[mxcad_3d API Document](../README. md)/Mx3dGeomBizierSurface

Class: Mx3dGeomBezierSurface

Represents a Bezier surface, inherited from Mx3dGeomSounddSurface. Provide multiple operations and query methods to handle Bezier surfaces.

Hierarchy

• Mx3dGeomBoundedSurface

  ↳ Mx3dGeomBezierSurface

Table of contents

Constructors

• constructor

Methods

• Bounds
• Continuity
• Copy
• D0
• D1
• D2
• D3
• DN
• DynCast
• DynamicType
• ExchangeUV
• Face
• Increase
• InsertPoleColAfter
• InsertPoleColBefore
• InsertPoleRowAfter
• InsertPoleRowBefore
• IsCNu
• IsCNv
• IsUClosed
• IsUPeriodic
• IsURational
• IsVClosed
• IsVPeriodic
• IsVRational
• MirrorByAxis
• MirrorByCSYSR
• MirrorByPoint
• MirroredByAxis
• MirroredByCSYSR
• MirroredByPoint
• NbUPoles
• NbVPoles
• Pole
• Poles
• RemovePoleCol
• RemovePoleRow
• Rotate
• Rotated
• Scale
• Scaled
• Segment
• SetPole
• SetPoleCol
• SetPoleRow
• SetWeight
• SetWeightCol
• SetWeightRow
• Transform
• TransformParameters
• Transformed
• TranslateBy2Points
• TranslateByVec
• TranslatedBy2Points
• TranslatedByVec
• UDegree
• UPeriod
• UReverse
• UReversed
• UReversedParameter
• VPeriod
• VReverse
• VReversed
• VReversedParameter
• Value
• Weight
• Weights
• DownCast

Constructors

constructor

• new Mx3dGeomBezierSurface(SurfacePoles, PoleWeights?)

Constructor is used to create a Bezier surface.

Parameters

Name	Type	Description
SurfacePoles	[Mx3dGePoint. md] []	Control point array, in the form of a two-dimensional array
PoleWeights?	Number [] []	Control point weight array (optional)

Overrides

Mx3dGeomBoundedSurface.constructor

Methods

Bounds

▸ Bounds(U1U2V1V2): void

Obtain the boundary range of the surface.

Parameters

Name	Type	Description
U1U2V1V2	[dU1: number, dU2: number, dV1: number, dV2: number]	Range array

Returns

void

---

Continuity

▸ Continuity(): MxGAShapeEnum

Obtain the continuity of the surface.

Returns

MxGAShapeEnum

Return the continuity enumeration value.

---

Copy

▸ Copy(): Mx3dGeomObject

Copy the current surface object.

Returns

Mx3dGeomObject

Return a new surface object.

---

D0

▸ D0(U, V, P): void

Calculate the zero derivative of a surface at a specified point.

Parameters

Name	Type	Description
U	number	parameter U value
V	number	parameter V value
P	[Mx3dGePoint] (Mx3dGePoint. md)	Output point

Returns

void

---

D1

▸ D1(U, V, P, D1U, D1V): void

Calculate the first derivative of a surface at a specified point.

Parameters

Name	Type	Description
U	number	parameter U value
V	number	parameter V value
P	[Mx3dGePoint] (Mx3dGePoint. md)	Output point
D1U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first-order derivative vector in the U direction
D1V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first derivative vector in the V direction

Returns

void

---

D2

▸ D2(U, V, P, D1U, D1V, D2U, D2V, D2UV): void

Calculate the second derivative of a surface at a specified point.

Parameters

Name	Type	Description
U	number	parameter U value
V	number	parameter V value
P	[Mx3dGePoint] (Mx3dGePoint. md)	Output point
D1U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first-order derivative vector in the U direction
D1V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first derivative vector in the V direction
D2U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative vector in the U direction
D2V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative vector in the V direction
D2UV	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative vector in the UV direction

Returns

void

---

D3

▸ D3(U, V, P, D1U, D1V, D2U, D2V, D2UV, D3U, D3V, D3UUV, D3UVV): void

Calculate the third derivative of a surface at a specified point.

