Interface ISurface

The ISurface interface must be implemented by all 3-dimensional unbound surfaces that are used by the Face object. The surface has a well defined 2-dimensional coordinate system, usually referred to as the u/v system.

Namespace: CADability.GeoObject

Assembly: CADability.dll

Syntax

public interface ISurface

Properties

IsRuled

returns wheather the surface is linear in u or v direction

Declaration

RuledSurfaceMode IsRuled { get; }

Property Value

Type	Description
RuledSurfaceMode

IsUPeriodic

Returns true, if this surface is periodic in the u direction (e.g. a cylinder) false otherwise.

Declaration

bool IsUPeriodic { get; }

Property Value

Type	Description
System.Boolean

IsVPeriodic

Returns true, if this surface is periodic in the v direction (e.g. a torus) false otherwise.

Declaration

bool IsVPeriodic { get; }

Property Value

Type	Description
System.Boolean

Oriented

Returns true, if this surface divides the space into two parts. If the surfaces is Oriented Orientation(GeoPoint) returns a valid result

Declaration

bool Oriented { get; }

Property Value

Type	Description
System.Boolean

UPeriod

Returns the u priod of this surface if it is IsUPeriodic 0.0 otherwise

Declaration

double UPeriod { get; }

Property Value

Type	Description
System.Double

UvChangesWithModification

Declaration

bool UvChangesWithModification { get; }

Property Value

Type	Description
System.Boolean

VPeriod

Returns the v priod of this surface if it is IsVPeriodic 0.0 otherwise

Declaration

double VPeriod { get; }

Property Value

Type	Description
System.Double

Methods

Approximate(Double, Double, Double, Double, Double)

Create a NurbSurface as an approximation of this surface

Declaration

NurbsSurface Approximate(double umin, double umax, double vmin, double vmax, double precision)

Parameters

Type	Name	Description
System.Double	umin
System.Double	umax
System.Double	vmin
System.Double	vmax
System.Double	precision

Returns

Type	Description
NurbsSurface

Clone()

Returns an identical but independant copy of this surface

Declaration

ISurface Clone()

Returns

Type	Description
ISurface

CopyData(ISurface)

Copies the data of the given surface to this surface. The two surfaces are guaranteed to be of the same type. (Used after Clone() and Modify(ModOp) to restore the original values).

Declaration

void CopyData(ISurface CopyFrom)

Parameters

Type	Name	Description
ISurface	CopyFrom	where to copy the data from

Derivation2At(GeoPoint2D, out GeoPoint, out GeoVector, out GeoVector, out GeoVector, out GeoVector, out GeoVector)

Returns the point, the two first derivations and the three second derivations of the surface at the provided parameter position.

Declaration

void Derivation2At(GeoPoint2D uv, out GeoPoint location, out GeoVector du, out GeoVector dv, out GeoVector duu, out GeoVector dvv, out GeoVector duv)

Parameters

Type	Name	Description
GeoPoint2D	uv	Point in the parameter space
GeoPoint	location	Resulting 3D point
GeoVector	du	Resulting derivation in u
GeoVector	dv	Resulting derivation in v
GeoVector	duu
GeoVector	dvv
GeoVector	duv

DerivationAt(GeoPoint2D, out GeoPoint, out GeoVector, out GeoVector)

Returns the point and the two derivations of the suface in a single call. It returns the same result as calling PointAt(GeoPoint2D), VDirection(GeoPoint2D) und VDirection(GeoPoint2D) succesively but is often faster than the three seperate calls.

Declaration

void DerivationAt(GeoPoint2D uv, out GeoPoint location, out GeoVector du, out GeoVector dv)

Parameters

Type	Name	Description
GeoPoint2D	uv	Point in the parameter space
GeoPoint	location	Resulting 3D point
GeoVector	du	Resulting derivation in u
GeoVector	dv	Resulting derivation in v

FixedU(Double, Double, Double)

Returns a curve where the u parameter of this surface is fixed and the v parameter starts a vmin and ends at vmax

Declaration

ICurve FixedU(double u, double vmin, double vmax)

Parameters

Type	Name	Description
System.Double	u
System.Double	vmin
System.Double	vmax

Returns

Type	Description
ICurve

FixedV(Double, Double, Double)

