A Solid Modeling Sample

Overview

This tutorial provides the basic usage of AMCAX kernel to model a valve model.

Required Knowledge

The developers need to have some basic knowledge including the modern C++ programming language, 3D geometric modeling concepts, and the B-Rep topology structure. In specific, the AMCAX kernel is designed by using C++ 17 standard, and STL containers and algorithms are used as basic data structures and utilities. The geometric entities are represented by a Boundary-Representation (B-Rep) structure, including geometry objects and topology structures.

Model Preview

This tutorial uses a simplified valve model to show some of main modeling functionalities in the AMCAX kernel. The model is shown in the figure below:

The valve model.

The model consists of three sub-parts:

1. The fixing structure at the inlet/outlet.
2. The curved pipes for the passage of liquids.
3. The block where a piston can be used to control the valve.

We will introduce the constructions step-by-step, and provide explanations in as much detail as possible.

Building the Hexagon Prism

Let's start with the inlet/outlet of the valve. A rounded-corner hexagon prism is created to represent the fixing structure.

Creating a Polygon

The first step is create a hexagon using the AMCAX::MakePolygon class. The resulting face can be constructed by using the AMCAX::MakeFace class.

AMCAX::Point3 p1(-80.0, 0.0, 56.0);
AMCAX::MakePolygon makePolygon;
int n = 6;
for (int i = 0; i < n; ++i)
{
    double t = M_PI * 2.0 * i / n;
    makePolygon.Add(p1.Translated(AMCAX::Vector3(0.0, std::cos(t), std::sin(t)) * 50.0));
}
makePolygon.Close();
AMCAX::TopoWire w = makePolygon;
AMCAX::TopoFace f = AMCAX::MakeFace(w, true);

Click here example1 to get the complete source code for the above example, which you can download according to your learning needs.

Applying 2D Fillets

To construct a round-corner hexagon, we apply a 2D fillet to each vertex of the hexagon by using the AMCAX::MakeFillet2d class.

AMCAX::MakeFillet2d makeFillet2d(f);
AMCAX::IndexSet<AMCAX::TopoShape> vertices;
AMCAX::TopoExplorerTool::MapShapes(f, AMCAX::ShapeType::Vertex, vertices);
for (int i = 0; i < vertices.size(); ++i)
{
    makeFillet2d.AddFillet(AMCAX::TopoCast::Vertex(vertices[i]), 5.0);
}
AMCAX::TopoShape face2 = makeFillet2d.Shape();

In the above sample code, the AMCAX::IndexSet class is essentially an unordered set whose elements have their own indices. The AMCAX::TopoExplorerTool::MapShapes function will find all the vertices in the shape. Click here example2 to get the complete source code for the above example, which you can download according to your learning needs.

Extruding a Prism

Next, we extrude the hexagon to create a prism by using the AMCAX::MakePrism class.

AMCAX::TopoShape hexagonPrism = AMCAX::MakePrism(face2, AMCAX::Vector3(14.0, 0.0, 0.0));

Click here example3 to get the complete source code for the above example, which you can download according to your learning needs.

Applying 3D Chamfers

Then, we apply 3D chamfers by using AMCAX::MakeChamfer class.

AMCAX::MakeChamfer makeChamfer(hexagonPrism);
for (AMCAX::TopoExplorer ex(hexagonPrism, AMCAX::ShapeType::Edge); ex.More(); ex.Next())
{
    const AMCAX::TopoEdge& edge = AMCAX::TopoCast::Edge(ex.Current());
    AMCAX::TopoVertex vFirst, vLast;
    AMCAX::TopoExplorerTool::Vertices(edge, vFirst, vLast);
    AMCAX::Point3 pFirst = AMCAX::TopoTool::Point(vFirst);
    AMCAX::Point3 pLast = AMCAX::TopoTool::Point(vLast);
    if (std::fabs(pFirst[0] - pLast[0]) < AMCAX::Precision::Confusion())
    {
        makeChamfer.Add(0.5, edge);
    }
}
AMCAX::TopoShape hex = makeChamfer.Shape();

Here, the AMCAX::TopoExplorer class is used to traverse all the edges in the shape. And if an edge has two vertices sharing the same x coordinate, then we chamfer along the edge. Click here example4 to get the complete source code for the above example, which you can download according to your learning needs.

