Defines an edge. More...

## Public Member Functions

ModelData_Edge (const ModelData_Vertex &theStartVertex, const ModelData_Vertex &theEndVertex)
Constructor. More...

void SetCurve (const ModelData_Curve &theCurve, double theFirstParameter, double theLastParameter)
Specifies 3D curve of the edge. More...

bool SetCurve (const ModelData_Curve &theCurve)
Specifies 3D curve of the edge. More...

void SetPCurve (const ModelData_Curve2d &thePCurve, const ModelData_Face &theFace, double theFirstParameter, double theLastParameter)
Specifies p-curve of the edge on the specified face. More...

bool SetPCurve (const ModelData_Curve2d &thePCurve, const ModelData_Face &theFace)
Specifies p-curve of the edge on the specified face. More...

void SetPCurve (const ModelData_Curve2d &thePCurveForward, const ModelData_Curve2d &thePCurveReversed, const ModelData_Face &theFace, double theFirstParameter, double theLastParameter)
Specifies p-curves of the seam-edge on the specified face. More...

bool SetPCurve (const ModelData_Curve2d &thePCurveForward, const ModelData_Curve2d &thePCurveReversed, const ModelData_Face &theFace)
Specifies p-curves of the seam-edge on the specified face. More...

ModelData_Vertex StartVertex () const
Returns a start vertex. More...

ModelData_Vertex EndVertex () const
Returns a start vertex. More...

ModelData_Curve Curve (double &theFirstParameter, double &theLastParameter) const
Returns edge 3D curve and its limits. More...

ModelData_Curve2d PCurve (const ModelData_Face &theFace, double &theFirstParameter, double &theLastParameter) const
Returns edge p-curve on a face and its limits. More...

void SetTolerance (double theTolerance)
Sets edge tolerance. More...

double Tolerance () const
Returns edge tolerance. More...

bool IsDegenerated () const
Returns true if the edge is degenerated. More...

bool IsSeam (const ModelData_Face &theFace) const
Returns true if the edge is a seam-edge. More...

Public Member Functions inherited from cadex::ModelData_Shape
ModelData_Shape ()
Constructor.

ModelData_Shape (const ModelData_Shape &theOther)
Constructor.

ModelData_Shape (ModelData_Shape &&theOther)
Move constructor.

~ModelData_Shape ()
Destructor.

ModelData_Shapeoperator= (const ModelData_Shape &theOther)
Assignment operator.

ModelData_Shapeoperator= (ModelData_Shape &&theOther)
Move assignment operator.

operator const TopoDS_Shape & () const
Casts this object to TopoDS_Shape. More...

ModelData_ShapeType Type () const
Returns a shape type. More...

ModelData_ShapeOrientation Orientation () const
Returns orientation flag. More...

ModelData_Shape Reversed () const
Returns a shape that shares the same geometry and subshape graph but has opposite orientation. More...

ModelData_Shape Oriented (ModelData_ShapeOrientation theOrientation) const
Returns a shape that shares the same geometry and subshape graph and has specified orientation. More...

void Nullify ()
Nullifies the object. More...

bool IsNull () const
Returns true if the object has not been initialized yet.

operator bool () const
Returns true if the object is not null. More...

bool IsEqual (const ModelData_Shape &theOther) const
Returns true if the shape shares the same geometry and subshape graph, and has equal orientation. More...

bool IsSame (const ModelData_Shape &theOther) const
Returns true if the shape shares the same geometry and subshape graph. More...

internal::ModelData_ShapeImpl * Impl () const
Returns internal implementation object.

## Static Public Member Functions

static const ModelData_EdgeCast (const ModelData_Shape &theShape)
Casts a base class object to ModelData_Edge. More...

static ModelData_EdgeCast (ModelData_Shape &theShape)
Casts a base class object to ModelData_Edge. More...

