一、前言

上一篇写了Solid的创建、展示、变换、布尔操作，这一篇写另一种Solid的创建方法。

需要再次强调的是，BrepBuilder不适合用来创建Solid。

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二、边界表示

【Wiki】：边界表示（Boundary representation，简称B-Rep），是一种通过定义其体积限制来表示3D形状的方法。实体表示为连接的曲面元素的集合，这些曲面元素定义内部点和外部点之间的边界。

还有个叫 CSG（Constructive Solid Geometry）的，和一些其它表示方法。我不知道Revit用的是哪种，当然了，API调用仔调API就行了，也只能按开放的接口用。如果不爽调用这破API，可以去看“Open Cascade”，整会了就可以自个儿玩了。

Brep，简单来讲，就是定义每个面，定义面上的范围（边），再把它们严丝合缝的拼起来。

“Geometric Modeling”里面介绍了一些几何建模的方法，了解一下就行了。

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三、BRepBuilder

3.1. 使用流程

以创建一个正方体为例。

Ⅰ 准备阶段：

1. 创建BRepBuilder实例
2. 创建Surface，即前后左右上下6个平面。
3. 创建Curve，即正方体12条直线边。

Ⅱ 组装填充阶段：

1. AddFace
2. AddEdge
3. AddLoop
4. AddCoEdge
5. FinishLoop,FinishFace
6. Finish

3.2. 样例代码解释

正方体生成的代码和其它例子，可以查看SDK目录下的“SDKSample/BRepBuilderExample/CreateCube.cs”，或者查看GitHub。

直接看代码可能有点迷糊，这里对组装填充的步骤进行解释。

请结合图来看。

// 摘自 RevitSdkSamples 
private BRepBuilder CreateCubeImpl()
{
    // create a BRepBuilder; add faces to build a cube

    // BRepType.Solid，表示面都需要朝外；朝内就是Void
    BRepBuilder brepBuilder = new BRepBuilder(BRepType.Solid);
    
    // a cube 100x100x100, from (0,0,0) to (100, 100, 100)
    
    // 1. Planes.
    // 6个面，面的朝向如图
    Plane bottom = Plane.CreateByOriginAndBasis(new XYZ(50, 50, 0), new XYZ(1, 0, 0), new XYZ(0, 1, 0)); // bottom. XY plane, Z = 0, normal pointing inside the cube.
    Plane top = Plane.CreateByOriginAndBasis(new XYZ(50, 50, 100), new XYZ(1, 0, 0), new XYZ(0, 1, 0)); // top. XY plane, Z = 100, normal pointing outside the cube.
    Plane front = Plane.CreateByOriginAndBasis(new XYZ(100, 50, 50), new XYZ(0, 0, 1), new XYZ(0, 1, 0)); // front side. ZY plane, X = 0, normal pointing inside the cube.
    Plane back = Plane.CreateByOriginAndBasis(new XYZ(0, 50, 50), new XYZ(0, 0, 1), new XYZ(0, 1, 0)); // back side. ZY plane, X = 0, normal pointing outside the cube.
    Plane left = Plane.CreateByOriginAndBasis(new XYZ(50, 0, 50), new XYZ(0, 0, 1), new XYZ(1, 0, 0)); // left side. ZX plane, Y = 0, normal pointing inside the cube
    Plane right = Plane.CreateByOriginAndBasis(new XYZ(50, 100, 50), new XYZ(0, 0, 1), new XYZ(1, 0, 0)); // right side. ZX plane, Y = 100, normal pointing outside the cube
                                                   
    // 2. Faces.
    // 填充Face，注意参数True/False，表示面是否需要翻转
    // 面需要朝外，看图，bottom/front/left 都需要翻转面朝向
    BRepBuilderGeometryId faceId_Bottom = brepBuilder.AddFace(BRepBuilderSurfaceGeometry.Create(bottom, null), true);
    BRepBuilderGeometryId faceId_Top = brepBuilder.AddFace(BRepBuilderSurfaceGeometry.Create(top, null), false);
    BRepBuilderGeometryId faceId_Front = brepBuilder.AddFace(BRepBuilderSurfaceGeometry.Create(front, null), true);
    BRepBuilderGeometryId faceId_Back = brepBuilder.AddFace(BRepBuilderSurfaceGeometry.Create(back, null), false);
    BRepBuilderGeometryId faceId_Left = brepBuilder.AddFace(BRepBuilderSurfaceGeometry.Create(left, null), true);
    BRepBuilderGeometryId faceId_Right = brepBuilder.AddFace(BRepBuilderSurfaceGeometry.Create(right, null), false);
    
    // 3. Edges.
    
