Summary

POINT Class for representing points in a geometry.

Point objects are typically used for defining Surface objects, to be meshed later.

Point objects behave in many ways like 2x1 vectors, allowing the operations

• pnew = p1 + p2
• pnew = p1 - p2 ** pnew = p1 ** scalar
• pnew = p1 / scalar
• r = norm(p1) = p1.norm()
• theta = angle(p1) = p1.angle()

Furthermore, the following operations are often useful for creating geometries for radial-flux motors:

• pnew = p1.mirror(theta)
• pnew = p1.normalize(radius)
• p1.translate( [x,y] )
• inplace variants of the above, for e.g. modifying existing Surface objects.

  PROPERTIES

• curves - Array of Curve objects that this point belongs to

• Point/is3D is a property.

• lcar - Characteristic length; representative of maximum edge length of the mesh near Point

• x - x-coordinate of Point

• y - y-coordinate of Point

• Point/z is a property.

Methods

Class methods are listed below. Inherited methods are not included.

* Point Constructor.

this = Point([x,y], lcar)

Create a new point at (x,y) with the characteristic length lcar.

* angle Angular coordinate.

theta = angle(this)

Returns the angular coordinate theta = atan2(this.y, this.x)

* copy Return a deep copy.

Returns a new point with the same coordinates and characteristic length.

* Point/last_copy is a function.

p2 = last_copy(this)

* minus Minus operator.

See Point.plus.

* mirror Mirroring across a segment center.

p2 = mirror(this, theta)

Returns a new Point, mirrored around the center of a circle segment of theta radians. For instance, if

angle(P) = 30 deg,

then angle(P.mirror(pi/4)) = 60 deg.

* mirror_inplace Mirror in-place.

The same as mirror, but instead of returning a new Point modifies this.

* mrdivide Scale coordinates by dividing with a scalar.

p2 = P1 / a

Returns a new Point p2, at (P1.x/a, P1.y/x), with the characteristic length equal to P1.lcar.

* mtimes Scale coordinates by multiplying with a scalar.

p2 = P1 * a

Returns a new Point p2, at (P1.xa, P1.yx), with the characteristic length equal to P1.lcar.

* norm Radial coordinate.

r = norm(this)

Returns the radial coordinate r = sqrt( this.x^2 + this.y^2 ).

* normalize point distance from origin.

this = normalize(this, new_r)

Modifies the coordinates of this point so that its distance from origin (norm(this)) is equal to new_r. The angular coordinate angle(this) remains unchanged.

* plot Plot point.

plot(this, text, args)

Plots the point using the marker style etc specified in args, annotated with text. Supply an empty string to skip.

* plus Plus operator.

pnew = p1 + p2

Returns a new point at (p1.x + p2.x, p1.y + p2.y), with a characteristic length equal to p1.lcar.

Also works when p is a 2-vector.

* rotate Create a new Point, rotated around the origin.

p2 = rotate(this, theta)

Return a new Point, rotated around the origin by theta radians.

* rotate Rotate this point around the origin.

p2 = rotate(this, theta)

Rotate this Point around the origin by theta radians.

* translate Create a new translated point.

pnew = translate(this, s)

Returns a new Point, translated with the vector s.

pnew = translate(this, s, lcar)

In addition to above, updates the characteristic length of the new Point.

* translate_inplace Translation inplace.

this = translate_inplace(this, Point)

Sets the coordinates of this equal to (Point.x, Point.y)

this = translate_inplace(this, [x, y])

Sets the coordinates of this equal to (x, y)

* xmirror Return a new Point, mirrored around the x-axis.

p2 = xmirror(this, x)

Returns a new Point at (x - this.x, this.y).

p2 = xmirror(this, x, lcar)

In addition to the above, sets the characteristic length of p2 to lcar.

* ymirror Return a new Point, mirrored around the y-axis.

p2 = ymirror(this, y)

Returns a new Point at (this.x, y-this.y).

p2 = ymirror(this)

Equivalent to p2 = ymirror(this, 0)

p2 = ymirror(this, y, lcar)

In addition to the above, sets the characteristic length of p2 to lcar.