3D Modeling

Classes
class	Axis3D
	The axis is a vector which is attached to a fixed point. More...
class	Curve3D
	Curve in three-dimensional space. More...
class	Matrix3D
	The matrix of transformation in a three-dimensional space. More...
class	Placement3D
	Local coordinate system in three dimensional space. More...
class	Point3D
	Three-dimensional point. More...
class	Solid
	Solid body. More...
class	Vector3D
	Three-dimensional vector. More...

Topics
	Operation parameters

Enumerations
enum	CoordinateSystem3D { Cartesian , Cylindrical , Spherical }
	Types of coordinate system in three dimensional space. More...

Functions
Curve3D	CreateLineSegment3D (Point3D startPoint, Point3D endPoint)
	Creates line segment.
Curve3D	CreateCircle3D (Point3D center, Vector3D normal, number radius)
	Creates circle.
Curve3D	CreateArc3DByThreePoints (Point3D startPoint, Point3D intermediatePoint, Point3D endPoint)
	Creates circular arc from startPoint to endPoint through intermediatePoint.
Curve3D	CreateArc3DByCenterStartEndPoints (Point3D centerPoint, Point3D startPoint, Point3D endPoint, bool clockwise)
	Creates circular arc by center, start and end points.
Curve3D	CreateEllipse3D (Point3D center, Vector3D normal, Vector3D majorVector, number majorRadius, number minorRadius)
	Creates ellipse.
Curve3D	CreateRectangle3D (Point3D center, Vector3D normal, Vector3D widthVector, number width, number height)
	Creates a rectangle as the closed composite curve of the four line segments in 3D space.
Curve3D	CreateEllipticalArc3D (Point3D center, Vector3D normal, Vector3D majorVector, number majorRadius, number minorRadius, Point3D startPoint, Point3D endPoint, boolean clockwise)
	Creates elliptical arc.
Curve3D	CreateParametricCurve3D (string xFunction, string yFunction, string zFunction, CoordinateSystem3D coordinateSystem, number tStart, number tEnd, Placement3D oPlacement)
	Creates a curve described by parametric functions in 3D space.
Curve3D	CreatePolyline3D (table points)
	Creates a composite curve from line segments by points.
Curve3D	CreateCompositeCurve3D (table curves)
	Creates a composite curve.The start point of every curve should be equal to the end point of previous one.
Axis3D	CreateXAxis3D ()
	Creates X axis.
Axis3D	CreateYAxis3D ()
	Creates Y axis.
Axis3D	CreateZAxis3D ()
	Creates Z axis.
Solid	CreateBlock (number xSize, number ySize, number zSize, Placement3D oPlacement)
	Creates a rectangular parallelepiped.
Solid	CreateRightCircularCylinder (number radius, number height, Placement3D oPlacement)
	Creates a right circular cylinder.
Solid	CreateRightEllipticalCylinder (number radiusX, number radiusY, number height, Placement3D oPlacement)
	Creates a right elliptical cylinder.
Solid	CreateRightPrism (table points, number height, Placement3D oPlacement)
	Creates a right prism.
Solid	CreateSphere (number radius, Point3D oPoint)
	Creates a sphere.
Solid	CreateRightCircularCone (number radius, number height, Placement3D oPlacement)
	Creates a cone.
Solid	CreateRectangularPyramid (number width, number depth, number height, Placement3D oPlacement)
	Creates a rectangular pyramid in local coordinate system.
Solid	CreateSweptDiskSolid (number radius, number innerRadius, Curve3D path)
	Creates a swept disk solid.
Solid	Extrude (Curve2D contour, ExtrusionParameters parameters, Placement3D oPlacement)
	Creates an extrusion solid.
Solid	Loft (table profiles, table placements, LoftParameters oParameters)
	Creates lofted solid.
Solid	Evolve (Curve2D profile, Placement3D placement, Curve3D path, EvolutionParameters oParameters)
	Creates an evolution solid.
Solid	Revolve (Curve2D generatrixCurve, Placement3D initialCurvePlacement, Axis3D rotationAxis, RevolutionParameters parameters)
	Creates a revolution solid. The revolution body is built by rotating a flat generatrix curve around the axis by a given angle.
nil	FilletCorners3D (Curve3D curve, number radius)
	Rounds all corners of a composite curve.
nil	FilletCornerAfterSegment3D (Curve3D curve, number segmentIndex, number radius)
	Rounds the corner between the segment with index segmentIndex and next one.
Solid	Unite (Solid solid1, Solid solid2)
	Performs a solids boolean union operation.
Solid	Unite (table solids)
	Performs a solids boolean union operation.
Solid	Subtract (Solid solid1, Solid solid2)
	Performs a solids boolean subtracting operation.
Solid	Intersect (Solid solid1, Solid solid2)
	Performs a solids boolean intersection operation.

