OpenCASCADE Chamfer 2D

二维的倒角Chamfer功能可以将两个不平行的曲线进行倒角。如下图所示为QCAD中进行倒角的效果图：选择要倒角的两个边，及设置两个边上的倒角距离。

在OpenCASCADE中也提供了这个二维曲线倒角功能，使用Tcl脚本在DRAW中显示如下：

polyline p 0 0 0 10 0 0 10 10 0

chamfer2d r p 3 5

vdisplay r

在源文件BRepTest_Fillet2DCommands.cxx中找到命令chamfer2d的实现：

//=======================================================================
//function : chamfer2d
//purpose : Chamfer 2d.
//usage : chamfer2d result wire (or edge1 edge2) length1 length2
//=======================================================================
static Standard_Integer chamfer2d(Draw_Interpretor& di, Standard_Integer n, const char** a)
{
if (n != 5 && n != 6)
{
di << \"Usage : chamfer2d result wire (or edge1 edge2) length1 length2\";
return 1;
}
TopoDS_Shape W;
TopoDS_Shape E1, E2;
if (n == 6)
{
// Get the edges.
E1 = DBRep::Get(a[2], TopAbs_EDGE, Standard_True);
E2 = DBRep::Get(a[3], TopAbs_EDGE, Standard_True);
}
else
{
W = DBRep::Get(a[2], TopAbs_WIRE, Standard_True);
}
// Get the lengths.
const Standard_Real length1 = (n == 6) ? Atof(a[4]) : Atof(a[3]);
const Standard_Real length2 = (n == 6) ? Atof(a[5]) : Atof(a[4]);
// Algo.
 ChFi2d_ChamferAPI algo;
if (n == 6)
{
const TopoDS_Edge& e1 = TopoDS::Edge(E1);
const TopoDS_Edge& e2 = TopoDS::Edge(E2);
algo.Init(e1, e2);
}
else
{
const TopoDS_Wire& w = TopoDS::Wire(W);
algo.Init(w);
}
// Prepare the chamfer.
 algo.Perform();
// Get the result.
TopoDS_Edge M1, M2; // modified E1 and E2
TopoDS_Edge chamfer = algo.Result(M1, M2, length1, length2);
if (chamfer.IsNull())
{
di << \"Error: the algrithm produced no result.\";
return 1;
}
if (n == 6)
{
// Set result for DRAW.
DBRep::Set(a[1], chamfer);
// Update neighbour edges in DRAW.
DBRep::Set(a[2], M1);
DBRep::Set(a[3], M2);
}
else // recreate the wire using the chamfer
 {
BRepBuilderAPI_MakeWire mkWire(M1, chamfer, M2);
if (mkWire.IsDone())
DBRep::Set(a[1], mkWire.Wire());
else
DBRep::Set(a[1], chamfer);
}
return 0;
}

从上述源码可以看出，二维曲线倒角功能主要是由类ChFi2d_ChamferAPI实现。OpenCASCADE中的算法类的大致套路就是：

l Init()：初始化：数据输入。给定几种条件的初始化函数，对应几种情况的数据输入。

l Perform()：执行计算。根据输入数据，计算出结果；

l Result()/Get()：得到计算结果。

二维曲线的倒角功能是相对简单的功能，所以找到类ChFi2d_ChamferAPI中源码看看实现过程：

// Constructs a chamfer edge.
// Returns true if the edge is constructed.
Standard_Boolean ChFi2d_ChamferAPI::Perform()
{
myCurve1 = BRep_Tool::Curve(myEdge1, myStart1, myEnd1);
myCurve2 = BRep_Tool::Curve(myEdge2, myStart2, myEnd2);
// searching for common points
if (myCurve1->Value(myStart1).IsEqual(myCurve2->Value(myEnd2), Precision::Confusion()))
{
myCommonStart1 = true;
myCommonStart2 = false;
}
else
{
if (myCurve1->Value(myEnd1).IsEqual(myCurve2->Value(myStart2), Precision::Confusion()))
{
myCommonStart1 = false;
myCommonStart2 = true;
}
else
{
if (myCurve1->Value(myEnd1).IsEqual(myCurve2->Value(myEnd2), Precision::Confusion()))
{
myCommonStart1 = false;
myCommonStart2 = false;
}
else
{
myCommonStart1 = true;
myCommonStart2 = true;
}
}
}
return Standard_True;
}

执行计算函数Perform中，根据边EDGE中的曲线数据，判断两个曲线的端点处是不是相连接的，并记录下连接状态：是首首连接、首尾连接等。这里面判断两个点是不是相等使用的gp_Pnt的IsEqual()函数，这个是根据两个点之间的距离来判断的，需要计算出两个点之间的距离。这里可以使用距离的平方来判断SquareDistance来判断两个点是不是相等，可以提高性能。因为计算距离需要要开方，开方比较耗时。关于开方的数值算法，还有个传奇故事：一个Sqrt函数引发的血案 https://www.cnblogs.com/pkuoliver/archive/2010/10/06/sotry-about-sqrt.html

// Returns the result (chamfer edge, modified edge1, modified edge2).
TopoDS_Edge ChFi2d_ChamferAPI::Result(TopoDS_Edge& theEdge1, TopoDS_Edge& theEdge2,
const Standard_Real theLength1, const Standard_Real theLength2)
{
TopoDS_Edge aResult;
if (Abs(myEnd1 - myStart1) < theLength1)
return aResult;
if (Abs(myEnd2 - myStart2) < theLength2)
return aResult;
Standard_Real aCommon1 = (myCommonStart1?myStart1:myEnd1) + (((myStart1 > myEnd1)^myCommonStart1)?theLength1:-theLength1);
Standard_Real aCommon2 = (myCommonStart2?myStart2:myEnd2) + (((myStart2 > myEnd2)^myCommonStart2)?theLength2:-theLength2);
// make chamfer edge
GC_MakeLine aML(myCurve1->Value(aCommon1), myCurve2->Value(aCommon2));
BRepBuilderAPI_MakeEdge aBuilder(aML.Value(), myCurve1->Value(aCommon1), myCurve2->Value(aCommon2));
aResult = aBuilder.Edge();
// divide first edge
BRepBuilderAPI_MakeEdge aDivider1(myCurve1, aCommon1, (myCommonStart1?myEnd1:myStart1));
theEdge1 = aDivider1.Edge();
// divide second edge
BRepBuilderAPI_MakeEdge aDivider2(myCurve2, aCommon2, (myCommonStart2?myEnd2:myStart2));
theEdge2 = aDivider2.Edge();
return aResult;
}