Returns a curve where the v parameter of this surface is fixed and the u parameter starts a umin and ends at umax

Declaration

ICurve FixedV(double v, double umin, double umax)

Parameters

Type	Name	Description
System.Double	v
System.Double	umin
System.Double	umax

Returns

Type	Description
ICurve

GetCanonicalForm(Double, Nullable<BoundingRect>)

Returns a simpler form of this surface: SurfaceOfLinearExtrusion might be a cylinder, NURBS might be a sphere etc. Returns null, if there is no simpler form

Declaration

ISurface GetCanonicalForm(double precision, BoundingRect? bounds = default(BoundingRect? ))

Parameters

Type	Name	Description
System.Double	precision	maximal allowed deviation of the new surface
System.Nullable<BoundingRect>	bounds

Returns

Type	Description
ISurface

GetContextMenuForParametrics(IFrame, Face)

Returns a context menu to change certain parameters of the surface of a face

Declaration

MenuWithHandler[] GetContextMenuForParametrics(IFrame frame, Face face)

Parameters

Type	Name	Description
IFrame	frame
Face	face

Returns

Type	Description
MenuWithHandler[]

GetDistance(GeoPoint)

Returns the distance of the provided point p to the (unlimited) surface.

Declaration

double GetDistance(GeoPoint p)

Parameters

Type	Name	Description
GeoPoint	p

Returns

Type	Description
System.Double

GetDualSurfaceCurves(BoundingRect, ISurface, BoundingRect, List<GeoPoint>, List<Tuple<Double, Double, Double, Double>>)

Returns intersectionCurves

Declaration

IDualSurfaceCurve[] GetDualSurfaceCurves(BoundingRect thisBounds, ISurface other, BoundingRect otherBounds, List<GeoPoint> seeds, List<Tuple<double, double, double, double>> extremePositions = null)

Parameters

Type	Name	Description
BoundingRect	thisBounds
ISurface	other
BoundingRect	otherBounds
System.Collections.Generic.List<GeoPoint>	seeds
System.Collections.Generic.List<System.Tuple<System.Double, System.Double, System.Double, System.Double>>	extremePositions

Returns

Type	Description
IDualSurfaceCurve[]

GetExtrema()

Returns an array of points in parametric space where there are extrema in direction of x-, y- or z-axis. The normal vector in a extremum is parallel to one of the axis and the surface has a relative maximum or minimum in this direction.

Declaration

GeoPoint2D[] GetExtrema()

Returns

Type	Description
GeoPoint2D[]	s.a.

GetExtremePositions(BoundingRect, ICurve, out List<Tuple<Double, Double, Double>>)

Find positions on the surface and on the curve where the connection of these points are perpendicular to the surface and to the curve

Declaration

int GetExtremePositions(BoundingRect domain, ICurve curve3D, out List<Tuple<double, double, double>> positions)

Parameters

Type	Name	Description
BoundingRect	domain	valid area for the surface
ICurve	curve3D	the curve
System.Collections.Generic.List<System.Tuple<System.Double, System.Double, System.Double>>	positions	the positions found: first two doubles are u,v on the surface, third is u on the curve

Returns

Type	Description
System.Int32

GetExtremePositions(BoundingRect, ISurface, BoundingRect, out List<Tuple<Double, Double, Double, Double>>)

Find positions in the uv system, where the connection of the points are perpendicular on both surfaces. the resulting list extremePositions may be only partially filled, the missing uv values may be double.NaN, because this is what we need in most cases.

Declaration

int GetExtremePositions(BoundingRect thisBounds, ISurface other, BoundingRect otherBounds, out List<Tuple<double, double, double, double>> extremePositions)

Parameters

Type	Name	Description
BoundingRect	thisBounds
ISurface	other
BoundingRect	otherBounds
System.Collections.Generic.List<System.Tuple<System.Double, System.Double, System.Double, System.Double>>	extremePositions

Returns

Type	Description
System.Int32

GetLineIntersection(GeoPoint, GeoVector)

Returns the intersectionpoints of this surface with the line given by the parameters. Teh returned point are in the parametric (u/v) space of this surface.