Enumeration Type Documentation

CoordinateSystem3D

enum CoordinateSystem3D

Types of coordinate system in three dimensional space.

Enumerator
Cartesian	Cartesian coordinate system.
Cylindrical	Cylindrical coordinate system.
Spherical	Spherical coordinate system.

Function Documentation

CreateArc3DByCenterStartEndPoints()

Curve3D CreateArc3DByCenterStartEndPoints	(	Point3D	centerPoint,
		Point3D	startPoint,
		Point3D	endPoint,
		bool	clockwise )

Creates circular arc by center, start and end points.

Parameters

centerPoint	The center of the arc.
startPoint	The start point of the arc. It defines the radius.
endPoint	The end point of the arc.
clockwise	The direction of the arc. If it is true, then the direction is clockwise, if viewed against of the vector product of the vectors (startPoint - centerPoint) and (endPoint - centerPoint).

CreateArc3DByThreePoints()

Curve3D CreateArc3DByThreePoints	(	Point3D	startPoint,
		Point3D	intermediatePoint,
		Point3D	endPoint )

Creates circular arc from startPoint to endPoint through intermediatePoint.

Parameters

startPoint	The start point of the arc.
intermediatePoint	The point lying on the arc.
endPoint	The end point of the arc.

CreateBlock()

Solid CreateBlock	(	number	xSize,
		number	ySize,
		number	zSize,
		Placement3D	oPlacement )

Creates a rectangular parallelepiped.

The bottom center is located at the origin of the given coordinate system, edges are parallel to axes.

Parameters

xSize	Length of edges parallel to the X axis.
ySize	Length of edges parallel to the Y axis.
zSize	Length of edges parallel to the Z axis.
oPlacement	[opt] The coordinate system in which the solid is created. If not specified, the global coordinate system is used.

CreateCircle3D()

Curve3D CreateCircle3D	(	Point3D	center,
		Vector3D	normal,
		number	radius )

Creates circle.

Parameters

center	A circle center.
normal	A vector orthogonal to the circle plane.
radius	Radius.

CreateCompositeCurve3D()

Curve3D CreateCompositeCurve3D

(

table

curves

)

Creates a composite curve.The start point of every curve should be equal to the end point of previous one.

Parameters

curves

A set of curves (Curve3D).

CreateEllipse3D()

Curve3D CreateEllipse3D	(	Point3D	center,
		Vector3D	normal,
		Vector3D	majorVector,
		number	majorRadius,
		number	minorRadius )

Creates ellipse.

Parameters

center	The center of the ellipse.
normal	The vector orthogonal to the plane of the ellipse.
majorVector	The vector co-directed with the first semi-axis. The second semi-axis is co-directed with the vector product normal*majorVector.
majorRadius	The value of the first semi-axis.
minorRadius	The value of the second semi-axis.

CreateEllipticalArc3D()

Curve3D CreateEllipticalArc3D	(	Point3D	center,
		Vector3D	normal,
		Vector3D	majorVector,
		number	majorRadius,
		number	minorRadius,
		Point3D	startPoint,
		Point3D	endPoint,
		boolean	clockwise )

Creates elliptical arc.

Parameters

center	The center of the ellipse.
normal	The vector orthogonal to the plane of the ellipse.
majorVector	The vector co-directed with the first semi-axis. The second semi-axis is co-directed with the vector product normal*majorVector.
majorRadius	The value of the first semi-axis.
minorRadius	The value of the second semi-axis.
startPoint	The start point of the arc.
endPoint	The end point of the arc.
clockwise	The arc direction. If equal to true, the arc directs clockwise if viewed against vector 'normal'.

CreateLineSegment3D()

Curve3D CreateLineSegment3D	(	Point3D	startPoint,
		Point3D	endPoint )

Creates line segment.

Parameters

startPoint	The start point of the segment.
endPoint	The end point of the segment.

CreateParametricCurve3D()

Curve3D CreateParametricCurve3D	(	string	xFunction,
		string	yFunction,
		string	zFunction,
		CoordinateSystem3D	coordinateSystem,
		number	tStart,
		number	tEnd,
		Placement3D	oPlacement )

Creates a curve described by parametric functions in 3D space.

This function generates a curve described by parametric functions xFunction, yFunction and zFunction. The type of coordinate system is indicated by the parameter coordinateSystem. The initial value of the parameter tStart and the final value tEnd are used to define the parameter range of the curve.

The parametric functions xFunction(t), yFunction(t) and zFunction(t) are scalar functions that depend on a common parameter t and are defined as symbolic expressions.

