相交线。 A Section is the intersection between a solid shape and a plane shape. It will return an intersection curve, a compound with edges
cylinder1 = Part.makeCylinder(3,10,Base.Vector(0,0,0),Base.Vector(1,0,0)) cylinder2 = Part.makeCylinder(3,10,Base.Vector(5,0,-5),Base.Vector(0,0,1)) section = cylinder1.section(cylinder2) section.Wires >  section.Edges > [<Edge object at 0D87CFE8>, <Edge object at 019564F8>, <Edge object at 0D998458>, <Edge object at 0D86DE18>, <Edge object at 0D9B8E80>, <Edge object at 012A3640>, <Edge object at 0D8F4BB0>]
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":
circle = Part.makeCircle(10) tube = circle.extrude(Base.Vector(0,0,2))
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:
wire = Part.Wire(circle) disc = Part.makeFace(wire) cylinder = disc.extrude(Base.Vector(0,0,2))
You can easily explore the topological data structure:
import Part b = Part.makeBox(100,100,100) b.Wires w = b.Wires w w.Wires w.Vertexes Part.show(w) w.Edges e = w.Edges e.Vertexes v = e.Vertexes v.Point
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.
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:
import Part box = Part.makeBox(100,100,100) anEdge = box.Edges print anEdge.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.
anEdge.tangentAt(0.0) # tangent direction at the beginning anEdge.valueAt(0.0) # Point at the beginning anEdge.valueAt(100.0) # Point at the end of the edge anEdge.derivative1At(50.0) # first derivative of the curve in the middle anEdge.derivative2At(50.0) # second derivative of the curve in the middle anEdge.derivative3At(50.0) # third derivative of the curve in the middle anEdge.centerOfCurvatureAt(50) # center of the curvature for that position anEdge.curvatureAt(50.0) # the curvature anEdge.normalAt(50) # normal vector at that position (if defined)
Here we see now how we can use the selection the user did in the viewer. First of all we create a box and shows it in the viewer
import Part Part.show(Part.makeBox(100,100,100)) Gui.SendMsgToActiveView("ViewFit")
Select now some faces or edges. With this script you can iterate all selected objects and their sub elements:
for o in Gui.Selection.getSelectionEx(): print o.ObjectName for s in o.SubElementNames: print "name: ",s for s in o.SubObjects: print "object: ",s
Select some edges and this script will calculate the length:
length = 0.0 for o in Gui.Selection.getSelectionEx(): for s in o.SubObjects: length += s.Length print "Length of the selected edges:" ,length
A typical example found on the OpenCasCade Getting Started Page is how to build a bottle. This is a good exercise for FreeCAD too. In fact, you can follow our example below and the OCC page simultaneously, you will understand well how OCC structures are implemented in FreeCAD. The complete script below is also included in FreeCAD installation (inside the Mod/Part folder) and can be called from the python interpreter by typing:
import Part import MakeBottle bottle = MakeBottle.makeBottle() Part.show(bottle)
Here is the complete MakeBottle script:
import Part, FreeCAD, math from FreeCAD import Base def makeBottle(myWidth=50.0, myHeight=70.0, myThickness=30.0): aPnt1=Base.Vector(-myWidth/2.,0,0) aPnt2=Base.Vector(-myWidth/2.,-myThickness/4.,0) aPnt3=Base.Vector(0,-myThickness/2.,0) aPnt4=Base.Vector(myWidth/2.,-myThickness/4.,0) aPnt5=Base.Vector(myWidth/2.,0,0) aArcOfCircle = Part.Arc(aPnt2,aPnt3,aPnt4) aSegment1=Part.Line(aPnt1,aPnt2) aSegment2=Part.Line(aPnt4,aPnt5) aEdge1=aSegment1.toShape() aEdge2=aArcOfCircle.toShape() aEdge3=aSegment2.toShape() aWire=Part.Wire([aEdge1,aEdge2,aEdge3]) aTrsf=Base.Matrix() aTrsf.rotateZ(math.pi) # rotate around the z-axis aMirroredWire=aWire.transformGeometry(aTrsf) myWireProfile=Part.Wire([aWire,aMirroredWire]) myFaceProfile=Part.Face(myWireProfile) aPrismVec=Base.Vector(0,0,myHeight) myBody=myFaceProfile.extrude(aPrismVec) myBody=myBody.makeFillet(myThickness/12.0,myBody.Edges) neckLocation=Base.Vector(0,0,myHeight) neckNormal=Base.Vector(0,0,1) myNeckRadius = myThickness / 4. myNeckHeight = myHeight / 10 myNeck = Part.makeCylinder(myNeckRadius,myNeckHeight,neckLocation,neckNormal) myBody = myBody.fuse(myNeck) faceToRemove = 0 zMax = -1.0 for xp in myBody.Faces: try: surf = xp.Surface if type(surf) == Part.Plane: z = surf.Position.z if z > zMax: zMax = z faceToRemove = xp except: continue myBody = myBody.makeThickness([faceToRemove],-myThickness/50 , 1.e-3) return myBody
import Part, FreeCAD, math from FreeCAD import Base
We will need,of course, the Part module, but also the FreeCAD.Base module, which contains basic FreeCAD structures like vectors and matrixes.