Parameters

Name	Type	Description
U	number	parameter U value
V	number	parameter V value
P	[Mx3dGePoint] (Mx3dGePoint. md)	Output point
D1U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first-order derivative vector in the U direction
D1V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first derivative vector in the V direction
D2U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative vector in the U direction
D2V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative vector in the V direction
D2UV	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative vector in the UV direction
D3U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the third derivative vector in the U direction
D3V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the third derivative vector in the V direction
D3UUV	[Mx3dGeVec] (Mx3dGeVec. md)	Output the third derivative vector in the UU direction
D3UVV	[Mx3dGeVec] (Mx3dGeVec. md)	Output the third derivative vector in the UV direction

Returns

void

---

DN

▸ DN(U, V, Nu, Nv): Mx3dGeVec

Calculate the Nth derivative of a surface at a specified point.

Parameters

Name	Type	Description
U	number	parameter U value
V	number	parameter V value
Nu	number	U-direction order
Nv	number	order in the V direction

Returns

Mx3dGeVec

Return the derivative vector.

---

DynCast

▸ DynCast(theObject): Mx3dGeomBezierSurface

Parameters

Name	Type
theObject	Mx3dGeomObject

Returns

Mx3dGeomBezierSurface

Overrides

Mx3dGeomBoundedSurface.DynCast

---

DynamicType

▸ DynamicType(): string

Return the dynamic type string of the object.

Returns

string

Dynamic type string.

Inherited from

Mx3dGeomBoundedSurface.DynamicType

---

ExchangeUV

▸ ExchangeUV(): void

Exchange the order of U and V directions.

Returns

void

---

Face

▸ Face(TolDegen): Mx3dShapeFace

Generate patches based on tolerance.

Parameters

Name	Type	Description
Tolerant	Number	Tolerance

Returns

Mx3dShapeFace

Return the generated patch object.

▸ Face(W, Inside): Mx3dShapeFace

Generate patches based on lines and whether they are generated internally.

Parameters

Name	Type	Description
W	[Mx3dShapeWire] (Mx3dShapeWire. md)	Line object
Inside	boolean	Is it inside

Returns

Mx3dShapeFace

Return the generated patch object.

▸ Face(UMin, UMax, VMin, VMax, TolDegen): Mx3dShapeFace

Generate patches based on U, V range and tolerance.

Parameters

Name	Type	Description
UMin	number	minimum value in the U direction
UMax	number	maximum value in the U direction
VMin	number	minimum value in the V direction
VMax	number	maximum value in the V direction
Tolerant	Number	Tolerance

Returns

Mx3dShapeFace

Return the generated patch object.

---

Increase

▸ Increase(UDeg, VDeg): void

Increase the order of the surface.

Parameters

Name	Type	Description
UDeg	number	increase order in the U direction
VDeg	number	increase order in the V direction

Returns

void

---

InsertPoleColAfter

▸ InsertPoleColAfter(VIndex, CPoles, CPoleWeights?): void

Insert a new control point column after the specified column.

Parameters

Name	Type	Description
Index of column 'VIndes'	' number '
CPoles	[Mx3dGePoint] (Mx3dGePoint. md) []	Control point array to be inserted
CPoleWeights?	Number []	Control point weight array (optional)

Returns

void

---

InsertPoleColBefore

▸ InsertPoleColBefore(VIndex, CPoles, CPoleWeights?): void

Insert a new control point column before the specified column.

Parameters

Name	Type	Description
Index of column 'VIndes'	' number '
CPoles	[Mx3dGePoint] (Mx3dGePoint. md) []	Control point array to be inserted
CPoleWeights?	Number []	Control point weight array (optional)

Returns

void

---

InsertPoleRowAfter

▸ InsertPoleRowAfter(UIndex, CPoles, CPoleWeights?): void

Insert a new control point row after the specified row.

Parameters

Name	Type	Description
The index of the 'UIndes'	' number '	row
CPoles	[Mx3dGePoint] (Mx3dGePoint. md) []	Control point array to be inserted
CPoleWeights?	Number []	Control point weight array (optional)

Returns

void

---

InsertPoleRowBefore

▸ InsertPoleRowBefore(UIndex, CPoles, CPoleWeights?): void

Insert a new control point line before the specified line.

Parameters

Name	Type	Description
The index of the 'UIndes'	' number '	row
CPoles	[Mx3dGePoint] (Mx3dGePoint. md) []	Control point array to be inserted
CPoleWeights?	Number []	Control point weight array (optional)

Returns

void

---

IsCNu

▸ IsCNu(N): boolean

Determine the continuous order in the U direction.

Parameters

Name	Type	Description
N	number	order

Returns

boolean

Returns a Boolean value indicating whether it is continuous.

---

IsCNv

▸ IsCNv(N): boolean

Determine the continuous order in the V direction.