For a cylindrical coordinate system, the functions xFunction, yFunction, zFunction describe the parameters p, φ, z, respectively. For a spherical coordinate system, the functions xFunction, yFunction, zFunction describe the parameters r, θ, φ, respectively.

Parameters

xFunction	Expression describing the dependence of the X coordinate on the parameter.
yFunction	Expression describing the dependence of the Y coordinate on the parameter.
zFunction	Expression describing the dependence of the Z coordinate on the parameter.
coordinateSystem	Coordinate system.
tStart	Minimum parameter value.
tEnd	Maximum parameter value.
oPlacement	[opt] The coordinate system in which the solid is created. If not specified, the global coordinate system is used.

CreatePolyline3D()

Curve3D CreatePolyline3D

(

table

points

)

Creates a composite curve from line segments by points.

Parameters

points

Set of points (Point3D).

CreateRectangle3D()

Curve3D CreateRectangle3D	(	Point3D	center,
		Vector3D	normal,
		Vector3D	widthVector,
		number	width,
		number	height )

Creates a rectangle as the closed composite curve of the four line segments in 3D space.

Parameters

center	The center of the rectangle.
normal	The vector orthogonal to the plane of the rectangle.
widthVector	The vector parallel to the rectangle side of size 'width'.
width	Width.
height	Height.

CreateRectangularPyramid()

Solid CreateRectangularPyramid	(	number	width,
		number	depth,
		number	height,
		Placement3D	oPlacement )

Creates a rectangular pyramid in local coordinate system.

The base center matches with the center of local coordinate system.

Parameters

width	Base width along the local X axis.
depth	Base depth along the local Y axis.
height	Height.
oPlacement	[opt] The coordinate system in which the solid is created. If not specified, the global coordinate system is used.

CreateRightCircularCone()

Solid CreateRightCircularCone	(	number	radius,
		number	height,
		Placement3D	oPlacement )

Creates a cone.

Base center at the origin, the axis is the same as the Z axis.

Parameters

radius	Base radius.
height	Height.
oPlacement	[opt] The coordinate system in which the solid is created. If not specified, the global coordinate system is used.

CreateRightCircularCylinder()

Solid CreateRightCircularCylinder	(	number	radius,
		number	height,
		Placement3D	oPlacement )

Creates a right circular cylinder.

The bottom center is located at the origin of the given coordinate system, the axis is the same as the Z axis.

Parameters

radius	Radius.
height	Height.
oPlacement	[opt] The coordinate system in which the solid is created. If not specified, the global coordinate system is used.

CreateRightEllipticalCylinder()

Solid CreateRightEllipticalCylinder	(	number	radiusX,
		number	radiusY,
		number	height,
		Placement3D	oPlacement )

Creates a right elliptical cylinder.

The bottom center is located at the origin of the given coordinate system, the axis is the same as the Z axis.

Parameters

radiusX	Radius along X axis.
radiusY	Radius along Y axis.
height	Height.
oPlacement	[opt] The coordinate system in which the solid is created. If not specified, the global coordinate system is used.

CreateRightPrism()

Solid CreateRightPrism	(	table	points,
		number	height,
		Placement3D	oPlacement )

Creates a right prism.

The bottom face is located on the XY-plane of the transferred coordinate system, the axis coincides with the Z axis.

Parameters

points	A list of points (Point2D) that defines the edges of the prism.
height	Height.
oPlacement	[opt] The coordinate system in which the solid is created. If not specified, the global coordinate system is used.

CreateSphere()

Solid CreateSphere	(	number	radius,
		Point3D	oPoint )

Creates a sphere.

Parameters

radius	Radius.
oPoint	[opt] Center of the sphere, the default origin.

CreateSweptDiskSolid()

Solid CreateSweptDiskSolid	(	number	radius,
		number	innerRadius,
		Curve3D	path )

Creates a swept disk solid.

A swept disk solid is the solid produced by sweeping a circular disk along a three dimensional curve.

Parameters

radius	The radius of the circular disk to be swept.
innerRadius	The radius of a circular hole in the center of the disk.
path	Guide curve.

Evolve()

Solid Evolve	(	Curve2D	profile,
		Placement3D	placement,
		Curve3D	path,
		EvolutionParameters	oParameters )

Creates an evolution solid.

The evolution solid is built by moving the generating curve along the guide curve.

Parameters

profile	Generatrix curve.
placement	Coordinate system (Placement3D) in the XY plane of which the profile is located.
path	Guide curve.
oParameters	[opt] Evolution operation parameters.