Building the Curved Pipe

Next, we create a curved pipe for inlet/outlet. The process seems a little bit complicated, but the main sub-steps are quite simple. The pipe is created by using the AMCAX::MakePipe class. This class requires a spine wire representing the sweeping path and a profile shape to be used to sweep.

Construct a Spine Wire

The spine wire is a 'S' type path, consisting of five curves: line – arc – line – arc – line. All the curves are G1 connected. This means that the middle line is tangent to both the arcs. Here, we first create 2D circles using the AMCAX::MakeGeom2Circle class, and then use the AMCAX::GccLine2Tangent class to find the line tangent to two circles.

AMCAX::Point2 center1(-26.3, 58.5);
AMCAX::Point2 center2(-63.8, 76.0);
std::shared_ptr<AMCAX::Geom2Circle> circle2d1 = AMCAX::MakeGeom2Circle(AMCAX::Axis2(center1, AMCAX::CartesianCoordinateSystem::DY2()), 20.0);
std::shared_ptr<AMCAX::Geom2Circle> circle2d2 = AMCAX::MakeGeom2Circle(AMCAX::Axis2(center2, -AMCAX::CartesianCoordinateSystem::DY2()), 20.0);
AMCAX::GccLine2Tangent gcc(AMCAX::GccEntity::Enclosing(AMCAX::AdaptorGeom2Curve(circle2d1)), AMCAX::GccEntity::Outside(AMCAX::AdaptorGeom2Curve(circle2d2)), 0.0);
if (!gcc.IsDone() || gcc.NSolutions() != 1)
{
    throw AMCAX::ConstructionError();
}
double parSol1, parArg1, parSol2, parArg2;
AMCAX::Point2 pointSol1, pointSol2;
gcc.Tangency1(0, parSol1, parArg1, pointSol1);
gcc.Tangency2(0, parSol2, parArg2, pointSol2);
AMCAX::Line2 tangentLine = gcc.Solution(0);

Then, we map the curves from 2D to 3D and build the five edges and the the spine wire. Here, the AMCAX::MakeArcOfCircle class is used to create arcs, the AMCAX::MakeSegment class is used to create line segments, the AMCAX::MakeEdge class is used to create edges from curves, and the AMCAX::MakeWire class is used to create the spine wire from edges.

AMCAX::Frame3 localframe(AMCAX::CartesianCoordinateSystem::Origin(), -AMCAX::CartesianCoordinateSystem::DY(), AMCAX::CartesianCoordinateSystem::DX());
std::shared_ptr<AMCAX::Geom3Curve> c13d = AMCAX::GeometryTool::To3d(localframe, circle2d1);
std::shared_ptr<AMCAX::Geom3Curve> c23d = AMCAX::GeometryTool::To3d(localframe, circle2d2);
AMCAX::Line3 line = AMCAX::CurveCalculation::To3d(localframe, tangentLine);
std::shared_ptr<AMCAX::Geom3TrimmedCurve> arc1 = AMCAX::MakeArcOfCircle(std::static_pointer_cast<AMCAX::Geom3Circle>(c13d)->Circle(), 0.0, parArg1, true);
std::shared_ptr<AMCAX::Geom3TrimmedCurve> arc2 = AMCAX::MakeArcOfCircle(std::static_pointer_cast<AMCAX::Geom3Circle>(c23d)->Circle(), 0.0, parArg2, true);
std::shared_ptr<AMCAX::Geom3TrimmedCurve> seg0 = AMCAX::MakeSegment(arc1->Value(0.0), arc1->Value(0.0).Translated(AMCAX::Vector3(26.3, 0.0, 0.0)));
std::shared_ptr<AMCAX::Geom3TrimmedCurve> seg1 = AMCAX::MakeSegment(line, parSol1, parSol2);
std::shared_ptr<AMCAX::Geom3TrimmedCurve> seg2 = AMCAX::MakeSegment(arc2->Value(0.0), arc2->Value(0.0).Translated(AMCAX::Vector3(-16.2, 0.0, 0.0)));
AMCAX::TopoEdge e0 = AMCAX::MakeEdge(seg0);
AMCAX::TopoEdge e1 = AMCAX::MakeEdge(arc1);
AMCAX::TopoEdge e2 = AMCAX::MakeEdge(seg1);
AMCAX::TopoEdge e3 = AMCAX::MakeEdge(arc2);
AMCAX::TopoEdge e4 = AMCAX::MakeEdge(seg2);
AMCAX::MakeWire makewire;
makewire.Add({e0, e1, e2, e3, e4});
AMCAX::TopoWire spine = makewire.Wire();

