Point Constructors Functions

This function lets you manage the creation of points by defining the formula using point constructors.

This page discusses:

centerofgravity
curvaturecenter
pointoncurveRatio
pointtangent
extremum
pointoncurve
point
pointbetween
center
pointonsurface
point2dto3d
pointonplane

centerofgravity

Gets the center of gravity.

Body->centerofgravity

Gets the center of gravity by valuating its three coordinates as output arguments.

Constructs the center of gravity of a solid (i. e. a PartBody type feature). In case of a face, the center of gravity of the equivalent volume is computed with a unit thickness. Whereas, for a profile, it is computed with a unit section swept along the boundary.

Signature

Body->centerofgravity (x: out Length, y: out Length, z: out Length): VoidType

Inputs

x(LENGTH): abscissa of the Body's center of gravity, as an output argument
y(LENGTH): ordinate of the Body's center of gravity, as an output argument
z(LENGTH): applicate of the Body's center of gravity, as an output argument

Returned Value

None

centerofgravity

Returns the center of gravity as a point.

Signature

centerofgravity (Body, ...): Point

Inputs

(Body): solid or face or profile whose center of gravity is sought

Returned Value

Point: center of gravity of the input solid, face or profile

Sample

Geometrical Set.1\Point.12 = centerofgravity (PartBody)

curvaturecenter

Constructs the curvature center of a curve at a given point.

Signature

curvaturecenter(crv: Curve, pt: Point):Point

Inputs

crv(Curve): curve whose curvature center is sought at some point
pt(Point): point located on crv crv's curvature center is sought at

Returned Value

Point: crv's curvature center at pt

Sample

Geometrical Set.1\Point.13 = curvaturecenter

(Geometrical Set.1\Circle.1, Geometrical Set.1\Point.6)

pointoncurveRatio

Creates a point on a curve.

Signature

pointoncurveRatio(crv :Curve, pt: Point, ratio: Real, orientation: Boolean): Point

Inputs

crv(Curve): curve where the point is to be created
pt(Point): curve's "origin" (does not have to belong to crv; if not, it is projected onto it)
ratio(Real): ratio = distance(point to be created, pt) / distance(point to be created, crv's extremity)
orientation(Boolean): boolean to choose crv's extremity to be considered in the ratio's formula

Returned Value

Point: point on crv whose location is given by ratio (and ratio is given by pt and orientation)

Sample

PartBody\Point.1 = point(2mm,3mm,5mm)
PartBody\Point.2 = point(7mm,11mm,13mm)
PartBody\Point.3 = point(17mm,19mm,23mm)
PartBody\Curve.1 = spline(PartBody\Point.1 ,PartBody\Point.2 ,PartBody\Point.3 )

PartBody\Point.4 = pointoncurveRatio(PartBody\Curve.1 ,PartBody\Point.2 ,0.5,true)/Point.4 and Point.7 are different
PartBody\Point.5 = pointoncurveRatio(PartBody\Curve.1 ,PartBody\Point.2 ,-0.5,true)/Point.5 and Point.6 are different
PartBody\Point.6 = pointoncurveRatio(PartBody\Curve.1 ,PartBody\Point.2 ,0.5,false)/Point.5 and Point.6 are different
PartBody\Point.7 = pointoncurveRatio(PartBody\Curve.1 ,PartBody\Point.2 ,-0.5,false)/Point.4 and Point.7 are different

pointtangent

Returns the input curve's point at which the tangent is directed by the input direction.

