[mxcad_3d API Document](../README. md)/Mx3dGeomToroidalSurface

Class: Mx3dGeomToroidalSurface

Representing a Toroidal Surface in three-dimensional space. This type encapsulates the functionality of manipulating torus properties and methods.

Hierarchy

• Mx3dGeomElementarySurface

  ↳ Mx3dGeomToroidalSurface

Table of contents

Constructors

• constructor

Methods

• Area
• Axis
• Bounds
• Coefficients
• Continuity
• Copy
• D0
• D1
• D2
• D3
• DN
• DynamicType
• Face
• IsCNu
• IsCNv
• IsUClosed
• IsUPeriodic
• IsVClosed
• IsVPeriodic
• Location
• MajorRadius
• MinorRadius
• MirrorByAxis
• MirrorByCSYSR
• MirrorByPoint
• MirroredByAxis
• MirroredByCSYSR
• MirroredByPoint
• Position
• Rotate
• Rotated
• Scale
• Scaled
• SetAxis
• SetLocation
• SetMajorRadius
• SetMinorRadius
• SetPosition
• Transform
• TransformParameters
• Transformed
• TranslateBy2Points
• TranslateByVec
• TranslatedBy2Points
• TranslatedByVec
• UPeriod
• UReverse
• UReversed
• UReversedParameter
• VPeriod
• VReverse
• VReversed
• VReversedParameter
• Value
• Volume
• DownCast

Constructors

constructor

• new Mx3dGeomToroidalSurface(A3, MajorRadius, MinorRadius)

Construct a torus with a given coordinate system and primary and secondary radii.

Parameters

Name	Type	Description
A3	Mx3dGeCSYSR (Mx3dGeCSYSR. md)	Surface Local Coordinate System (Mx3dGeCSYSR)
MajorRadius	number	The main radius of the torus
MinorRadius	number	The minor radius of the torus

Overrides

Mx3dGeomElementarySurface.constructor

Methods

Area

▸ Area(): number

Calculate and return the surface area of the torus.

Returns

number

Surface area.

---

Axis

▸ Axis(): Mx3dGeAxis

Obtain the main axis (Z-axis) of the surface.

Returns

Mx3dGeAxis

Definition of the main axis on the surface.

Inherited from

Mx3dGeomElementarySurface.Axis

---

Bounds

▸ Bounds(U1U2V1V2): void

Set the boundary of the parameter range.

Parameters

Name	Type	Description
U1U2V1V2	[dU1: number, dU2: number, dV1: number, dV2: number]	Parameter range [U1, U2, V1, V2]

Returns

void

---

Coefficients

▸ Coefficients(Coef): void

Obtain implicit equation coefficients.

Parameters

Name	Type	Description
Coef	number []	coefficient array, with a length of at least 31

Returns

void

---

Continuity

▸ Continuity(): MxGAShapeEnum

Return the global continuity of the surface (MxGAShapeenum).

Returns

MxGAShapeEnum

The continuity of the surface on a global scale.

Inherited from

Mx3dGeomElementarySurface.Continuity

---

Copy

▸ Copy(): Mx3dGeomObject

Create a new object that is a copy of this torus.

Returns

Mx3dGeomObject

Copy of the torus (Mx3dGeomObject).

---

D0

▸ D0(U, V, P): void

Calculate and return the point at the specified U and V parameters.

Parameters

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

Returns

void

---

D1

▸ D1(U, V, P, D1U, D1V): void

Calculate the first derivative of the current point and the U and V directions.

Parameters

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

Returns

void

---

D2

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

Calculate the current point, first and second derivatives.

Parameters

Name	Type	Description
U	number	parameter U
V	number	parameter V
P	[Mx3dGePoint] (Mx3dGePoint. md)	Output Point (Mx3dGePoint)
D1U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first derivative in the U direction (Mx3dGeVec)
D1V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first derivative in the V direction (Mx3dGeVec)
D2U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative in the U direction (Mx3dGeVec)
D2V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative in the V direction (Mx3dGeVec)
D2UV	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second-order mixed derivative in the U and V directions (Mx3dGeVec)

Returns

void

---

D3

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

Calculate the current point, first, second, and third derivatives.