Declaration

GeoPoint2D[] GetLineIntersection(GeoPoint startPoint, GeoVector direction)

Parameters

Type	Name	Description
GeoPoint	startPoint	startpoint of the line
GeoVector	direction	direction of the line

Returns

Type	Description
GeoPoint2D[]

GetModified(ModOp)

Returns a clone of this surface modified by the given ModOp.

Declaration

ISurface GetModified(ModOp m)

Parameters

Type	Name	Description
ModOp	m	how to modify

Returns

Type	Description
ISurface

GetNaturalBounds(out Double, out Double, out Double, out Double)

Returns the natural bounds of the surface. The returned values may be infinite

Declaration

void GetNaturalBounds(out double umin, out double umax, out double vmin, out double vmax)

Parameters

Type	Name	Description
System.Double	umin
System.Double	umax
System.Double	vmin
System.Double	vmax

GetNonPeriodicSurface(ICurve[])

If this surface is periodic in u or v or both return a non-periodic surface which describes the same geometric surface but with a different parametric system. It also removes poles and is useful for non-periodic surfaces with a single pole.

Declaration

ISurface GetNonPeriodicSurface(ICurve[] orientedCurves)

Parameters

Type	Name	Description
ICurve[]	orientedCurves	3d curves, which describe the outline, that will be used. this is needed by some surfaces to determine the maximum definition area

Returns

Type	Description
ISurface

GetNormal(GeoPoint2D)

Returns the normal vector (perpendicular to the surface) at the given u/v point

Declaration

GeoVector GetNormal(GeoPoint2D uv)

Parameters

Type	Name	Description
GeoPoint2D	uv	position of normal

Returns

Type	Description
GeoVector	normal vector

GetOffsetSurface(Double)

Returns a surface that is "parallel" to this surface, i.e. each point on this surface corresponds a point on the returned surface that has the same (u,v) coordinates and has the 3d coordinates oft the point plus offset*Normal at this point

Declaration

ISurface GetOffsetSurface(double offset)

Parameters

Type	Name	Description
System.Double	offset	Offset to this surface

Returns

Type	Description
ISurface	The offset surface

GetPatchExtent(BoundingRect, Boolean)

Returns the extent of a patch of the surface clipped rectangular in the 2d parameter space

Declaration

BoundingCube GetPatchExtent(BoundingRect uvPatch, bool rough = false)

Parameters

Type	Name	Description
BoundingRect	uvPatch
System.Boolean	rough

Returns

Type	Description
BoundingCube

GetPatchHull(BoundingRect, out GeoPoint, out GeoVector, out GeoVector, out GeoVector)

Returns a parallelepiped (a prism with parallelograms) defined by the parameters loc, dir1, dir2, dir3 which completeley covers or encloses the patch of the surface defined by the uvpatch. There are obviously many solutions to this problem but a parallelepiped with minimum volume would be preferred. This method is used to optimate intersection algorithms.

Declaration

void GetPatchHull(BoundingRect uvpatch, out GeoPoint loc, out GeoVector dir1, out GeoVector dir2, out GeoVector dir3)

Parameters

Type	Name	Description
BoundingRect	uvpatch	The patch of the surface in parametric space
GeoPoint	loc	One vertex of the result
GeoVector	dir1	One of the three vectors of the parallelepiped
GeoVector	dir2	One of the three vectors of the parallelepiped
GeoVector	dir3	One of the three vectors of the parallelepiped

GetPlaneIntersection(PlaneSurface, Double, Double, Double, Double, Double)

Returns the intersection curve(s) of this surface with the given plane. An empty array is returned if there is no intersection. umin, umax, vmin, vmax define the Parameterspace of this surface (not of the PlaneSurface) for the intersection. It is also the periodic domain in which the 2d curve for this surface will be returned, if this surface is periodic. the resulting curves may exceed the area provided by umin, umax, vmin, vmax.