Protected Member Functions inherited from cadex::ModelData_Shape
ModelData_Shape (const TopoDS_Shape &theOther, bool)
Constructor.

ModelData_Shape (internal::ModelData_ShapeImpl *theImpl)
Constructor.

internal::Base_Handle myImpl
Internal implementation object.

## Detailed Description

Defines an edge.

The following image depicts an example of an edge:

Edge

An edge resides on a curve (returned by Curve()) and is bounded by two vertices returned by StartVertex() and EndVertex(). StartVertex() corresponds to smaller parameter along the curve and EndVertex() - to greater parameter (regardless of own edge orientation). Vertices must always be explicitly defined.

If an edge has forward Orientation() then it is considered to align with its underlying curve. If Orientation() is reversed, then the edge is considered to have an opposite orientation comparing to its underlying curve.

If an edge is owned by a face (via its wire) then this edge must also have a p-curve (parametric curve) defined in a parametric domain of the face surface. If an edge is shared by two faces in a shell then it must have pcurve on each parent face. P-curves are oriented in the same direction as 3D curve.

# Curve Representations

Each curve representation (3D curve and p-curves) has explicit parametric range $$[t_{min}, t_{max}]$$, where $$t_{min}$$ is a curve parameter corresponding to start vertex and $$t_{max}$$ corresponding to end vertex. These points on the curve must be within vertex tolerances, i.e.:

• $$\|\mathbf{C}(t_{min}) - \mathbf{P}_{start}\| \leq \mathrm{tolerance}_{start}$$
• $$\|\mathbf{C}(t_{max}) - \mathbf{P}_{end}\| \leq \mathrm{tolerance}_{end}$$

The $$t_{min}$$ parameter must always be smaller than $$t_{max}$$. If the curve is not periodic then both parameters must be within the curve's definition range. If the curve is periodic then $$t_{min}$$ should be within the curve's definition range. For instance, a closed edge lying on a circle (which has a definition range $$[0, 2\pi]$$) may have a range $$[0.5\pi, 2.5\pi]$$.

When importing models from external files or creating from scratch CAD Exchanger also tries to ensure two more strict requirements:

• "same range": all curve representations (3D curve and all p-curves) have the same definition parametric range (e.g. $$[a, b]$$);
• "same parameter": for any parameter t from range $$[a, b]$$ a 3D point computed from 3D curve must be within an edge tolerance from a 3D point computed from p-curve and corresponding surface, i.e. $$\|\mathbf{C}(t) - \mathbf{S}(p(t))\| \leq \mathrm{tolerance}$$.

# Special Types of Edges

## Degenerated Edge

An edge is called degenerated if it corresponds to a degenerated curve, e.g. a sphere pole, a cone apex or a B-Spline singularity point. In this case it does not have a 3D curve and only has a pcurve. For instance in the case of a sphere 'north' pole the pcurve is V-isoline $$V=\frac{\pi}{2}$$.

IsDegenerated() returns true for a degenerated edge, and Curve() returns a null curve.

## Seam-edge

An edge is called seam-edge if it corresponds to a curve on a periodical suface that has two pcurve representations in the surface parametric domain. Examples include a curve corresponding to U-isolines of a cylindrical surface with $$U=0$$ and $$U=2\pi$$.

Although, such seam-edges typically have pcurves corresponding to surface boundary iso-lines (e.g. one corresponding to surface $$U_{min}$$ and another to $$U_{max}$$), this is not always the case. Some seam-edges may have pcurves corresponding to arbitrary pairs of isolines shifted by surface period (e.g. one is $$V^*$$ and another $$V^* + V_{period}$$). Some seam-edges may have even a pair of free-form pcurves, one shifted by surface period from another. This often happens when importing a file generated by CAD systems/kernels which do not explicitly support seam-edges.

A seam edge occured twice in its parent wire - with forward and reversed orientations. Edge orientation defines which pcurve will be returned by PCurve(). IsSeam() returns true for the seam-edge.