def makeBottle(myWidth=50.0, myHeight=70.0, myThickness=30.0): aPnt1=Base.Vector(-myWidth/2.,0,0) aPnt2=Base.Vector(-myWidth/2.,-myThickness/4.,0) aPnt3=Base.Vector(0,-myThickness/2.,0) aPnt4=Base.Vector(myWidth/2.,-myThickness/4.,0) aPnt5=Base.Vector(myWidth/2.,0,0)
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.
aArcOfCircle = Part.Arc(aPnt2,aPnt3,aPnt4) aSegment1=Part.Line(aPnt1,aPnt2) aSegment2=Part.Line(aPnt4,aPnt5)
Here we actually define the geometry: an arc, made of 3 points, and two line segments, made of 2 points.
aEdge1=aSegment1.toShape() aEdge2=aArcOfCircle.toShape() aEdge3=aSegment2.toShape() aWire=Part.Wire([aEdge1,aEdge2,aEdge3])
Remember the difference between geometry and shapes? Here we build shapes out of our construction geometry. 3 edges (edges can be straight or curved), then a wire made of those three edges.
aTrsf=Base.Matrix() aTrsf.rotateZ(math.pi) # rotate around the z-axis aMirroredWire=aWire.transformGeometry(aTrsf) myWireProfile=Part.Wire([aWire,aMirroredWire])
Until now we built only a half profile. Easier than building the whole profile the same way, we can just mirror what we did, and glue both halfs together. So 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 suffer (move, rotate and scale). Here, after we create the matrix, we mirror it, and 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.
myFaceProfile=Part.Face(myWireProfile) aPrismVec=Base.Vector(0,0,myHeight) myBody=myFaceProfile.extrude(aPrismVec) myBody=myBody.makeFillet(myThickness/12.0,myBody.Edges)
Now that we have a closed wire, it can be turned into a face. Once we have a face, we can extrude it. Doing so, we actually made a solid. Then we apply a nice little fillet to our object because we care about good design, don't we?
neckLocation=Base.Vector(0,0,myHeight) neckNormal=Base.Vector(0,0,1) myNeckRadius = myThickness / 4. myNeckHeight = myHeight / 10 myNeck = Part.makeCylinder(myNeckRadius,myNeckHeight,neckLocation,neckNormal)
Then, the body of our bottle is made, we still need to create a neck. So we make a new solid, with a cylinder.
myBody = myBody.fuse(myNeck)
The fuse operation, which in other apps is sometimes called 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. That Part solid, like any other Part shape, can be attributed to an object in a FreeCAD document, with:
myObject = FreeCAD.ActiveDocument.addObject("Part::Feature","myObject") myObject.Shape = bottle
or, more simple:
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 availables for all shape objects. So, doing:
import Part s = Part.makeBox(0,0,0,10,10,10) s.exportStep("test.stp")
this will save our box into a STEP file. To load a BREP, IGES or STEP file, simply do the contrary:
import Part s = Part.Shape() s.read("test.stp")
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 is with File -> Export