Signature

pointtangent(Curve, Direction): Point

Inputs

(Curve): curve containing the sought point
(Direction): direction that should be the input curve's tangent's direction at the returned point

Returned Value

Point: the input curve's point at which the tangent is directed by the input direction

Sample

PartBody\Point.1 = point(2mm,3mm,5mm)
PartBody\Point.2 = point(7mm,11mm,13mm)
PartBody\Point.3 = point(17mm,19mm,23mm)
PartBody\Curve.1 = spline(PartBody\Point.1 ,PartBody\Point.2 ,PartBody\Point.3 )

PartBody\Point.4 = pointtangent(PartBody\Curve.1 ,direction(`xy plane` ))

extremum

computes the set of points as a subset of the input set of points (a curve, surface or solid) that meet given extremum criteria (e. g. they are the points that have got the smallest x-coordinate given the x-axis is directed by the following direction...; they are the points that have got the biggest x-coordinate given the x-axis is directed by the following direction... among the set of points that have got the smallest y-coordinate given the y-axis is directed by the following direction...).

Signature

extremum(Curve, Direction, Boolean, Direction, Boolean, Direction, Boolean): Point

extremum(Surface, Direction, Boolean, Direction, Boolean, Direction, Boolean): Point

extremum(Solid, Direction, Boolean, Direction, Boolean, Direction, Boolean): Point

Inputs

(Curve, Surface or Solid): initial set of points from which the extremum will be computed
(Direction): direction that defines the x-axis
(Boolean): boolean that defines whether the points of the first subset of points (computed from the initial set of points) should have got the smallest (when false) or biggest (when true) x-coordinate
(Direction): direction that defines the y-axis (please note that the x- and y-axes do not have to be orthogonal or even different)
(Boolean): boolean that defines whether the points of the second subset of points (computed from the first set of points) should have got the smallest (when false) or biggest (when true) y-coordinate
(Direction): direction that defines the z-axis (please note that the x-, y- and z-axes do not have to be orthogonal or even different)
(Boolean): boolean that defines whether the points of the third subset of points (computed from the second set of points) should have got the smallest (when false) or biggest (when true) z-coordinate

Returned Value

Point: first of all, the returned value is a set of points. If it contains one point, then it is a point. Otherwise, it may be a curve or even a surface. But it can valuate only a parameter of type "Point", what does not necessarily mean that the result will be a point.

The returned set of points is computed as follows:

the first extremum criterion (first direction, first boolean) enables to compute a first set of points containing the points that belong to the initial set of points (first argument of the function) and that meet the first criterion;
the second extremum criterion enables to compute a second set of points containing the points that belong to the first set of points and that meet the second criterion (please note that the second criterion can and may be identical to the first criterion if only one criterion is requested);
the third extremum criterion enables to compute a third set of points containing the points that belong to the second set of points and that meet the third extremum criterion (please note that the third extremum criterion can and may be identical to the second criterion);
the returned set of points is the third set of points (and the third set of points is a subset of the second set of points, the second set of points is a subset of the first set of points, and the first set of points is a subset of the initial set of points).

Sample

PartBody\Line.1 = line(point(0mm,0mm,0mm),point(1mm,0mm,0mm))
PartBody\Line.2 = line(point(0mm,0mm,0mm),point(0mm,-1mm,0mm))
PartBody\Curve.1 = assemble(PartBody\Line.1 ,PartBody\Line.2 )

//In the following Sample, the element is an "L" contained in the XY
/plane and there is only one direction and one boolean (the three
//directions and booleans are idendical) and the direction is the XY
/plane. As a result, the result is Curve.1, so it is monodimensional. 
PartBody\Point.1 = extremum(PartBody\Curve.1 ,direction(`xy plane` ),false,direction(`xy plane` ),false,direction(`xy plane` ),false)

//Now, the only direction is the YZ plane, so the result is the set of
/points that have got the smallest x-coordinate if the boolean is false,
//and the set of points that have got the biggest x-coordinate if the
//boolean is true. 
//When it is false, the result is Line.2, so it is monodimensional. 
PartBody\Point.2 = extremum(PartBody\Curve.2 ,direction(`yz plane` ),false,direction(`yz plane` ),false,direction(`yz plane` ),false)
//When it is true, the result is a point. 
PartBody\Point.3 = extremum(PartBody\Curve.2 ,direction(`yz plane` ),true,direction(`yz plane` ),true,direction(`yz plane` ),true)