Parameters

Name	Type	Description
N	number	order

Returns

boolean

Returns a Boolean value indicating whether it is continuous.

---

IsUClosed

▸ IsUClosed(): boolean

Determine whether the U direction is closed.

Returns

boolean

Returns a Boolean value indicating whether it is closed or not.

---

IsUPeriodic

▸ IsUPeriodic(): boolean

Determine whether the U direction is periodic.

Returns

boolean

Return a Boolean value indicating whether it is periodic.

---

IsURational

▸ IsURational(): boolean

Determine whether the U direction is a rational surface.

Returns

boolean

Returns the Boolean value of a rational surface.

---

IsVClosed

▸ IsVClosed(): boolean

Determine whether the V direction is closed.

Returns

boolean

Returns a Boolean value indicating whether it is closed or not.

---

IsVPeriodic

▸ IsVPeriodic(): boolean

Determine whether the V direction is periodic.

Returns

boolean

Return a Boolean value indicating whether it is periodic.

---

IsVRational

▸ IsVRational(): boolean

Determine whether the V direction is a rational surface.

Returns

boolean

Returns the Boolean value of a rational surface.

---

MirrorByAxis

▸ MirrorByAxis(A1): void

Mirror transform geometric objects through axes.

Parameters

Name	Type	Description
A1	[Mx3dGeAxis] (Mx3dGeAxis. md)	Axis object

Returns

void

Inherited from

Mx3dGeomBoundedSurface.MirrorByAxis

---

MirrorByCSYSR

▸ MirrorByCSYSR(A2): void

Mirror transform geometric objects using a right-handed coordinate system.

Parameters

Name	Type	Description
A2	[Mx3dGeCSYSR] (Mx3dGeCSYSR. md)	Right hand coordinate system object

Returns

void

Inherited from

Mx3dGeomBoundedSurface.MirrorByCSYSR

---

MirrorByPoint

▸ MirrorByPoint(P): void

Mirror transform geometric objects through points.

Parameters

Name	Type	Description
P	[Mx3dGePoint] (Mx3dGePoint. md)	Point object

Returns

void

Inherited from

Mx3dGeomBoundedSurface.MirrorByPoint

---

MirroredByAxis

▸ MirroredByAxis(A1): Mx3dGeomBezierSurface

Return the new geometric object transformed through axis mirroring.

Parameters

Name	Type	Description
A1	[Mx3dGeAxis] (Mx3dGeAxis. md)	Axis object

Returns

Mx3dGeomBezierSurface

New geometric objects.

Inherited from

Mx3dGeomBoundedSurface.MirroredByAxis

---

MirroredByCSYSR

▸ MirroredByCSYSR(A2): Mx3dGeomBezierSurface

Return the new geometric object after mirror transformation through the right-handed coordinate system.

Parameters

Name	Type	Description
A2	[Mx3dGeCSYSR] (Mx3dGeCSYSR. md)	Right hand coordinate system object

Returns

Mx3dGeomBezierSurface

New geometric objects.

Inherited from

Mx3dGeomBoundedSurface.MirroredByCSYSR

---

MirroredByPoint

▸ MirroredByPoint(P): Mx3dGeomBezierSurface

Return the new geometric object after point mirror transformation.

Parameters

Name	Type	Description
P	[Mx3dGePoint] (Mx3dGePoint. md)	Point object

Returns

Mx3dGeomBezierSurface

New geometric objects.

Inherited from

Mx3dGeomBoundedSurface.MirroredByPoint

---

NbUPoles

▸ NbUPoles(): number

Obtain the number of control points in the U direction.

Returns

number

Return the number of control points in the U direction.

---

NbVPoles

▸ NbVPoles(): number

Obtain the number of control points in the V direction.

Returns

number

Return the number of control points in the V direction.

---

Pole

▸ Pole(UIndex, VIndex): Mx3dGePoint

Retrieve the specified control point location.

Parameters

Name	Type	Description
UIndes	number	U-direction index
VIndes	number	index in the V direction

Returns

Mx3dGePoint

Return to the control point location.

---

Poles

▸ Poles(): Mx3dGePoint[][]

Retrieve all control point arrays.

Returns

Mx3dGePoint[][]

Return a two-dimensional array of control points.

---

RemovePoleCol

▸ RemovePoleCol(VIndex): void

Remove the control point of the specified column.

Parameters

Name	Type	Description
Index of column 'VIndes'	' number '

Returns

void

---

RemovePoleRow

▸ RemovePoleRow(UIndex): void

Remove the control point of the specified row.