Creating Profile Wires

The profile is a simple circle and is created by using the AMCAX::MakeGeom3Circle class.

AMCAX::MakeGeom3Circle makecircle(AMCAX::Point3(-26.3, 0.0, 78.5), AMCAX::Direction3(1.0, 0.0, 0.0), 10.0);
AMCAX::MakeEdge makeedge(makecircle.Value());
AMCAX::TopoWire profile1 = AMCAX::MakeWire(makeedge.Edge());

Creating 2D Offset Wire

Since the pipe is tunnel which has an inner face and an outer face, we create an offset shape for the profile of the outer face. The shape is copied by the AMCAX::CopyShape class, and then use the AMCAX::MakeOffset class to create a 2D offset wire.

AMCAX::TopoWire profile2 = AMCAX::TopoCast::Wire(AMCAX::CopyShape(profile1));
AMCAX::MakeOffset offset(profile2);
offset.Perform(6.0);
if (offset.IsDone())
{
    profile2 = AMCAX::TopoCast::Wire(offset.Shape());
}

Creating Pipes

Next, we use the AMCAX::MakePipe class to create sweeping solids by using a face, generated by the AMCAX::MakeFace class, as the profile shape. We will compute a boolean cut of these two solid at the next step.

AMCAX::TopoShape pipe1 = AMCAX::MakePipe(spine, AMCAX::MakeFace(profile1));
AMCAX::TopoShape pipe2 = AMCAX::MakePipe(spine, AMCAX::MakeFace(profile2));

Click here example5 to obtain the complete source code for curved track pipe1, which you can download according to your learning needs. Click here example6 to obtain the complete source code for curved track pipe2, which you can download according to your learning needs.

Building the Valve

Finally, we build the central part of the valve, which is simplified to a cylinder where a piston can be used to control the valve.

Creating a Cylinder

A cylinder is created by using the AMCAX::MakeCylinder class.

AMCAX::TopoShape middleCylinder = AMCAX::MakeCylinder(AMCAX::Frame3(AMCAX::Point3(0.0, 0.0, 0.0), AMCAX::CartesianCoordinateSystem::DZ()), 31.0, 114.0);

Click here example7 to get the complete source code for the above example, which you can download according to your learning needs.

Applying 3D Fillets

Here, we additionally add a small 3D fillet example to the middle cylinder by using the AMCAX::MakeFillet class as follows:

AMCAX::MakeFillet fillet(middleCylinder);
for (AMCAX::TopoExplorer ex(middleCylinder, AMCAX::ShapeType::Edge); ex.More(); ex.Next())
{
    const auto& edge = AMCAX::TopoCast::Edge(ex.Current());
    if (AMCAX::TopoTool::IsClosed(edge))
    {
        fillet.Add(1.0, edge);
    }
}
middleCylinder = fillet.Shape();

Click here example8 to get the complete source code for the above example, which you can download according to your learning needs.

Mirroring the Curved Pipe

As the valve should have both the inlet and the outlet, we have to mirror the pipe by using the AMCAX::TransformShape class.