//Now, the only direction is the ZX plane, so the result is the set of
/points that have got the smallest y-coordinate if the boolean is false,
//and the set of points that have got the biggest y-coordinate if the
//boolean is true. 
//When it is false, the result is a point. 
PartBody\Point.4 = extremum(PartBody\Curve.2 ,direction(`zx plane` ),false,direction(`zx plane` ),false,direction(`zx plane` ),false)
//When it is true, the result is Line.1, so it is monodimensional. 
PartBody\Point.5 = extremum(PartBody\Curve.2 ,direction(`zx plane` ),true,direction(`zx plane` ),true,direction(`zx plane` ),true)

PartBody\Surface.1 = extrude(PartBody\Line.1 ,direction(`xy plane` ),0mm,1mm,true)
//In the following Sample, the element is a filled square and there is only
//one direction and one boolean (the three directions and booleans are
//idendical) and the direction is perpendicular to two sides and parallel to
//two sides. As a result, the result is an edge. 
PartBody\Point.1 = extremum(PartBody\Surface.1 ,direction(`xy plane` ),false,direction(`xy plane` ),false,direction(`xy plane` ),false)
PartBody\Point.2 = extremum(PartBody\Surface.1 ,direction(`xy plane` ),true,direction(`xy plane` ),true,direction(`xy plane` ),true)

pointoncurve

Creates a point on a curve.

The point is to be created at a given curvilinear distance from a reference point specified in the second argument.

The boolean specified in the fourth argument allows you to reverse the direction in which the point is to be created.

If the point specified in the second argument is not on the curve, the projection of this point onto the curve becomes the actual reference point.

Signature

pointoncurve(crv: Curve, pt: Point, distance: LENGTH, orientation: Boolean): Point

Inputs

crv(Curve): curve the point is to be created on
pt(Point): crv's "origin" (does not have to belong to crv; if not, it is projected onto it)
distance(LENGTH): curvilinear distance on crv between pt and the point to be created
orientation(Boolean): boolean to specify where, starting from pt, the positive algebraic distances are and where the negative ones are

Returned Value

Point: point on crv at a curvilinear distance from pt of distance and located on a side of crv determined by orientation

Sample

PartBody\Point.1 = point(2mm,3mm,5mm)
PartBody\Point.2 = point(7mm,11mm,13mm)
PartBody\Point.3 = point(17mm,19mm,23mm)
PartBody\Curve.1 = spline(PartBody\Point.1 ,PartBody\Point.2 ,PartBody\Point.3 )

PartBody\Point.4 = pointoncurve(PartBody\Curve.1 , PartBody\Point.2, 5mm, true)/Point.4 and Point.5 are identical
PartBody\Point.5 = pointoncurve(PartBody\Curve.1 , PartBody\Point.2, -5mm, false)/Point.4 and Point.5 are identical

point

Creates a point from its three coordinates. Values or parameter names can be used to pass the Inputs.

Signature

point(x: LENGTH, y: LENGTH, z: LENGTH): Point

Inputs

x(LENGTH): abscissa of the point to be created
y(LENGTH): ordinate of the point to be created
z(LENGTH): applicate of the point to be created

Returned Value

Point: point whose coordinates are (x, y, z)

Sample

Specifying values:

Geometrical Set.1\Point.1 = point(10mm,10mm,10mm)

Specifying parameter names:

Geometrical Set.1\Point.4 = point(0mm,L3,L1)

pointbetween

Creates a point between (or not) two given points.

Signature

pointbetween(pt1: Point, pt2: Point, ratio: Real, orientation: Boolean): Point

Inputs

pt1(Point): first point
pt2(Point): second point
ratio(Real): number specifying how close or far the result point is from pt1 or pt2. If ratio = 0, the result point is pt1 if orientation's value is true andpt2 if its value is false. If ratio = 1, the result point is pt2 if orientation's value is true and pt1 if its value is false. If ratio = 0.5, the result point is in the middle of the input points, whatever orientation's value. If ratio < 0 or ratio > 1, the result point is outside the pt1-pt2 line, that is to say not between pt1 and pt2.
orientation(Boolean): let pt3 be the result point. If orientation is true, then pt3 = (1 - ratio) pt1 + ratio pt2. If orientation is false, then pt3 = ratio pt1 + (1 - ratio) pt2.