Parameters

Name	Type	Description
The index of the 'UIndes'	' number '	row

Returns

void

---

Rotate

▸ Rotate(A1, Ang): void

Rotate geometric objects.

Parameters

Name	Type	Description
A1	[Mx3dGeAxis] (Mx3dGeAxis. md)	Axis object
Ang	number	Rotation angle

Returns

void

Inherited from

Mx3dGeomBoundedSurface.Rotate

---

Rotated

▸ Rotated(A1, Ang): Mx3dGeomBezierSurface

Return the rotated new geometric object.

Parameters

Name	Type	Description
A1	[Mx3dGeAxis] (Mx3dGeAxis. md)	Axis object
Ang	number	Rotation angle

Returns

Mx3dGeomBezierSurface

New geometric objects.

Inherited from

Mx3dGeomBoundedSurface.Rotated

---

Scale

▸ Scale(P, S): void

Scale geometric objects.

Parameters

Name	Type	Description
P	[Mx3dGePoint] (Mx3dGePoint. md)	Point object
S	number	scaling ratio

Returns

void

Inherited from

Mx3dGeomBoundedSurface.Scale

---

Scaled

▸ Scaled(P, S): Mx3dGeomBezierSurface

Return the scaled new geometric object.

Parameters

Name	Type	Description
P	[Mx3dGePoint] (Mx3dGePoint. md)	Point object
S	number	scaling ratio

Returns

Mx3dGeomBezierSurface

New geometric objects.

Inherited from

Mx3dGeomBoundedSurface.Scaled

---

Segment

▸ Segment(U1, U2, V1, V2): void

Define a part of the surface and specify the range of U and V.

Parameters

Name	Type	Description
U1	number	Starting U value
U2	number	End U value
V1	number	Starting V value
V2	Number	End V value

Returns

void

---

SetPole

▸ SetPole(UIndex, VIndex, P, Weight?): void

Set control points and weights for the specified location.

Parameters

Name	Type	Description
UIndes	number	U-direction index
VIndes	number	index in the V direction
P	[Mx3dGePoint] (Mx3dGePoint. md)	Control point position
Weight?	Number	Control point weights (optional)

Returns

void

---

SetPoleCol

▸ SetPoleCol(VIndex, CPoles, CPoleWeights?): void

Set the control points and weights for the specified column.

Parameters

Name	Type	Description
Index of column 'VIndes'	' number '
CPoles	[Mx3dGePoint] (Mx3dGePoint. md) []	Control point array
CPoleWeights?	Number []	Control point weight array (optional)

Returns

void

---

SetPoleRow

▸ SetPoleRow(UIndex, CPoles, CPoleWeights?): void

Set the control points and weights for the specified row.

Parameters

Name	Type	Description
The index of the 'UIndes'	' number '	row
CPoles	[Mx3dGePoint] (Mx3dGePoint. md) []	Control point array
CPoleWeights?	Number []	Control point weight array (optional)

Returns

void

---

SetWeight

▸ SetWeight(UIndex, VIndex, Weight): void

Set the weight of the specified control point.

Parameters

Name	Type	Description
UIndes	number	U-direction index
VIndes	number	index in the V direction
Weight	number	weight value

Returns

void

---

SetWeightCol

▸ SetWeightCol(VIndex, CPoleWeights): void

Set the control point weights for the specified column.

Parameters

Name	Type	Description
Index of column 'VIndes'	' number '
CPoleWeights	number []	Control point weight array

Returns

void

---

SetWeightRow

▸ SetWeightRow(UIndex, CPoleWeights): void

Set the control point weights for the specified row.

Parameters

Name	Type	Description
The index of the 'UIndes'	' number '	row
CPoleWeights	number []	Control point weight array

Returns

void

---

Transform

▸ Transform(T): void

Apply transformation matrix to surface.

Parameters

Name	Type	Description
T	[Mx3dGetStrf] (Mx3dGetStrf. md)	Transform matrix

Returns

void

---

TransformParameters

▸ TransformParameters(UV, T): void

Transform the surface parameters according to the given transformation matrix T.

Parameters

Name	Type	Description
UV	[dU: number, dV: number]	Parameter array containing the values of U and V
T	[Mx3dGetStrf] (Mx3dGetStrf. md)	Transform matrix

Returns

void

Inherited from

Mx3dGeomBoundedSurface.TransformParameters

---

Transformed

▸ Transformed(T): Mx3dGeomBezierSurface

Return the transformed new geometric object.