Declaration

IDualSurfaceCurve[] GetPlaneIntersection(PlaneSurface pl, double umin, double umax, double vmin, double vmax, double precision)

Parameters

Type	Name	Description
PlaneSurface	pl	plane to intersect with
System.Double	umin
System.Double	umax
System.Double	vmin
System.Double	vmax
System.Double	precision

Returns

Type	Description
IDualSurfaceCurve[]	intersection curves

GetPolynomialParameters()

Declaration

double[] GetPolynomialParameters()

Returns

Type	Description
System.Double[]

GetProjectedCurve(ICurve, Double)

Returns the projection of the given curve in 2D coordinates. Should only be used for curves that are close to the surface.

Declaration

ICurve2D GetProjectedCurve(ICurve curve, double precision)

Parameters

Type	Name	Description
ICurve	curve
System.Double	precision

Returns

Type	Description
ICurve2D

GetPropertyEntry(IFrame)

Gets the IPropertyEntry to display this surface in the property grid (may be null)

Declaration

IPropertyEntry GetPropertyEntry(IFrame frame)

Parameters

Type	Name	Description
IFrame	frame

Returns

Type	Description
IPropertyEntry

GetSafeParameterSteps(Double, Double, Double, Double, out Double[], out Double[])

Gets spans of the parameterspace that are guaranteed to contain only one inflection point. The returned intu should contain umin as first and umax as last value (same with v)

Declaration

void GetSafeParameterSteps(double umin, double umax, double vmin, double vmax, out double[] intu, out double[] intv)

Parameters

Type	Name	Description
System.Double	umin
System.Double	umax
System.Double	vmin
System.Double	vmax
System.Double[]	intu
System.Double[]	intv

GetSelfIntersections(BoundingRect)

Returns a List of self intersection curves in the u/v system

Declaration

ICurve2D[] GetSelfIntersections(BoundingRect bounds)

Parameters

Type	Name	Description
BoundingRect	bounds

Returns

Type	Description
ICurve2D[]

GetTangentCurves(GeoVector, Double, Double, Double, Double)

Returns curves where direction is perpendicular to the normal vector

Declaration

ICurve2D[] GetTangentCurves(GeoVector direction, double umin, double umax, double vmin, double vmax)

Parameters

Type	Name	Description
GeoVector	direction
System.Double	umin
System.Double	umax
System.Double	vmin
System.Double	vmax

Returns

Type	Description
ICurve2D[]

GetTouchingPoints(BoundingRect, ISurface, BoundingRect)

Returns a list of points where the surfaces touch each other (where the surfaces are tangential)

Declaration

GeoPoint[] GetTouchingPoints(BoundingRect thisBounds, ISurface other, BoundingRect otherBounds)

Parameters

Type	Name	Description
BoundingRect	thisBounds
ISurface	other
BoundingRect	otherBounds

Returns

Type	Description
GeoPoint[]

GetUSingularities()

returns the values for the u parameter where this surface is singular i.e. changing v with this u parameter fixed doesn't change the 3D point.

Declaration

double[] GetUSingularities()

Returns

Type	Description
System.Double[]	list of u singularities

GetVSingularities()

returns the values for the v parameter where this surface is singular i.e. changing u with this v parameter fixed doesn't change the 3D point.

Declaration

double[] GetVSingularities()

Returns

Type	Description
System.Double[]	list of v singularities

GetZMinMax(Projection, Double, Double, Double, Double, ref Double, ref Double)

Gets the minimum and maximumm valus for the z-coordinate of a rectangular patch (in parametric space) of this surface under a certain projection

Declaration

void GetZMinMax(Projection p, double umin, double umax, double vmin, double vmax, ref double zMin, ref double zMax)

Parameters

Type	Name	Description
Projection	p	the projection
System.Double	umin	left bound of the rectangular patch
System.Double	umax	right bound of the rectangular patch
System.Double	vmin	bottom bound of the rectangular patch
System.Double	vmax	top bound of the rectangular patch
System.Double	zMin	returned minimum
System.Double	zMax	returned maximum

HasDiscontinuousDerivative(out ICurve2D[])

Declaration

bool HasDiscontinuousDerivative(out ICurve2D[] discontinuities)

Parameters

Type	Name	Description
ICurve2D[]	discontinuities

Returns

Type	Description
System.Boolean

HitTest(BoundingCube, out GeoPoint2D)

Returns true, if this surface interferes with the provided cube. If this is the case uv will contain a point (in the parameter system of the surface) which is inside the cube

Declaration

bool HitTest(BoundingCube cube, out GeoPoint2D uv)

Parameters

Type	Name	Description
BoundingCube	cube
GeoPoint2D	uv

Returns

Type	Description
System.Boolean

HitTest(BoundingCube, Double, Double, Double, Double)

Checks whether this surface restricted by the provided parameters interferes with the provided cube.