# Tolerance

The edge tolerance (returned by Tolerance()) defines a radius of a pipe around edge's 3D curve, in which all p-curves (reconstructed on surfaces) must reside.

Any edge is created with a default tolerance (returned by Tolerance()) of 1e-7mm. Vertex tolerance (see ModelData_Vertex::Tolerance()) defines a radius of a sphere around vertex point. Edge curves' ends must be inside those spheres.

Edge tolerance should not exceed vertices tolerances.

# Bottom-up Creation

Creating an edge from scratch must be done in the following order:

• Start and end vertices must be created in advance (from 3D points they will lie upon);
• The edge is then constructed using those vertices. In the case of creating edges belonging to the same wire, the vertices must be shared by adjacent edges in order to ensure topological connectivity between the edges;
• A 3D curve must be then added using the SetCurve() method. If the start/end parameters along the curve (corresponding to start/end vertices respectively) are reliably known then they should be specified. Otherwise they will be computed by projecting the vertices onto the curve;
• If the edge belongs to face(s) then p-curves for that(those) face(s) must be added with SetPCurve(). Similar to SetCurve(), if the p-curve range is known then it should be specified. Otherwise the range will be computed by projecting the vertices.
• If needed, the edge tolerance must be updated using SetTolerance().

The following example demonstrates creation of an edge in a solid cylinder, which is shared by top planar face and lateral cylindrical one. Note that the edge only has a 3D curve and a p-curve on the cylindrical surface. The p-curve on the planar face is not created as explicit p-curves on planar surface are not required.

double R = 5., H = 10.; //radius and height
//3D curves
ModelData_Circle aCircle2 (ModelData_Axis2Placement (
ModelData_Point (0, 0, H),
ModelData_Direction::ZDir(),
ModelData_Direction::XDir()), R); //top
//surfaces
ModelData_Plane aPlane2 (aCircle2.Position());
ModelData_CylindricalSurface aCyl (ModelData_Axis3Placement (
ModelData_Point::Origin(),
ModelData_Direction::ZDir(),
ModelData_Direction::XDir()), R);
//vertices
ModelData_Vertex aV2 (ModelData_Point (R, 0, H));
//edges
ModelData_Edge aE2 (aV2, aV2); //top
//faces
ModelData_Face aFace2 (aPlane2, false);
ModelData_Face aFace3 (aCyl , false);
aE2.SetCurve (aCircle2, 0, 2 * M_PI);
ModelData_Line2d aLine23 (ModelData_Point2d (0, H), ModelData_Direction2d::XDir());
aE2.SetPCurve (aLine23, aFace3, 0, 2 * M_PI);
Examples
exploring/brepgeometry/main.cxx, exploring/breprepresentation/main.cxx, modeling/assembly/main.cxx, modeling/brep/main.cxx, and modeling/brepfeatures/main.cxx.

## ◆ ModelData_Edge()

 cadex::ModelData_Edge::ModelData_Edge ( const ModelData_Vertex & theStartVertex, const ModelData_Vertex & theEndVertex )

Constructor.

Creates an edge from a explicitly specified bounding vertices.

theStartVertex must correspond to curve start parameter and theEndVertex to the end parameter (regardless of own edge orientation).

Orientation of the vertices is not important. Internally they will be assigned forward and reversed orientations respectively (however this will not modify input arguments).

For a closed edge (e.g. lying on a full circle) the vertices must be the same object (not just lie on geometrically coincident points), i.e. IsSame() on each vertex must return true for the other.

To complete edge construction the SetCurve() and/or SetPCurve() methods must be called. Refer to Bottom-up Creation.

## ◆ Cast() [1/2]

 const ModelData_Edge & cadex::ModelData_Edge::Cast ( const ModelData_Shape & theShape )
static

Casts a base class object to ModelData_Edge.

theShape must be initialized and be of an instance of ModelData_Edge. Otherwise behavior is undefined.