    // 3.a (define edge geometry)
    // 定义12条边，边的方向如图
    // walk around bottom face
    BRepBuilderEdgeGeometry edgeBottomFront = BRepBuilderEdgeGeometry.Create(new XYZ(100, 0, 0), new XYZ(100, 100, 0));
    BRepBuilderEdgeGeometry edgeBottomRight = BRepBuilderEdgeGeometry.Create(new XYZ(100, 100, 0), new XYZ(0, 100, 0));
    BRepBuilderEdgeGeometry edgeBottomBack = BRepBuilderEdgeGeometry.Create(new XYZ(0, 100, 0), new XYZ(0, 0, 0));
    BRepBuilderEdgeGeometry edgeBottomLeft = BRepBuilderEdgeGeometry.Create(new XYZ(0, 0, 0), new XYZ(100, 0, 0));
    
    // now walk around top face
    BRepBuilderEdgeGeometry edgeTopFront = BRepBuilderEdgeGeometry.Create(new XYZ(100, 0, 100), new XYZ(100, 100, 100));
    BRepBuilderEdgeGeometry edgeTopRight = BRepBuilderEdgeGeometry.Create(new XYZ(100, 100, 100), new XYZ(0, 100, 100));
    BRepBuilderEdgeGeometry edgeTopBack = BRepBuilderEdgeGeometry.Create(new XYZ(0, 100, 100), new XYZ(0, 0, 100));
    BRepBuilderEdgeGeometry edgeTopLeft = BRepBuilderEdgeGeometry.Create(new XYZ(0, 0, 100), new XYZ(100, 0, 100));
    
    // sides
    BRepBuilderEdgeGeometry edgeFrontRight = BRepBuilderEdgeGeometry.Create(new XYZ(100, 100, 0), new XYZ(100, 100, 100));
    BRepBuilderEdgeGeometry edgeRightBack = BRepBuilderEdgeGeometry.Create(new XYZ(0, 100, 0), new XYZ(0, 100, 100));
    BRepBuilderEdgeGeometry edgeBackLeft = BRepBuilderEdgeGeometry.Create(new XYZ(0, 0, 0), new XYZ(0, 0, 100));
    BRepBuilderEdgeGeometry edgeLeftFront = BRepBuilderEdgeGeometry.Create(new XYZ(100, 0, 0), new XYZ(100, 0, 100));

    // 3.b (define the edges themselves)
    // 填充边
    BRepBuilderGeometryId edgeId_BottomFront = brepBuilder.AddEdge(edgeBottomFront);
    BRepBuilderGeometryId edgeId_BottomRight = brepBuilder.AddEdge(edgeBottomRight);
    BRepBuilderGeometryId edgeId_BottomBack = brepBuilder.AddEdge(edgeBottomBack);
    BRepBuilderGeometryId edgeId_BottomLeft = brepBuilder.AddEdge(edgeBottomLeft);
    BRepBuilderGeometryId edgeId_TopFront = brepBuilder.AddEdge(edgeTopFront);
    BRepBuilderGeometryId edgeId_TopRight = brepBuilder.AddEdge(edgeTopRight);
    BRepBuilderGeometryId edgeId_TopBack = brepBuilder.AddEdge(edgeTopBack);
    BRepBuilderGeometryId edgeId_TopLeft = brepBuilder.AddEdge(edgeTopLeft);
    BRepBuilderGeometryId edgeId_FrontRight = brepBuilder.AddEdge(edgeFrontRight);
    BRepBuilderGeometryId edgeId_RightBack = brepBuilder.AddEdge(edgeRightBack);
    BRepBuilderGeometryId edgeId_BackLeft = brepBuilder.AddEdge(edgeBackLeft);
    BRepBuilderGeometryId edgeId_LeftFront = brepBuilder.AddEdge(edgeLeftFront);

