概述

本教程提供了如何自底向上建模，将会以构建一个正方体为例进行讲解。

构建一个正方体正确的做法应该是：构建 8 个 Vertex，再使用 8 个 Vertex 构建 12 个 Edge，再用 Edge 构建 Wire 和 Face。以下是本次要构建的正方体的 Vertex、Edge、Face 编号，以方便您的理解。

注：图片中的箭头表示 edge 的方向。

构建正方体

构建 Vertex

std::vector<AMCAX::TopoShape> BuildBoxVertices()
{
    AMCAX::TopoBuilder builder;
    // Define the 8 corner points of a box
    std::vector<AMCAX::Point3> points;
    points.push_back(AMCAX::Point3(0.5, -0.5, -0.5));
    points.push_back(AMCAX::Point3(-0.5, -0.5, -0.5));
    points.push_back(AMCAX::Point3(-0.5, 0.5, -0.5));
    points.push_back(AMCAX::Point3(0.5, 0.5, -0.5));
    points.push_back(AMCAX::Point3(0.5, -0.5, 0.5));
    points.push_back(AMCAX::Point3(-0.5, -0.5, 0.5));
    points.push_back(AMCAX::Point3(-0.5, 0.5, 0.5));
    points.push_back(AMCAX::Point3(0.5, 0.5, 0.5));
 
    std::vector<AMCAX::TopoShape> vertices;
    for (const AMCAX::Point3& p : points)
    {
        AMCAX::TopoVertex v;
        builder.MakeVertex(v, p, AMCAX::Precision::Confusion());
        vertices.push_back(v);
    }
    return vertices;
}

构建 Edge

std::vector<AMCAX::TopoShape> BuildBoxEdges(const std::vector<AMCAX::TopoShape>& vertices)
{
    AMCAX::TopoBuilder builder;
    // Vertex index pairs defining all box edges
    std::vector<std::pair<int, int>> edgeVerticesID = { {0,1},{1,2},{2,3},{3,0},{4,5},{5,6},{6,7},{7,4},{0,4},{1,5},{2,6},{3,7} };
 
    std::vector<AMCAX::TopoShape> edges;
    for (const auto& [beginVID, endVID] : edgeVerticesID)
    {
        // Get oriented vertices (forward/reversed)
        AMCAX::TopoVertex v1 = AMCAX::TopoCast::Vertex(vertices[beginVID].Oriented(AMCAX::OrientationType::Forward));
        AMCAX::TopoVertex v2 = AMCAX::TopoCast::Vertex(vertices[endVID].Oriented(AMCAX::OrientationType::Reversed));
        // Create 3D curve
        AMCAX::Point3 p1 = AMCAX::TopoTool::Point(v1);
        AMCAX::Point3 p2 = AMCAX::TopoTool::Point(v2);
        AMCAX::Direction3 dir(p2.Coord() - p1.Coord());
        std::shared_ptr<AMCAX::Geom3Curve> gline = std::make_shared<AMCAX::Geom3Line>(p1, dir);
        // Build edge
        AMCAX::TopoEdge edge;
        builder.MakeEdge(edge, gline, AMCAX::Precision::Confusion());
        builder.Add(edge, v1);
        builder.UpdateVertex(v1, 0.0, edge, AMCAX::Precision::Confusion());
        builder.Add(edge, v2);
        builder.UpdateVertex(v2, p1.Distance(p2), edge, AMCAX::Precision::Confusion());
        edges.push_back(edge);
    }
    return edges;
}

在构建 edge 时需要注意：在给 edge 添加 vertex 时，需要提前设置 vertex 的 Orientation，因为 Edge 的起始 Vertex 是 Forward，终止 Vertex 是 Reversed。