AMCAX::Transformation3 tr;
tr.SetMirror(AMCAX::Axis3(AMCAX::Point3(0.0, 0.0, 56.0), AMCAX::CartesianCoordinateSystem::DY()));
AMCAX::TopoShape pipe3 = AMCAX::TransformShape(pipe1, tr, true);
AMCAX::TopoShape pipe4 = AMCAX::TransformShape(pipe2, tr, true);
AMCAX::TopoShape hex2 = AMCAX::TransformShape(hex, tr, true);

Click here example9 to obtain the mirror curved track pipe1, the complete source code to construct pipe3, you can download according to your learning needs. Click here example10 to obtain the mirror curved track pipe2, to construct the complete source code of pipe4, you can download according to your learning needs. Click here example11 to obtain the mirror hex, construct hex2 complete source code, you can download according to your learning needs.

Boolean Operations

The final step is boolean all the parts together by using the AMCAX::BoolBRepFuse class and the AMCAX::BoolBRepCut class. Here shows the sample code:

AMCAX::TopoShape result = AMCAX::BoolBRepFuse(middleCylinder, pipe2);
result = AMCAX::BoolBRepFuse(result, pipe4);
result = AMCAX::BoolBRepFuse(result, hex);
result = AMCAX::BoolBRepFuse(result, hex2);
result = AMCAX::BoolBRepCut(result, pipe1);
result = AMCAX::BoolBRepCut(result, pipe3);

Don't forget to construct a tunnel for pistons to contol the valve, although the construction is simplified to be a cylinder.

AMCAX::TopoShape hole = AMCAX::MakeCylinder(AMCAX::Frame3(AMCAX::Point3(0.0, 0.0, 0.0), AMCAX::CartesianCoordinateSystem::DZ()), 25.0, 114.0);
result = AMCAX::BoolBRepCut(result, hole);

Meshing

After generated a shape, you may want to render the shape by modern rendering engines like OpenGL. Thus, we also provide a simple meshing tool to generate meshes for shapes.

Building Meshes

The AMCAX::BRepMeshIncrementalMesh class is often used to generate a mesh for each face in the shape. The edges have a polygon on mesh in each adjacent face, but the meshes only coincide at the boundary edges and are not topological connected. You can also use AMCAX::MakeShapeTool::EnsureNormalConsistency() to compute normals for vertices in the mesh. The sample code is as follows:

AMCAX::BRepMeshIncrementalMesh mesher(result, 0.005, true);
if (mesher.IsDone())
{
    AMCAX::MakeShapeTool::EnsureNormalConsistency(result);
}

Exporting to a STL file

We provide tools for exporting meshes to STL files and OBJ files. Here is an example of exporting to a STL file.

AMCAX::STLTool::WriteShape(result, "partSample.stl");

Click here example12 to obtain the full source code of the entity modeling example, you can download it according to your needs.

Appendix

The complete code of this sample is listed here:

void MakeValve()
{
    // Make a polygon
    AMCAX::Point3 p1(-80.0, 0.0, 56.0);
    AMCAX::MakePolygon makePolygon;
    int n = 6;
    for (int i = 0; i < n; ++i)
    {
        double t = M_PI * 2.0 * i / n;
        makePolygon.Add(p1.Translated(AMCAX::Vector3(0.0, std::cos(t), std::sin(t)) * 50.0));
    }
    makePolygon.Close();
    AMCAX::TopoWire w = makePolygon;
    AMCAX::TopoFace f = AMCAX::MakeFace(w, true);
 
    // 2D fillet
    AMCAX::MakeFillet2d makeFillet2d(f);
    AMCAX::IndexSet<AMCAX::TopoShape> vertices;
    AMCAX::TopoExplorerTool::MapShapes(f, AMCAX::ShapeType::Vertex, vertices);
    for (int i = 0; i < vertices.size(); ++i)
    {
        makeFillet2d.AddFillet(AMCAX::TopoCast::Vertex(vertices[i]), 5.0);
    }
    AMCAX::TopoShape face2 = makeFillet2d.Shape();
 
    // Extrusion
    AMCAX::TopoShape hexagonPrism = AMCAX::MakePrism(face2, AMCAX::Vector3(14.0, 0.0, 0.0));
 
