cadex::ModelData::Edge Class Reference

Defines an edge. More...

#include <cadex/ModelData/Edge.hxx>

Inheritance diagram for cadex::ModelData::Edge:

Public Member Functions
	Edge (const Vertex &theStartVertex, const Vertex &theEndVertex)
	Constructor.
	Edge (const Geom::Curve &theCurve, const Vertex &theStartVertex, const Vertex &theEndVertex)
	Constructor.
void	SetCurve (const Geom::Curve &theCurve, double theFirstParameter, double theLastParameter)
	Specifies 3D curve of the edge.
bool	SetCurve (const Geom::Curve &theCurve)
	Specifies 3D curve of the edge.
Geom::Curve	Curve (double &theFirstParameter, double &theLastParameter) const
	Returns edge 3D curve and its limits.
void	SetPCurve (const Geom::Curve2d &thePCurve, const Face &theFace, double theFirstParameter, double theLastParameter)
	Specifies p-curve of the edge on the specified face.
bool	SetPCurve (const Geom::Curve2d &thePCurve, const Face &theFace)
	Specifies p-curve of the edge on the specified face.
void	SetPCurve (const Geom::Curve2d &thePCurveForward, const Geom::Curve2d &thePCurveReversed, const Face &theFace, double theFirstParameter, double theLastParameter)
	Specifies p-curves of the seam-edge on the specified face.
bool	SetPCurve (const Geom::Curve2d &thePCurveForward, const Geom::Curve2d &thePCurveReversed, const Face &theFace)
	Specifies p-curves of the seam-edge on the specified face.
Geom::Curve2d	PCurve (const Face &theFace, double &theFirstParameter, double &theLastParameter) const
	Returns edge p-curve on a face and its limits.
Vertex	StartVertex () const
	Returns a start vertex.
Vertex	EndVertex () const
	Returns an end vertex.
void	SetTolerance (double theTolerance)
	Sets edge tolerance.
double	Tolerance () const
	Returns edge tolerance.
bool	IsDegenerated () const
	Returns true if the edge is degenerated.
bool	IsSeam (const Face &theFace) const
	Returns true if the edge is a seam-edge.
PolylineSet	Triangulation () const
	Returns a polyline approximation of the curve.
Public Member Functions inherited from cadex::ModelData::Shape
ShapeType	Type () const
	Returns a shape type. For a null object returns Undefined.
ShapeOrientation	Orientation () const
	Returns orientation flag.
Shape	Reversed () const
	Returns a shape that shares the same geometry and subshape graph but has opposite orientation.
Shape	Oriented (ShapeOrientation theOrientation) const
	Returns a shape that shares the same geometry and subshape graph and has specified orientation.
bool	IsEqual (const Shape &theOther) const
	Returns true if the shape shares the same geometry and subshape graph, and has equal orientation.
bool	IsSame (const Shape &theOther) const
	Returns true if the shape shares the same geometry and subshape graph.
void	SetName (const UTF16String &theName)
UTF16String	Name () const
Public Member Functions inherited from cadex::BaseObject
size_t	Id () const
	Return unique identifier of public object.
internal::BaseObjectImpl *	Impl () const
bool	IsNull () const
	operator bool () const
template<typename T >
bool	IsOfType () const
template<typename T >
T *	Impl () const
	Reserved for internal use.

Static Public Member Functions
static const Edge &	Cast (const Shape &theShape)
	Casts a base class object to Edge.
static Edge &	Cast (Shape &theShape)
	Casts a base class object to Edge.
static bool	CompareType (const BaseObject &theObject)
	Check the type of object. Returns true if the specified object is this class type.
Static Public Member Functions inherited from cadex::ModelData::Shape
static bool	CompareType (const BaseObject &theObject)
	Check the type of object. Returns true if the specified object is this class type.