构建 Wire

std::vector<AMCAX::TopoShape> BuildBoxWires(const std::vector<AMCAX::TopoShape>& edges)
{
    AMCAX::TopoBuilder builder;
    // Edge connectivity for each face wire: {edge index, orientation} pairs (true=forward, false=reversed)
    std::vector<std::vector<std::pair<int, bool>>> wireEdgesVec =
    {
            { {0,true},{1,true},{2,true},{3,true} },
            { {4,false},{7,false},{6,false},{5,false} },
            { {4,true},{9,false},{0,false},{8,true} },
            { {6,true},{11,false},{2,false},{10,true} },
            { {3,false},{11,true},{7,true},{8,false} },
            { {5,true},{10,false},{1,false},{9,true} }
    };
 
    std::vector<AMCAX::TopoShape> wires;
    for (const auto& wireEdges : wireEdgesVec)
    {
        AMCAX::TopoWire wire;
        builder.MakeWire(wire);
        for (const auto& [edgeID, isForward] : wireEdges)
        {
            // Add edge with proper orientation
            AMCAX::TopoEdge edge;
            AMCAX::TopoShape crshape = edges[edgeID];
            if (isForward)
            {
                edge = AMCAX::TopoCast::Edge(crshape.Oriented(AMCAX::OrientationType::Forward));
            }
            else
            {
                edge = AMCAX::TopoCast::Edge(crshape.Oriented(AMCAX::OrientationType::Reversed));
            }
            builder.Add(wire, edge);
        }
        // Ensure wire closure
        bool isClosedWire = AMCAX::TopoTool::IsClosed(wire);
        wire.Closed(isClosedWire);
        wires.push_back(wire);
    }
    return wires;
}

在构建 wire 时需要注意：所有 wire 必须遵循逆时针方向（CCW），观察视角应为面法向的反向（即从实体外部看向内部）。

构建 Face

std::vector<AMCAX::TopoShape> BuildBoxFaces(const std::vector<AMCAX::TopoShape>& wires)
{
    // Create reference frames for each face plane
    AMCAX::Direction3 x = AMCAX::CartesianCoordinateSystem::DX();
    AMCAX::Direction3 y = AMCAX::CartesianCoordinateSystem::DY();
    AMCAX::Direction3 z = AMCAX::CartesianCoordinateSystem::DZ();
    AMCAX::Frame3 frameBottom(AMCAX::Point3(0.0, 0.0, -0.5), -z, -x);
    AMCAX::Frame3 frameTop(AMCAX::Point3(0.0, 0.0, 0.5), z, x);
    AMCAX::Frame3 frameLeft(AMCAX::Point3(0.0, -0.5, 0.0), -y, -x);
    AMCAX::Frame3 frameRight(AMCAX::Point3(0.0, 0.5, 0.0), y, x);
    AMCAX::Frame3 frameFront(AMCAX::Point3(0.5, 0.0, 0.0), x, -z);
    AMCAX::Frame3 frameBack(AMCAX::Point3(-0.5, 0.0, 0.0), -x, z);
    std::vector<AMCAX::Frame3> planeFrames = { frameBottom,frameTop,frameLeft,frameRight,frameFront,frameBack };
    // Create 3D plane
    std::vector<std::shared_ptr<AMCAX::Geom3Plane>> planes;
    for (const AMCAX::Frame3& frame : planeFrames)
    {
        planes.push_back(std::make_shared<AMCAX::Geom3Plane>(frame));
    }
 
    AMCAX::TopoBuilder builder;
    std::vector<AMCAX::TopoShape> faces;
    for (int i = 0; i < static_cast<int>(wires.size()); i++)
    {
        //Make a face with a surface
        AMCAX::TopoFace face;
        builder.MakeFace(face, planes[i], AMCAX::Precision::Confusion());
        builder.Add(face, wires[i]);
        faces.push_back(face);
    }
    return faces;
}

构建 Shell

std::vector<AMCAX::TopoShape> vertices = BuildBoxVertices();
std::vector<AMCAX::TopoShape> edges = BuildBoxEdges(vertices);
std::vector<AMCAX::TopoShape> wires = BuildBoxWires(edges);
std::vector<AMCAX::TopoShape> faces = BuildBoxFaces(wires);
//Make a shell and add all faces in the shell
AMCAX::TopoShell shell;
AMCAX::TopoBuilder builder;
builder.MakeShell(shell);
for (const auto& face : faces)
{
    builder.Add(shell, face);
}