    // 3D Chamfer
    AMCAX::MakeChamfer makeChamfer(hexagonPrism);
    for (AMCAX::TopoExplorer ex(hexagonPrism, AMCAX::ShapeType::Edge); ex.More(); ex.Next())
    {
        const AMCAX::TopoEdge& edge = AMCAX::TopoCast::Edge(ex.Current());
        AMCAX::TopoVertex vFirst, vLast;
        AMCAX::TopoExplorerTool::Vertices(edge, vFirst, vLast);
        AMCAX::Point3 pFirst = AMCAX::TopoTool::Point(vFirst);
        AMCAX::Point3 pLast = AMCAX::TopoTool::Point(vLast);
        if (std::fabs(pFirst[0] - pLast[0]) < AMCAX::Precision::Confusion())
        {
            makeChamfer.Add(0.5, edge);
        }
    }
    AMCAX::TopoShape hex = makeChamfer.Shape();
 
    // Spine of pipe
    AMCAX::Point2 center1(-26.3, 58.5);
    AMCAX::Point2 center2(-63.8, 76.0);
    std::shared_ptr<AMCAX::Geom2Circle> circle2d1 = AMCAX::MakeGeom2Circle(AMCAX::Axis2(center1, AMCAX::CartesianCoordinateSystem::DY2()), 20.0);
    std::shared_ptr<AMCAX::Geom2Circle> circle2d2 = AMCAX::MakeGeom2Circle(AMCAX::Axis2(center2, -AMCAX::CartesianCoordinateSystem::DY2()), 20.0);
    AMCAX::GccLine2Tangent gcc(AMCAX::GccEntity::Enclosing(AMCAX::AdaptorGeom2Curve(circle2d1)), AMCAX::GccEntity::Outside(AMCAX::AdaptorGeom2Curve(circle2d2)), 0.0);
    if (!gcc.IsDone() || gcc.NSolutions() != 1)
    {
        throw AMCAX::ConstructionError();
    }
    double parSol1, parArg1, parSol2, parArg2;
    AMCAX::Point2 pointSol1, pointSol2;
    gcc.Tangency1(0, parSol1, parArg1, pointSol1);
    gcc.Tangency2(0, parSol2, parArg2, pointSol2);
    AMCAX::Line2 tangentLine = gcc.Solution(0);
 
    AMCAX::Frame3 localframe(AMCAX::CartesianCoordinateSystem::Origin(), -AMCAX::CartesianCoordinateSystem::DY(), AMCAX::CartesianCoordinateSystem::DX());
    std::shared_ptr<AMCAX::Geom3Curve> c13d = AMCAX::GeometryTool::To3d(localframe, circle2d1);
    std::shared_ptr<AMCAX::Geom3Curve> c23d = AMCAX::GeometryTool::To3d(localframe, circle2d2);
    AMCAX::Line3 line = AMCAX::CurveCalculation::To3d(localframe, tangentLine);
    std::shared_ptr<AMCAX::Geom3TrimmedCurve> arc1 = AMCAX::MakeArcOfCircle(std::static_pointer_cast<AMCAX::Geom3Circle>(c13d)->Circle(), 0.0, parArg1, true);
    std::shared_ptr<AMCAX::Geom3TrimmedCurve> arc2 = AMCAX::MakeArcOfCircle(std::static_pointer_cast<AMCAX::Geom3Circle>(c23d)->Circle(), 0.0, parArg2, true);
    std::shared_ptr<AMCAX::Geom3TrimmedCurve> seg0 = AMCAX::MakeSegment(arc1->Value(0.0), arc1->Value(0.0).Translated(AMCAX::Vector3(26.3, 0.0, 0.0)));
    std::shared_ptr<AMCAX::Geom3TrimmedCurve> seg1 = AMCAX::MakeSegment(line, parSol1, parSol2);
    std::shared_ptr<AMCAX::Geom3TrimmedCurve> seg2 = AMCAX::MakeSegment(arc2->Value(0.0), arc2->Value(0.0).Translated(AMCAX::Vector3(-16.2, 0.0, 0.0)));
    AMCAX::TopoEdge e0 = AMCAX::MakeEdge(seg0);
    AMCAX::TopoEdge e1 = AMCAX::MakeEdge(arc1);
    AMCAX::TopoEdge e2 = AMCAX::MakeEdge(seg1);
    AMCAX::TopoEdge e3 = AMCAX::MakeEdge(arc2);
    AMCAX::TopoEdge e4 = AMCAX::MakeEdge(seg2);
    AMCAX::MakeWire makewire;
    makewire.Add({e0, e1, e2, e3, e4});
    AMCAX::TopoWire spine = makewire.Wire();
 