Returned Value

Point: point equal to the mean of pt1 and pt2 weighted by ratio and 1-ratio or 1-ratio and ratio, depending on orientation's value

Sample

PartBody\Point.1 = point(2mm,3mm,5mm)
PartBody\Point.2 = point(7mm,11mm,13mm)

PartBody\Point.3 = pointbetween(PartBody\Point.1, PartBody\Point.2, -0.1, true)
PartBody\Point.4 = pointbetween(PartBody\Point.1, PartBody\Point.2, 0.1, true)
PartBody\Point.5 = pointbetween(PartBody\Point.1, PartBody\Point.2, 0.9, true)
PartBody\Point.6 = pointbetween(PartBody\Point.1, PartBody\Point.2, 1.1, true)

center

Returns the center of a given circle of any type.

Signature

center(Circle): Point

Inputs

(Circle): circle whose center is to be returned. The circle can be of any type (created within the Generative Shape Design workbench or using the Sketch command).

Returned Value

Point: the input circle's center

Sample

Geometrical Set.1\Point.10 = circle (Geometrical Set.1\Circle.1)

pointonsurface

Creates a point on a surface determined by its distance to a reference point along a direction.

Signature

pointonsurface(sur: Surface, pt: Point, dir: Direction, dist: LENGTH): Point

Inputs

sur(Surface): surface the returned point is to be created on
pt(Point): reference point to locate the returned point at a certain distance from it
dir(Direction): direction to specify where the returned point is to be located given its distance to the reference point
dist(LENGTH): distance between the returned point and pt

Returned Value

Point: point on sur located at a distance of dist from pt along dir

Sample

PartBody\Line.1 = line(point(0mm,0mm,0mm),point(1mm,0mm,0mm))
PartBody\Surface.1 = extrude(PartBody\Line.1 ,direction(`xy plane` ),0mm,1mm,true)
PartBody\Point.1 = point(0.5mm,0mm,0.5mm)

PartBody\Point.2 = pointonsurface(PartBody\Surface.1 ,PartBody\Point.1 ,direction(1mm,1mm,1mm),0.5mm)

point2dto3d

Converts a 2D point (i. e. a point in a 2D sketch) into a 3D point by valuating the parameters. You can valuate a 2D point which can be an existing datum point or a volatile point. The constructor computes the new 3D point at the same coordinates as those of the 2D point.

Signature

point2dto3d(2DPoint: 2DPoint): Point

Inputs

2DPoint(2DPoint): 2D point

Returned Value

Point: the 3D point corresponding to 2DPoint

Sample

In this Sample, two points were created within a sketch (PartBody\Sketch.1)

Let L1 (List)
L1 = PartBody\Sketch.1.Query("2DPoint", "")

PartBody\Point.1 = point2dto3d(L1.GetItem(1))
PartBody\Point.2 = point2dto3d(L1.GetItem(2))

pointonplane

Creates a point on a given plane.

Signature

pointonplane(pln: Plane, pt: Point, dx: LENGTH, dy: LENGTH): Point

Inputs

pln(Plane): plane the result point is to be created on
pt(Point): pln's "origin"
dx (LEN GTH): abscissa of the result point within pln's axis system (pt, pln's first direction, pln's second direction)
dy(LENGTH): ordinate of the result point within pln's axis system (pt, pln's first direction, pln's second direction)

Returned Value

Point: point belonging to pln with the (dx, dy) coordinates within pln's axis system (pt, pln's first direction, pln's second direction)

Sample

PartBody\Point.1 = point(0.5mm,0mm,0.5mm)
PartBody\Point.2 = pointonplane(`zx plane`, PartBody\Point.1, 0.5mm, 0mm)