## ◆ Cast() [2/2]

 ModelData_Edge & cadex::ModelData_Edge::Cast ( ModelData_Shape & theShape )
static

Casts a base class object to ModelData_Edge.

theShape must be initialized and be of an instance of ModelData_Edge. Otherwise behavior is undefined.

## ◆ Curve()

 ModelData_Curve cadex::ModelData_Edge::Curve ( double & theFirstParameter, double & theLastParameter ) const

Returns edge 3D curve and its limits.

Returns null curve for a degenerated edge (see IsDegenerated()).

SetCurve().
Examples
exploring/brepgeometry/main.cxx, exploring/breprepresentation/main.cxx, and modeling/assembly/main.cxx.

## ◆ EndVertex()

Returns a start vertex.

End vertex corresponds to a point on a curve with greater parameter (regardless of edge orientation).

StartVertex().
Examples
modeling/assembly/main.cxx.

## ◆ IsDegenerated()

Returns true if the edge is degenerated.

A degenerated edge has no 3D curve.

Examples
exploring/brepgeometry/main.cxx, and exploring/breprepresentation/main.cxx.

## ◆ IsSeam()

 bool cadex::ModelData_Edge::IsSeam ( const ModelData_Face & theFace ) const

Returns true if the edge is a seam-edge.

Seam-edge.

## ◆ PCurve()

 ModelData_Curve2d cadex::ModelData_Edge::PCurve ( const ModelData_Face & theFace, double & theFirstParameter, double & theLastParameter ) const

Returns edge p-curve on a face and its limits.

For a seam-edge (IsSeam() returns true), selects p-curve depending on this edge orientation. For a seam-edge both p-curves have the same definition range.

SetPCurve().
Examples
exploring/brepgeometry/main.cxx.

## ◆ SetCurve() [1/2]

 bool cadex::ModelData_Edge::SetCurve ( const ModelData_Curve & theCurve )

Specifies 3D curve of the edge.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

The curve must go from the start to the end vertex (specified in the constructor) in the direction of increasing curve's parameter.

The vertices must lie on the curve within their tolerances and within curve's definition range (see ModelData_Curve::Domain()) unless it is periodic.

Curve's range (explicitly stored inside) is computed by projecting vertices onto the curve. If the curve's range is known upfront it is recommended to use another SetCurve() overload accepting the range. If the range cannot be computed then returns false and does not store the curve.

If theCurve is null then removes 3D curve from the edge's curve representations.

For degenerated edges (e.g. sphere pole or cone apex) this method should not be called.

Curve Representations.

## ◆ SetCurve() [2/2]

 void cadex::ModelData_Edge::SetCurve ( const ModelData_Curve & theCurve, double theFirstParameter, double theLastParameter )

Specifies 3D curve of the edge.

The curve must go from the start to the end vertex (specified in the constructor) in the direction of increasing curve's parameter. The point on theCurve at theFirstParameter must correspond to the start vertex, and the point at theLastParameter must correspond to the end vertex.

theFirstParameter must be smaller than theLastParameter. Both must be within curve's definition range (see ModelData_Curve::Domain()). If the curve is periodic, then theFirstParameter should be within the definition range.

The vertices must lie on the curve within their tolerances and within curve's definition range (see ModelData_Curve::Domain()) unless it is periodic.

If theCurve is null then removes 3D curve from the edge's curve representations.

For degenerated edges (e.g. sphere pole or cone apex) this method should not be called.

Curve Representations.

## ◆ SetPCurve() [1/4]

 bool cadex::ModelData_Edge::SetPCurve ( const ModelData_Curve2d & thePCurve, const ModelData_Face & theFace )

Specifies p-curve of the edge on the specified face.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

The p-curve must go from the start to the end vertex (specified in the constructor) in the direction of increasing curve's parameter.

theFace must already be created on an underlying surface (i.e. ModelData_Face::Surface() must return a non-null object).

