Plane Constructors Functions

This function lets you manage the creation of planes by defining the formulae using plane constructors.

This page discusses:

planemean

Computes a plane from a set of points.

When three or more points are present, the command first computes a center of gravity and then computes inertia matrix at this new point. In the next step, eigenvalues and eigenvectors of this matrix are computed. Thus, the returned origin is the center of the gravity and the returned vectors are the eigenvectors of the inertia matrix, from which a mean plane is computed.

Signature

planemean(Point, ..): Plane

Inputs

  • (Point): three or more points

Returned Value

  • Plane: plane as explained above

Sample

PartBody\Plane.1 = planemean(point(2mm,3mm,5mm),point(7mm,11mm,13mm),point(17mm,19mm,23mm) )
PartBody\Plane.2 = planemean(point(2mm,3mm,5mm),point(7mm,11mm,13mm),point(17mm,19mm,23mm),point(29mm,31mm,37mm) )

plane

Creates a plane.

plane (three points)

Creates a plane passing through the three input points.

Signature

plane( Point, Point, Point): Plane

Inputs

  • (Point): first point the result plane is to pass through
  • (Point): second point the result plane is to pass through
  • (Point): third point the result plane is to pass through

Returned Value

  • Plane: plane passing through the three input points

Sample

PartBody\Plane.1 = plane(PartBody\Point.1,PartBody\Point.2,PartBody\Point.3)

plane (equation)

Creates a plane defined by a Cartesian equation.

Signature

plane(a: Real, b: Real, c: Real, d: Length): Plane

Inputs

  • a(Real): abscissa of the vector intended to be the result plane's normal vector
  • b(Real): ordinate of the vector intended to be the result plane's normal vector
  • c(Real): applicate of the vector intended to be the result plane's normal vector
  • d(LENGTH): value of the dot product of the vector intended to be the result plane's normal vector by the vector canonically associated to any point of the result plane

Returned Value

  • Plane: plane defined by the following Cartesian equation: ax + by + cz = d

Sample

PartBody\Plane.2 = plane(1, -2, 5, 7)

plane (two lines)

Creates a plane passing through the first input line and that has got, as directions, the two input lines' directions.

Signature

plane(Line, Line): Plane

Inputs

  • - (Line): line the result plane will pass through and that defines the plane's first direction
  • - (Line): line defining the result plane's second direction

Returned Value

  • Plane: plane passing through the first input line and that has got, as directions, the two input lines' directions

Sample

PartBody\Plane.3 = plane(PartBody\Line.1, PartBody\Line.2)

plane (point line)

Creates a plane passing through a line and point.

Signature

plane(Point, Line): Plane

Inputs

  • (Point): point the result plane is to pass through
  • (Line): line the result plane is to pass through

Returned Value

  • Plane: plane passing through the given line and point

Sample

PartBody\Plane.4 = plane(PartBody\Line.1, PartBody\Point.1)

plane (planar curve)

Creates a plane passing through a given planar curve.

Signature

plane(Curve): Plane

Inputs

  • (Curve): planar curve whose support plane will be the result plane

Returned Value

  • Plane: plane passing through the input planar curve

Sample

PartBody\Plane.5 = plane(PartBody\Curve.1)

planeoffset

Creates an offset plane.

planeoffset

Creates an offset plane from another at a given distance from it and above or below it, according to a given orientation.

Signature

planeoffset(Plane, offset: LENGTH, orientation: Boolean): Plane

Inputs

  • (Plane): plane to offset
  • offset(LENGTH): algebraic distance between the reference plane and the result plane
  • orientation(Boolean): boolean to set whether the result plane should be above or below the reference plane

Returned Value

  • Plane: plane parallel to the input plane, at offset's distance from it and above or below it, according to orientation's value

planeoffset

Creates an offset plane from another one passing through a point.

Signature

planeoffset(Plane, Point): Plane

Inputs

  • (Plane): plane to offset
  • (Point): point the result plane is to pass through

Returned Value

  • Plane: plane parallel to the input plane and passing through the input point

Sample

PartBody\Plane.1 = planemean(point(2mm,3mm,5mm),point(7mm,11mm,13mm),point(17mm,19mm,23mm) )

PartBody\Plane.2 = planeoffset(PartBody\Plane.1 ,10mm,true)/Plane.2 and Plane.5 are identical
PartBody\Plane.3 = planeoffset(PartBody\Plane.1 ,-10mm,true)/Plane.3 and Plane.4 are identical
PartBody\Plane.4 = planeoffset(PartBody\Plane.1 ,10mm,false)/Plane.3 and Plane.4 are identical
PartBody\Plane.5 = planeoffset(PartBody\Plane.1 ,-10mm,false)/Plane.2 and Plane.5 are identical

PartBody\Plane.6 = planeoffset(PartBody\Plane.1 ,point(20mm,0mm,0mm) )

planetangent

Creates a plane tangent to a surface at a given point.

Signature

planetangent(Surface, Point): Plane

Inputs

  • (Surface): surface the plane is to be tangent to
  • (Point): point on the surface the plane is to be tangent at

Returned Value

  • Plane: plane tangent to the input surface at the input point

Sample

PartBody\Plane.1 = planetangent(PartBody\Surface.1, PartBody\Point.1)

planeangle

Creates an angle plane.

Signature

planeangle(pln: Plane, axis: Line, angle: ANGLE, orientation: Boolean): Plane

Inputs

  • pln(Plane): reference plane
  • axis(Line): intersection between the reference plane and the result plane to be created
  • angle(ANGLE): angle between the reference plane and the result plane
  • orientation(Boolean): boolean to reverse the side of the reference plane the angle should start from

Returned Value

  • Plane: plane making an angle of angle with pln at axis if boolean's value is 'true', or plane making an angle of -angle with pln at axis if boolean's value is 'false'

Sample

PartBody\Plane.2 = planeangle(PartBody\Plane.1, PartBody\Line.1, 60deg, true)

planenormal

Creates a plane normal to a curve at a given point.

Signature

planenormal(Curve, Point): Plane

Inputs

  • (Curve): curve the plane is to be normal to
  • (Point): point on the curve the plane is to be normal at

Returned Value

  • Plane: plane normal to the input curve at the input point

Sample

PartBody\Plane.1 = planenormal(PartBody\Curve.1, PartBody\Point.1)