Parameters

Name	Type	Description
U	number	parameter U
V	number	parameter V
P	[Mx3dGePoint] (Mx3dGePoint. md)	Output Point (Mx3dGePoint)
D1U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first derivative in the U direction (Mx3dGeVec)
D1V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the first derivative in the V direction (Mx3dGeVec)
D2U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative in the U direction (Mx3dGeVec)
D2V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second derivative in the V direction (Mx3dGeVec)
D2UV	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second-order mixed derivative in the U and V directions (Mx3dGeVec)
D3U	[Mx3dGeVec] (Mx3dGeVec. md)	Output the third derivative in the U direction (Mx3dGeVec)
D3V	[Mx3dGeVec] (Mx3dGeVec. md)	Output the third derivative in the V direction (Mx3dGeVec)
D3UUV	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second-order mixed third-order derivative in the U direction (Mx3dGeVec)
D3UVV	[Mx3dGeVec] (Mx3dGeVec. md)	Output the second-order mixed third-order derivative in the V direction (Mx3dGeVec)

Returns

void

---

DN

▸ DN(U, V, Nu, Nv): Mx3dGeVec

Calculate the higher-order derivative at the specified parameters (U, V).

Parameters

Name	Type	Description
U	number	parameter U
V	number	parameter V
Nu	number	The U-direction order of higher-order derivatives
Nv	number	The V-direction order of higher-order derivatives

Returns

Mx3dGeVec

Higher order derivative (Mx3dGeVec).

---

DynamicType

▸ DynamicType(): string

Return the dynamic type string of the object.

Returns

string

Dynamic type string.

Overrides

Mx3dGeomElementarySurface.DynamicType

---

Face

▸ Face(TolDegen): Mx3dShapeFace

Create a plane representing a torus (represented by a face).

Parameters

Name	Type	Description
TolDegen	number	Degradation tolerance

Returns

Mx3dShapeFace

Flat (Mx3dShapeFace).

▸ Face(W, Inside): Mx3dShapeFace

Create a plane representing a torus (represented by lines).

Parameters

Name	Type	Description
W	[Mx3dShapeWire] (Mx3dShapeWire. md)	Line (Mx3dShapeWire)
Inside	boolean	indicates whether the torus is inside

Returns

Mx3dShapeFace

Flat (Mx3dShapeFace).

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

Create a plane representing a torus (specifying the range of U, V).

Parameters

Name	Type	Description
UMin	number	minimum U parameter
UMax	number	Maximum U parameter
VMin	number	minimum V parameter
VMax	number	maximum V parameter
TolDegen	number	Degradation tolerance

Returns

Mx3dShapeFace

Flat (Mx3dShapeFace).

---

IsCNu

▸ IsCNu(N): boolean

Check if the continuity of the surface in the U parameter direction meets the specified level.

Parameters

Name	Type	Description
N	number	The continuity level to be checked

Returns

boolean

If the continuity level meets the condition, return true; Otherwise, return false.

Inherited from

Mx3dGeomElementarySurface.IsCNu

---

IsCNv

▸ IsCNv(N): boolean

Check if the continuity of the surface in the V-parameter direction meets the specified level.

Parameters

Name	Type	Description
N	number	The continuity level to be checked

Returns

boolean

If the continuity level meets the condition, return true; Otherwise, return false.

Inherited from

Mx3dGeomElementarySurface.IsCNv

---

IsUClosed

▸ IsUClosed(): boolean

Check if the torus U direction is closed.

Returns

boolean

If the U direction is closed, return true; otherwise, return false.

---

IsUPeriodic

▸ IsUPeriodic(): boolean

Check if the U direction of the torus is periodic.