Declaration

bool HitTest(BoundingCube cube, double umin, double umax, double vmin, double vmax)

Parameters

Type	Name	Description
BoundingCube	cube	Bounding cube for the test
System.Double	umin	Minimum for the u parameter
System.Double	umax	Maximum for the u parameter
System.Double	vmin	Minimum for the v parameter
System.Double	vmax	Maximum for the v parameter

Returns

Type	Description
System.Boolean	true if the cube and the surface interfere

Intersect(BoundingRect, ISurface, BoundingRect)

Returns the intersection curves between this surface and the provided other surface. Both surfaces are bound by rectangles.

Declaration

ICurve[] Intersect(BoundingRect thisBounds, ISurface other, BoundingRect otherBounds)

Parameters

Type	Name	Description
BoundingRect	thisBounds	Bounds for this surface
ISurface	other	Other surface
BoundingRect	otherBounds	Bounds of other surface

Returns

Type	Description
ICurve[]	Array of intersection curves

Intersect(BoundingRect, ISurface, BoundingRect, GeoPoint)

Returns the intersection curves between this surface and the provided other surface. Both surfaces are bound by rectangles.

Declaration

ICurve Intersect(BoundingRect thisBounds, ISurface other, BoundingRect otherBounds, GeoPoint seed)

Parameters

Type	Name	Description
BoundingRect	thisBounds	Bounds for this surface
ISurface	other	Other surface
BoundingRect	otherBounds	Bounds of other surface
GeoPoint	seed

Returns

Type	Description
ICurve	Array of intersection curves

Intersect(ICurve, BoundingRect, out GeoPoint[], out GeoPoint2D[], out Double[])

Returns the intersection of the provided curve with this surface. The result may be empty.

Declaration

void Intersect(ICurve curve, BoundingRect uvExtent, out GeoPoint[] ips, out GeoPoint2D[] uvOnFaces, out double[] uOnCurve3Ds)

Parameters

Type	Name	Description
ICurve	curve	The curve to be intersected with
BoundingRect	uvExtent
GeoPoint[]	ips	Resulting 3d intersection points
GeoPoint2D[]	uvOnFaces	u/v values of the intersection points on this surface
System.Double[]	uOnCurve3Ds	u parameter of intersection points on the curve

IsExtruded(GeoVector)

returns true, if the provided direction can be interpreted as an extrusion direction of the surface

Declaration

bool IsExtruded(GeoVector direction)

Parameters

Type	Name	Description
GeoVector	direction

Returns

Type	Description
System.Boolean

IsVanishingProjection(Projection, Double, Double, Double, Double)

Returns true if the given projection makes the surface disappear, i.e. degenerate to an edge.

Declaration

bool IsVanishingProjection(Projection p, double umin, double umax, double vmin, double vmax)

Parameters

Type	Name	Description
Projection	p	the projection
System.Double	umin
System.Double	umax
System.Double	vmin
System.Double	vmax

Returns

Type	Description
System.Boolean	true if vanishing, falso otherwise

Make3dCurve(ICurve2D)

Returns a 3-dimensional curve from the given 2-dimensional curve. the 2-dimensional curve is interpreted in the u/v system of the surface.

Declaration

ICurve Make3dCurve(ICurve2D curve2d)

Parameters

Type	Name	Description
ICurve2D	curve2d	the base curve

Returns

Type	Description
ICurve	corresponding 3-d curve

MakeCanonicalForm()

Modifies this surface into a more canonical form and returns the modification for the parametric space which reverses this modification in 2d. Curves in the parametric space of this surface will become invalid unless modified by the returned transformation.

Declaration

ModOp2D MakeCanonicalForm()

Returns

Type	Description
ModOp2D	2d modification for the parametric space

MakeFace(SimpleShape)

Makes a Face from this surface with the given bounds in the parametric (u/v) space.