Example

local profile = CreateCircle2D(Point2D(0, 0), 25)
local placement = Placement3D(Point3D(0, 0, 0), Vector3D(0, 0, 1), Vector3D(1, 0, 0))
local path = CreateCompositeCurve3D{CreateLineSegment3D(Point3D(0, 0, 0), Point3D(0, 0, 400)),
                                    CreateArc3DByThreePoints(Point3D(0, 0, 400), Point3D(250, 0, 650), Point3D(500, 0, 400))}
parameter = EvolutionParameters()
parameter.OutwardOffset = 10
solid = Evolve(profile, placement, path, parameter):ShowTangentEdges(false)

Extrude()

Solid Extrude	(	Curve2D	contour,
		ExtrusionParameters	parameters,
		Placement3D	oPlacement )

Creates an extrusion solid.

The base lies in the XY-plane, solid depth, direction, draft angle are determined by operation parameters.

Parameters

contour	Base contour.
parameters	Extrusion operation parameters.
oPlacement	[opt] The coordinate system in which the solid is created. If not specified, the global coordinate system is used.

Example

local contour = CreateEllipse2D(Point2D(0, 0), 0, 200, 100)
local placement = Placement3D(Point3D(0, 0, 0), Vector3D(1, 0, 0), Vector3D(0, 1, 0))
local parameters = ExtrusionParameters (200, 200)
parameters.OutwardOffset = 5
parameters.InwardOffset = 5
solid = Extrude(contour, parameters, placement)

FilletCornerAfterSegment3D()

nil FilletCornerAfterSegment3D	(	Curve3D	curve,
		number	segmentIndex,
		number	radius )

Rounds the corner between the segment with index segmentIndex and next one.

Parameters

curve	Composite curve with corners to fillet.
segmentIndex	The index of the first segment of the contour, 1 <= segmentIndex < N-1 for open curve or 1 <= segmentIndex < N for closed curve, where N - the count of the segments in the composite curve.
radius	Fillet radius.

FilletCorners3D()

nil FilletCorners3D	(	Curve3D	curve,
		number	radius )

Rounds all corners of a composite curve.

Parameters

curve	Composite curve with corners to fillet.
radius	Fillet radius.

Intersect()

Solid Intersect	(	Solid	solid1,
		Solid	solid2 )

Performs a solids boolean intersection operation.

Parameters

solid1	The first operand of the operation.
solid2	The second operand of the operation.

Loft()

Solid Loft	(	table	profiles,
		table	placements,
		LoftParameters	oParameters )

Creates lofted solid.

The surface of the body passes along all given plane curves. The size of the profiles array must be equal to the size of the placements array.

Parameters

profiles	Array of 2D section curves (Curve2D).
placements	Array of coordinate systems (Placement3D). The curves are located in the XY-planes.
oParameters	[opt] Loft operation parameters.

Example

local profiles = {CreateRectangle2D(Point2D(0, 0), 0, 100, 200),
                 CreateCircle2D(Point2D(0, 0), 300)}
local placements = {Placement3D(Point3D(0, 0, 0), Vector3D(0, 0, 1), Vector3D(1, 0, 0)),
                    Placement3D(Point3D(1000, 0, 1000), Vector3D(1, 0, 0), Vector3D(0, 0, 1))}
parameters = LoftParameters()
parameters.GuideCurve = CreateArc3DByCenterStartEndPoints(Point3D(1000, 0, 0), Point3D(0, 0, 0), Point3D(1000, 0, 1000))
solid = Loft(profiles, placements, parameters)

Revolve()

Solid Revolve	(	Curve2D	generatrixCurve,
		Placement3D	initialCurvePlacement,
		Axis3D	rotationAxis,
		RevolutionParameters	parameters )

Creates a revolution solid. The revolution body is built by rotating a flat generatrix curve around the axis by a given angle.

Parameters

generatrixCurve	A generatrix curve.
initialCurvePlacement	A coordinate system. The generatrix curve lies in the XY-plane.
rotationAxis	A rotation axis.
parameters	Revolution operation parameters.

Example

local generatrixCurve = CreateLineSegment2D(Point2D(0, 300), Point2D(400, 0))
local initialCurvePlacement = Placement3D(Point3D(0, 0, 0), Vector3D(1, 0, 0), Vector3D(0, 1, 0))
local parameters =  RevolutionParameters(math.pi)
parameters.InwardOffset = 10
solid = Revolve(generatrixCurve, initialCurvePlacement, CreateZAxis3D(), parameters)

Subtract()

Solid Subtract	(	Solid	solid1,
		Solid	solid2 )

Performs a solids boolean subtracting operation.

Parameters

solid1	The solid to subtract from.
solid2	The solid to be subtracted.

Unite() [1/2]

Solid Unite	(	Solid	solid1,
		Solid	solid2 )

Performs a solids boolean union operation.

Parameters

solid1	The first operand of the operation.
solid2	The second operand of the operation.

Unite() [2/2]

Solid Unite

(

table

solids

)

Performs a solids boolean union operation.

Parameters

solids

Solids for the union operation.