Returns

boolean

If the U direction is periodic, return true; otherwise, return false.

---

IsVClosed

▸ IsVClosed(): boolean

Check if the V-direction of the torus is closed.

Returns

boolean

If the V direction is closed, return true; otherwise, return false.

---

IsVPeriodic

▸ IsVPeriodic(): boolean

Check if the V-direction of the torus is periodic.

Returns

boolean

If the V direction is periodic, return true; otherwise, return false.

---

Location

▸ Location(): Mx3dGePoint

Obtain the position points of the local coordinate system on the surface.

Returns

Mx3dGePoint

Surface location points.

Inherited from

Mx3dGeomElementarySurface.Location

---

MajorRadius

▸ MajorRadius(): number

Return the main radius of the torus.

Returns

number

Main radius.

---

MinorRadius

▸ MinorRadius(): number

Return the secondary radius of the torus.

Returns

number

Secondary radius.

---

MirrorByAxis

▸ MirrorByAxis(A1): void

Mirror transform geometric objects through axes.

Parameters

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

Returns

void

Inherited from

Mx3dGeomElementarySurface.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

Mx3dGeomElementarySurface.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

Mx3dGeomElementarySurface.MirrorByPoint

---

MirroredByAxis

▸ MirroredByAxis(A1): Mx3dGeomToroidalSurface

Return the new geometric object transformed through axis mirroring.

Parameters

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

Returns

Mx3dGeomToroidalSurface

New geometric objects.

Inherited from

Mx3dGeomElementarySurface.MirroredByAxis

---

MirroredByCSYSR

▸ MirroredByCSYSR(A2): Mx3dGeomToroidalSurface

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

Mx3dGeomToroidalSurface

New geometric objects.

Inherited from

Mx3dGeomElementarySurface.MirroredByCSYSR

---

MirroredByPoint

▸ MirroredByPoint(P): Mx3dGeomToroidalSurface

Return the new geometric object after point mirror transformation.

Parameters

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

Returns

Mx3dGeomToroidalSurface

New geometric objects.

Inherited from

Mx3dGeomElementarySurface.MirroredByPoint

---

Position

▸ Position(): Mx3dGeCSYSR

Obtain the local coordinate system of the surface.

Returns

Mx3dGeCSYSR

The local coordinate system of the surface.

Inherited from

Mx3dGeomElementarySurface.Position

---

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

Mx3dGeomElementarySurface.Rotate

---

Rotated

▸ Rotated(A1, Ang): Mx3dGeomToroidalSurface

Return the rotated new geometric object.

Parameters

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

Returns

Mx3dGeomToroidalSurface

New geometric objects.

Inherited from

Mx3dGeomElementarySurface.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

Mx3dGeomElementarySurface.Scale

---

Scaled

▸ Scaled(P, S): Mx3dGeomToroidalSurface

Return the scaled new geometric object.

Parameters

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

Returns

Mx3dGeomToroidalSurface

New geometric objects.

Inherited from

Mx3dGeomElementarySurface.Scaled

---

SetAxis

▸ SetAxis(theA1): void

Set the main axis (Z-axis) of the surface.

Parameters

Name	Type	Description
TheA1	[Mx3dGeAxis] (Mx3dGeAxis. md)	Definition of the principal axis of the surface

Returns

void

Inherited from

Mx3dGeomElementarySurface.SetAxis

---

SetLocation

▸ SetLocation(theLoc): void

Set the position points of the surface local coordinate system.

Parameters

Name	Type	Description
TheLoc	[Mx3dGePoint] (Mx3dGePoint. md)	New location point

Returns

void

Inherited from

Mx3dGeomElementarySurface.SetLocation

---

SetMajorRadius

▸ SetMajorRadius(MajorRadius): void

Set the main radius of the torus.

Parameters

Name	Type	Description
MajorRadius	number	New primary radius. It must be non negative

Returns

void

---

SetMinorRadius

▸ SetMinorRadius(MinorRadius): void

Set the secondary radius of the torus.