Additional Inherited Members
Public Types inherited from cadex::BaseObject
typedef std::shared_ptr< internal::BaseObjectImpl >	ImplType
Protected Member Functions inherited from cadex::ModelData::Shape
	Shape (const ImplType &theImpl)
Protected Member Functions inherited from cadex::BaseObject
	BaseObject (const ImplType &theImpl)

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 MTK 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
Geom::Circle aCircle2 (Geom::Axis3d (
    Geom::Point (0, 0, H), 
    Geom::Direction::ZDir(), 
    Geom::Direction::XDir()), R); // top
 
// surfaces
Geom::Plane aPlane2 (aCircle2.Position());
Geom::CylindricalSurface aCyl (Geom::Axis3d (
    Geom::Point::Origin(), 
    Geom::Direction::ZDir(), 
    Geom::Direction::XDir()), R);
 
// vertices
ModelData::Vertex aV2 (Geom::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);
Geom::Line2d aLine23 (Geom::Point2d (0, H), Geom::Direction2d::XDir());
aE2.SetPCurve (aLine23, aFace3, 0, 2 * M_PI);

Constructor & Destructor Documentation

Edge() [1/2]

cadex::ModelData::Edge::Edge	(	const Vertex &	theStartVertex,
		const 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.

Edge() [2/2]

cadex::ModelData::Edge::Edge	(	const Geom::Curve &	theCurve,
		const Vertex &	theStartVertex,
		const Vertex &	theEndVertex )

Constructor.

Creates an edge from a curve and explicitly specified bounding vertices:

Constructing edge from curve and vertices

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

Member Function Documentation

Cast() [1/2]

const Edge & cadex::ModelData::Edge::Cast ( const Shape & theShape )

static

Casts a base class object to Edge.

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

Cast() [2/2]

Edge & cadex::ModelData::Edge::Cast ( Shape & theShape )

static

Casts a base class object to Edge.

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

Curve()

Geom::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()).

See also

SetCurve().

EndVertex()

Vertex cadex::ModelData::Edge::EndVertex

(

)

const

Returns an end vertex.

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

See also

StartVertex().

IsDegenerated()

bool cadex::ModelData::Edge::IsDegenerated

(

)

const

Returns true if the edge is degenerated.

A degenerated edge has no 3D curve.

IsSeam()

bool cadex::ModelData::Edge::IsSeam

(

const Face &

theFace

)

const

Returns true if the edge is a seam-edge.

See also

Seam-edge.

PCurve()

Geom::Curve2d cadex::ModelData::Edge::PCurve	(	const 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.

See also

SetPCurve().

SetCurve() [1/2]

bool cadex::ModelData::Edge::SetCurve

(

const Geom::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 Geom::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.

See also

Curve Representations.

SetCurve() [2/2]

void cadex::ModelData::Edge::SetCurve	(	const Geom::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 Geom::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 Geom::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.

See also

Curve Representations.

SetPCurve() [1/4]

bool cadex::ModelData::Edge::SetPCurve	(	const Geom::Curve2d &	thePCurve,
		const 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 Geom::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.

See also

Curve Representations.

SetPCurve() [2/4]

void cadex::ModelData::Edge::SetPCurve	(	const Geom::Curve2d &	thePCurve,
		const 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 Geom::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 Geom::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.

See also

Curve Representations.

SetPCurve() [3/4]

bool cadex::ModelData::Edge::SetPCurve	(	const Geom::Curve2d &	thePCurveForward,
		const Geom::Curve2d &	thePCurveReversed,
		const 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 Geom::Curve2d &	thePCurveForward,
		const Geom::Curve2d &	thePCurveReversed,
		const 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.

See also

Tolerance().

StartVertex()

Vertex cadex::ModelData::Edge::StartVertex

(

)

const

Returns a start vertex.

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

See also

EndVertex().

Tolerance()

double cadex::ModelData::Edge::Tolerance

(

)

const

Returns edge tolerance.

See also

SetTolerance(), Vertex::Tolerance().

Triangulation()

PolylineSet cadex::ModelData::Edge::Triangulation

(

)

const

Returns a polyline approximation of the curve.

An empty object may be returned.