Parameters

Name	Type	Description
T	[Mx3dGetStrf] (Mx3dGetStrf. md)	Transform the object

Returns

Mx3dGeomBezierSurface

New geometric objects.

Inherited from

Mx3dGeomBoundedSurface.Transformed

---

TranslateBy2Points

▸ TranslateBy2Points(P1, P2): void

Translate geometric objects through two points.

Parameters

Name	Type	Description
P1	[Mx3dGePoint] (Mx3dGePoint. md)	Starting point object
P2	[Mx3dGePoint] (Mx3dGePoint. md)	End point object

Returns

void

Inherited from

Mx3dGeomBoundedSurface.TranslateBy2Points

---

TranslateByVec

▸ TranslateByVec(V): void

Translate geometric objects through vectors.

Parameters

Name	Type	Description
V	[Mx3dGeVec] (Mx3dGeVec. md)	Vector object

Returns

void

Inherited from

Mx3dGeomBoundedSurface.TranslateByVec

---

TranslatedBy2Points

▸ TranslatedBy2Points(P1, P2): Mx3dGeomBezierSurface

Return the new geometric object after translating through two points.

Parameters

Name	Type	Description
P1	[Mx3dGePoint] (Mx3dGePoint. md)	Starting point object
P2	[Mx3dGePoint] (Mx3dGePoint. md)	End point object

Returns

Mx3dGeomBezierSurface

New geometric objects.

Inherited from

Mx3dGeomBoundedSurface.TranslatedBy2Points

---

TranslatedByVec

▸ TranslatedByVec(V): Mx3dGeomBezierSurface

Return the new geometric object after vector translation.

Parameters

Name	Type	Description
V	[Mx3dGeVec] (Mx3dGeVec. md)	Vector object

Returns

Mx3dGeomBezierSurface

New geometric objects.

Inherited from

Mx3dGeomBoundedSurface.TranslatedByVec

---

UDegree

▸ UDegree(): number

Obtain the order in the U direction.

Returns

number

Return the order in the U direction.

---

UPeriod

▸ UPeriod(): number

Return the period of the surface in the U direction.

Returns

number

The period of the surface in the U direction.

Inherited from

Mx3dGeomBoundedSurface.UPeriod

---

UReverse

▸ UReverse(): void

Reverse the parameter in the U direction.

Returns

void

---

UReversed

▸ UReversed(): Mx3dGeomBezierSurface

Parameterization of reversing the U direction.

Returns

Mx3dGeomBezierSurface

Return the current object to implement a chain call.

Inherited from

Mx3dGeomBoundedSurface.UReversed

---

UReversedParameter

▸ UReversedParameter(U): number

Calculate the reverse U parameter.

Parameters

Name	Type	Description
U	number	parameter U value

Returns

number

Return the reverse parameter.

---

VPeriod

▸ VPeriod(): number

Return the period of the surface in the V direction.

Returns

number

The period of the surface in the V direction.

Inherited from

Mx3dGeomBoundedSurface.VPeriod

---

VReverse

▸ VReverse(): void

Reverse the parameters in the V direction.

Returns

void

---

VReversed

▸ VReversed(): Mx3dGeomBezierSurface

Parameterization of reversing the V direction.

Returns

Mx3dGeomBezierSurface

Return the current object to implement a chain call.

Inherited from

Mx3dGeomBoundedSurface.VReversed

---

VReversedParameter

▸ VReversedParameter(V): number

Calculate the reverse V parameter.

Parameters

Name	Type	Description
V	number	parameter V value

Returns

number

Return the reverse parameter.

---

Value

▸ Value(U, V): Mx3dGePoint

Calculate the points on the surface corresponding to the parameters (U, V).

Parameters

Name	Type	Description
U	number	Surface parameter U
V	number	Surface parameter V

Returns

Mx3dGePoint

Corresponding point.

Inherited from

Mx3dGeomBoundedSurface.Value

---

Weight

▸ Weight(UIndex, VIndex): number

Obtain the weight of the specified control point.

Parameters

Name	Type	Description
UIndes	number	U-direction index
VIndes	number	index in the V direction

Returns

number

Return weight values.

---

Weights

▸ Weights(): number[][]

Retrieve an array of all control point weights.

Returns

number[][]

Return a two-dimensional array of control point weights.

---

DownCast

▸ Static DownCast(theObject): Mx3dGeomBezierSurface

Parameters

Name	Type
theObject	Mx3dGeomObject

Returns

Mx3dGeomBezierSurface