Parameters

Name	Type	Description
MinorRadius	number	New secondary radius. It must be non negative

Returns

void

---

SetPosition

▸ SetPosition(theAx3): void

Set the local coordinate system of the surface.

Parameters

Name	Type	Description
TheAx3	[Mx3dGeCSYSR] (Mx3dGeCSYSR. md)	A new coordinate system that includes position and orientation

Returns

void

Inherited from

Mx3dGeomElementarySurface.SetPosition

---

Transform

▸ Transform(T): void

Apply the transformation T to the torus.

Parameters

Name	Type	Description
T	[Mx3dGeTsf] (Mx3dGeTsf. md)	Transform (Mx3dGeTsf)

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

Mx3dGeomElementarySurface.TransformParameters

---

Transformed

▸ Transformed(T): Mx3dGeomToroidalSurface

Return the transformed new geometric object.

Parameters

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

Returns

Mx3dGeomToroidalSurface

New geometric objects.

Inherited from

Mx3dGeomElementarySurface.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

Mx3dGeomElementarySurface.TranslateBy2Points

---

TranslateByVec

▸ TranslateByVec(V): void

Translate geometric objects through vectors.

Parameters

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

Returns

void

Inherited from

Mx3dGeomElementarySurface.TranslateByVec

---

TranslatedBy2Points

▸ TranslatedBy2Points(P1, P2): Mx3dGeomToroidalSurface

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

Mx3dGeomToroidalSurface

New geometric objects.

Inherited from

Mx3dGeomElementarySurface.TranslatedBy2Points

---

TranslatedByVec

▸ TranslatedByVec(V): Mx3dGeomToroidalSurface

Return the new geometric object after vector translation.

Parameters

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

Returns

Mx3dGeomToroidalSurface

New geometric objects.

Inherited from

Mx3dGeomElementarySurface.TranslatedByVec

---

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

Mx3dGeomElementarySurface.UPeriod

---

UReverse

▸ UReverse(): void

Reverse the parameterization direction of the surface in the U parameter direction.

Returns

void

Inherited from

Mx3dGeomElementarySurface.UReverse

---

UReversed

▸ UReversed(): Mx3dGeomToroidalSurface

Parameterization of reversing the U direction.

Returns

Mx3dGeomToroidalSurface

Return the current object to implement a chain call.

Inherited from

Mx3dGeomElementarySurface.UReversed

---

UReversedParameter

▸ UReversedParameter(U): number

Calculate the parameter value of the torus U direction reversed on a given U parameter.

Parameters

Name	Type	Description
U	number	The original U parameter

Returns

number

The inverted U parameter value.

---

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

Mx3dGeomElementarySurface.VPeriod

---

VReverse

▸ VReverse(): void

Reverse the parameterization direction of the surface in the V parameter direction.

Returns

void

Inherited from

Mx3dGeomElementarySurface.VReverse

---

VReversed

▸ VReversed(): Mx3dGeomToroidalSurface

Parameterization of reversing the V direction.

Returns

Mx3dGeomToroidalSurface

Return the current object to implement a chain call.

Inherited from

Mx3dGeomElementarySurface.VReversed

---

VReversedParameter

▸ VReversedParameter(V): number

Calculate the parameter value of the torus V direction reversed on the given V parameter.

Parameters

Name	Type	Description
V	number	The original V parameter

Returns

number

The inverted value of the V 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

Mx3dGeomElementarySurface.Value

---

Volume

▸ Volume(): number

Calculate and return the volume of the torus.

Returns

number

Volume.

---

DownCast

▸ Static DownCast(theObject): Mx3dGeomToroidalSurface

Convert parent object to Mx3dGeomToroidalSurface class object

Parameters

Name	Type	Description
TheObject	[Mx3dGeomObject] (Mx3dGeomObject. md)	Parent class object

Returns

Mx3dGeomToroidalSurface

Mx3dGeomToroidalSurface class object