    // 4. Loops.
    // 填充轮廓
    BRepBuilderGeometryId loopId_Bottom = brepBuilder.AddLoop(faceId_Bottom);
    BRepBuilderGeometryId loopId_Top = brepBuilder.AddLoop(faceId_Top);
    BRepBuilderGeometryId loopId_Front = brepBuilder.AddLoop(faceId_Front);
    BRepBuilderGeometryId loopId_Back = brepBuilder.AddLoop(faceId_Back);
    BRepBuilderGeometryId loopId_Right = brepBuilder.AddLoop(faceId_Right);
    BRepBuilderGeometryId loopId_Left = brepBuilder.AddLoop(faceId_Left);
    
    // 5. Co-edges. 
    // 定义轮廓，即 向loop中填充边，
    // ① 边需要首尾相连；② 边按右手螺旋定则，方向需要和面一致（即朝外）
    // Bottom face. All edges reversed
    brepBuilder.AddCoEdge(loopId_Bottom, edgeId_BottomFront, true); // other direction in front loop
    brepBuilder.AddCoEdge(loopId_Bottom, edgeId_BottomLeft, true);  // other direction in left loop
    brepBuilder.AddCoEdge(loopId_Bottom, edgeId_BottomBack, true);  // other direction in back loop
    brepBuilder.AddCoEdge(loopId_Bottom, edgeId_BottomRight, true); // other direction in right loop
    brepBuilder.FinishLoop(loopId_Bottom);  // 完成底面轮廓的定义
    brepBuilder.FinishFace(faceId_Bottom);  // 完成底面的定义
    
    // Top face. All edges NOT reversed.
    brepBuilder.AddCoEdge(loopId_Top, edgeId_TopFront, false);  // other direction in front loop.
    brepBuilder.AddCoEdge(loopId_Top, edgeId_TopRight, false);  // other direction in right loop
    brepBuilder.AddCoEdge(loopId_Top, edgeId_TopBack, false);   // other direction in back loop
    brepBuilder.AddCoEdge(loopId_Top, edgeId_TopLeft, false);   // other direction in left loop
    brepBuilder.FinishLoop(loopId_Top);
    brepBuilder.FinishFace(faceId_Top);
    
    // Front face.
    // 略，详情看源码
    // Back face
    // Right face
    // Left face
    
    brepBuilder.Finish();  // 完成构建
    return brepBuilder;
}

// 获取构件结果
Solid mySolid = CreateCubeImpl().GetResult();

3.3. API实用性分析

第一点就是使用繁杂，容易出错。我们看到了，即使是生成一个最简单的正方体，都要大费周章。

而若是使用上一篇写的“GeometryCreationUtilities”呢？

public Solid CreateBox()
{
    XYZ point1 = XYZ.Zero;
    XYZ point2 = new XYZ(100, 0, 0);
    XYZ point3 = new XYZ(100, 100, 0);
    XYZ point4 = new XYZ(0, 100, 0);

    CurveLoop curveLoop = new CurveLoop();
    curveLoop.Append(Line.CreateBound(point1, point2));
    curveLoop.Append(Line.CreateBound(point2, point3));
    curveLoop.Append(Line.CreateBound(point3, point4));
    curveLoop.Append(Line.CreateBound(point4, point1));

    Solid solid = GeometryCreationUtilities.CreateExtrusionGeometry(new List<CurveLoop>() { curveLoop }, XYZ.BasisZ, 100);

    return solid;
}

第二点就是使用难度高。正方体是简单，但若复杂一点呢？曲面、锥面、直纹面、赫尔米特曲面的组合呢，这些面都有现成的API，但问题在于“Edge”，如何去计算多个曲面的交界边是BrepBuilder使用难度高的主要原因。

我这小卡拉米，是算不出曲面与曲面的交线的，就算是最简单的一个平面斜切圆柱，都得写写画画好一会儿。

虽然 Revit Face类提供了计算面交线的方法，但是Surface可没有。Face没有构造方法，只能从Solid上获取。而要使用Brep生成Solid，就需要知道面的交线。这样就死循环了，所以还是得算，这也就是使用难度高。

当然了，该方法有时还是挺好用的，比如说，对一个现有的曲面进行拉伸。

四、总结

这一篇简单写了BrepBilder的使用流程，结合示例进行了解释。