    // Profile of pipe
    AMCAX::MakeGeom3Circle makecircle(AMCAX::Point3(-26.3, 0.0, 78.5), AMCAX::Direction3(1.0, 0.0, 0.0), 10.0);
    AMCAX::MakeEdge makeedge(makecircle.Value());
    AMCAX::TopoWire profile1 = AMCAX::MakeWire(makeedge.Edge());
    AMCAX::TopoWire profile2 = AMCAX::TopoCast::Wire(AMCAX::CopyShape(profile1));
 
    // Make 2D offset
    AMCAX::MakeOffset offset(profile2);
    offset.Perform(6.0);
    if (offset.IsDone())
    {
        profile2 = AMCAX::TopoCast::Wire(offset.Shape());
    }
 
    // Make pipe
    AMCAX::TopoShape pipe1 = AMCAX::MakePipe(spine, AMCAX::MakeFace(profile1));
    AMCAX::TopoShape pipe2 = AMCAX::MakePipe(spine, AMCAX::MakeFace(profile2));
 
    // Make a cylinder
    AMCAX::TopoShape middleCylinder = AMCAX::MakeCylinder(AMCAX::Frame3(AMCAX::Point3(0.0, 0.0, 0.0), AMCAX::CartesianCoordinateSystem::DZ()), 31.0, 114.0);
 
    // 3D fillet
    AMCAX::MakeFillet fillet(middleCylinder);
    for (AMCAX::TopoExplorer ex(middleCylinder, AMCAX::ShapeType::Edge); ex.More(); ex.Next())
    {
        const auto& edge = AMCAX::TopoCast::Edge(ex.Current());
        if (AMCAX::TopoTool::IsClosed(edge))
        {
            fillet.Add(1.0, edge);
        }
    }
    middleCylinder = fillet.Shape();
 
    // Mirror tranformation
    AMCAX::Transformation3 tr;
    tr.SetMirror(AMCAX::Axis3(AMCAX::Point3(0.0, 0.0, 56.0), AMCAX::CartesianCoordinateSystem::DY()));
    AMCAX::TopoShape pipe3 = AMCAX::TransformShape(pipe1, tr, true);
    AMCAX::TopoShape pipe4 = AMCAX::TransformShape(pipe2, tr, true);
    AMCAX::TopoShape hex2 = AMCAX::TransformShape(hex, tr, true);
 
    // Boolean
    AMCAX::TopoShape result = AMCAX::BoolBRepFuse(middleCylinder, pipe2);
    result = AMCAX::BoolBRepFuse(result, pipe4);
    result = AMCAX::BoolBRepFuse(result, hex);
    result = AMCAX::BoolBRepFuse(result, hex2);
    result = AMCAX::BoolBRepCut(result, pipe1);
    result = AMCAX::BoolBRepCut(result, pipe3);
 
    // Make a hole
    AMCAX::TopoShape hole = AMCAX::MakeCylinder(AMCAX::Frame3(AMCAX::Point3(0.0, 0.0, 0.0), AMCAX::CartesianCoordinateSystem::DZ()), 25.0, 114.0);
    result = AMCAX::BoolBRepCut(result, hole);
 
    // Meshing
    AMCAX::BRepMeshIncrementalMesh mesher(result, 0.005, true);
    if (mesher.IsDone())
    {
        AMCAX::MakeShapeTool::EnsureNormalConsistency(result);
    }
 
    // Export to a STL file
    AMCAX::STLTool::WriteShape(result, "partSample.stl");
}