Declaration

Face MakeFace(SimpleShape simpleShape)

Parameters

Type	Name	Description
SimpleShape	simpleShape	the bounds

Returns

Type	Description
Face	the created face or null

MaxDist(GeoPoint2D, GeoPoint2D, out GeoPoint2D)

used internally. the maximum distance of the 3d curve, formed by the uv-line from sp to ep, to the 3d-line from PointAt(sp) to PointAt(ep)

Declaration

double MaxDist(GeoPoint2D sp, GeoPoint2D ep, out GeoPoint2D mp)

Parameters

Type	Name	Description
GeoPoint2D	sp
GeoPoint2D	ep
GeoPoint2D	mp	The uv point where this distance occurres

Returns

Type	Description
System.Double

Modify(ModOp)

Modifies this surface with the given operation

Declaration

void Modify(ModOp m)

Parameters

Type	Name	Description
ModOp	m	how to modif

Orientation(GeoPoint)

Returns the orientation of the provided point. The sign of the result may be used to distinguish between inside and outside.

Declaration

double Orientation(GeoPoint p)

Parameters

Type	Name	Description
GeoPoint	p

Returns

Type	Description
System.Double

PerpendicularFoot(GeoPoint)

Returns a list of perpendicular foot points of the surface. The list may be empty

Declaration

GeoPoint2D[] PerpendicularFoot(GeoPoint fromHere)

Parameters

Type	Name	Description
GeoPoint	fromHere	Source point for the perpendicular foot

Returns

Type	Description
GeoPoint2D[]	Array of foot-points, may be empty

PointAt(GeoPoint2D)

Returns the 3-dimensional point at the given u/v point

Declaration

GeoPoint PointAt(GeoPoint2D uv)

Parameters

Type	Name	Description
GeoPoint2D	uv	position

Returns

Type	Description
GeoPoint	point

PositionOf(GeoPoint)

Returns the u/v position of the given point. It is assumed that the point is on the surface, if not the result is undetermined.

Declaration

GeoPoint2D PositionOf(GeoPoint p)

Parameters

Type	Name	Description
GeoPoint	p	point

Returns

Type	Description
GeoPoint2D	position

ReverseOrientation()

Reverses the orientation of this surface. The normal vector will point to the other side after this operation. The returned ModOp2D determins how (u,v) coordinates of the parameter space have to be transformed to define the same 3d point.

Declaration

ModOp2D ReverseOrientation()

Returns

Type	Description
ModOp2D	Transformation of the parameter space

SameGeometry(BoundingRect, ISurface, BoundingRect, Double, out ModOp2D)

Returns true if this surface and the other surface are geometrically identical, i.e. describe the same surface in 3D space. The may have a different u/v system. The returned firstToSecond contains the ModOp to convert from the u/v system of the first surface to the second surface.

Declaration

bool SameGeometry(BoundingRect thisBounds, ISurface other, BoundingRect otherBounds, double precision, out ModOp2D firstToSecond)

Parameters

Type	Name	Description
BoundingRect	thisBounds	Bounds for this surface
ISurface	other	Other surface
BoundingRect	otherBounds	Bounds of other surface
System.Double	precision	Required precision
ModOp2D	firstToSecond	Transformation between different u/v systems

Returns

Type	Description
System.Boolean	True if the surfaces are geometrically equal

SetBounds(BoundingRect)

Mostly used internally

Declaration

void SetBounds(BoundingRect boundingRect)

Parameters

Type	Name	Description
BoundingRect	boundingRect

UDirection(GeoPoint2D)

Returns the direction at the given u/v point in direction of the u-axis

Declaration

GeoVector UDirection(GeoPoint2D uv)

Parameters

Type	Name	Description
GeoPoint2D	uv	position

Returns

Type	Description
GeoVector	direction

VDirection(GeoPoint2D)

Returns the direction at the given u/v point in direction of the v-axis

Declaration

GeoVector VDirection(GeoPoint2D uv)

Parameters

Type	Name	Description
GeoPoint2D	uv	position

Returns

Type	Description
GeoVector	direction