The vertices must lie on the curve within their tolerances and within curve's definition range (see ModelData_Curve::Domain()) unless it is periodic.

Curve's range (explicitly stored inside) is computed by projecting vertices onto the curve. If the curve's range is known upfront it is recommended to use another SetPCurve() overload accepting the range. If the range cannot be computed then returns false and does not store the p-curve.

For degenerated edge, if the p-curve corresponds to surface singularity, the other SetPCurve() overalod should be used as projection will most likely fail.

If thePCurve is null then removes p-curve for theFace from the edge's curve representations.

Curve Representations.

## ◆ SetPCurve() [2/4]

 void cadex::ModelData_Edge::SetPCurve ( const ModelData_Curve2d & thePCurve, const ModelData_Face & theFace, double theFirstParameter, double theLastParameter )

Specifies p-curve of the edge on the specified face.

The curve must go from the start to the end vertex (specified in the constructor) in the direction of increasing curve's parameter. The point on theCurve at theFirstParameter must correspond to the start vertex, and the point at theLastParameter must correspond to the end vertex.

theFace must already be created on an underlying surface (i.e. ModelData_Face::Surface() must return a non-null object).

theFirstParameter must be smaller than theLastParameter. Both must be within curve's definition range (see ModelData_Curve::Domain()). If the curve is periodic, then theFirstParameter should be within the definition range.

The vertices must lie on the curve within their tolerances and within curve's definition range (see ModelData_Curve::Domain()) unless it is periodic.

If the p-curve corresponds to surface singularity, the IsDegenerated() flag is automatically set. For degenerated edges, theFirstParameter and theLastParameter must be specified such that in 2D parametric space the p-curve ends correspond to ends of the adjacent edges' p-curves.

If thePCurve is null then removes p-curve for theFace from the edge's curve representations.

Curve Representations.

## ◆ SetPCurve() [3/4]

 bool cadex::ModelData_Edge::SetPCurve ( const ModelData_Curve2d & thePCurveForward, const ModelData_Curve2d & thePCurveReversed, const ModelData_Face & theFace )

Specifies p-curves of the seam-edge on the specified face.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

This method is fully equivalent to SetPCurve() for a single p-curve and face case but must be used when constructing seam-edges.

Both p-curves must have the same parametrization (i.e. a point along one curve equals to a point along the other).

thePCurveForward corresponds to the edge when it has forward orientation in the parent wire, thePCurveReversed to the edge when it has reversed orientation. To determine material location with respect to the edge, only a surface normal is taken into account (i.e. face orientation is ignored). Refer to Face Boundaries).

Curves' range (explicitly stored inside) is computed by projecting vertices onto the curves. If the range is known upfront it is recommended to use another SetPCurve() overload accepting the range. If the range cannot be computed or ranges differ then returns false and does not store the p-curves.

## ◆ SetPCurve() [4/4]

 void cadex::ModelData_Edge::SetPCurve ( const ModelData_Curve2d & thePCurveForward, const ModelData_Curve2d & thePCurveReversed, const ModelData_Face & theFace, double theFirstParameter, double theLastParameter )

Specifies p-curves of the seam-edge on the specified face.

This method is fully equivalent to SetPCurve() for a single p-curve and face case but must be used when constructing seam-edges.

Both p-curves must have the same parametrization (i.e. a point along one curve equals to a point along the other).

thePCurveForward corresponds to the edge when it has forward orientation in the parent wire, thePCurveReversed to the edge when it has reversed orientation. To determine material location with respect to the edge, only a surface normal is taken into account (i.e. face orientation is ignored). Refer to Face Boundaries).

## ◆ SetTolerance()

 void cadex::ModelData_Edge::SetTolerance ( double theTolerance )

Sets edge tolerance.

If theTolerance is less than 1e-7 then it is ignored.

Tolerance().