Transforms

A transform returns the shape moved; the receiver is unchanged. Which shapes have which:

Method	Solid	Sketch	Path	Assembly
translate	✓	✓	✓	✓
rotate	✓	✓	✓
scale	✓	✓	✓
mirror	✓	✓	✓
resize	✓
center	✓	✓		✓
align	✓	✓
transform	✓	✓
repeat_linear	✓	✓
repeat_polar	✓	✓

A vector argument (an offset, angles, factors, a normal) is three numbers, one Array, or the keywords x:, y: and z:: translate(1, 2, 3), translate([1, 2, 3]) and translate(x: 1, y: 2, z: 3) are the same. A Sketch or a Path lies in the XY plane, so a component that would move it out of the plane (translate(z: 5), rotate(x: 45)) is a ValueError: extrude it first.

A copy of a part moved by translate or rotate is the same part in the parts list; one mirrored or scaled is a part of its own.

translate

shape.translate(x, y, z)
shape.translate([x, y, z])
shape.translate(x: 0, y: 0, z: 0)

Moves the shape by the offset. A missing axis is 0. A Sketch and a Path take x and y.

Returns: the receiver’s kind.

puts cube(10).translate(z: 5).bbox.z_min   # 5

rotate

shape.rotate(a)
shape.rotate(x, y, z)
shape.rotate(angle: a, about: [x, y, z])
solid.rotate(a, axis: [x, y, z])

Turns the shape, in degrees.

• rotate(a) or rotate(angle: a) turns about the z axis, for every kind of shape.
• rotate(x, y, z) turns about x, then about y, then about z.
• axis: turns a Solid by a about any axis through the origin, right-handed.
• about: turns about that point instead of the origin: [x, y, z], or [x, y] for a Sketch or a Path.

A Sketch and a Path turn about z only.

Parameter	Type	Default	Description
x, y, z	Number	0	Angles about each axis.
angle	Number	—	An angle about z, or about axis:.
axis	Array	—	The axis [x, y, z] to turn about (Solids only).
about	Array	origin	The point to turn about.

Returns: the receiver’s kind.

Raises: ArgumentError for axis: with angles x, y, z, or on a Sketch or a Path.

bar = cube([10, 1, 1])
puts bar.rotate(90).bbox.min.inspect                          # [-1, 0, 0]
puts bar.rotate(90, about: [5, 0, 0]).bbox.min.inspect        # [4, -5, 0]
tilted = bar.rotate(30, axis: [1, 1, 0])

scale

shape.scale(s)
shape.scale(x, y, z)
shape.scale([x, y, z])
shape.scale(x: 2)

Scales the shape about the origin. One number scales every axis by it. A missing axis keeps its size (factor 1).

Returns: the receiver’s kind.

Raises: ValueError for a factor of 0, and for an uneven scale of a Path with arcs.

puts cube(10).scale(2).bbox.max.inspect         # [20, 20, 20]
puts cube(10).scale(x: 2).bbox.max.inspect      # [20, 10, 10]

mirror

shape.mirror(nx, ny, nz)
shape.mirror([nx, ny, nz])
sketch.mirror(nx, ny)

Reflects the shape across the plane through the origin with normal [nx, ny, nz]; a Sketch or a Path across the line through the origin with normal [nx, ny].

Returns: the receiver’s kind.

left = cube([10, 5, 5]).translate(5, 0, 0)
right = left.mirror(1, 0, 0)
puts right.bbox.min.inspect   # [-15, 0, 0]

resize

solid.resize([x, y, z], auto: false)

Scales a Solid so its bounding box has the sizes given. A size of 0, or one left out, keeps that axis; with auto: true it scales instead by the factor of the first size given, keeping the proportions. An empty Solid has no box to scale, and comes back as it is.

Parameter	Type	Default	Description
size	Array	—	The target sizes [x, y, z]; 1 to 3 of them.
auto	Boolean	false	Scale the axes given as 0 in proportion.

Returns: Solid.

Raises: ValueError for a negative size.

puts cube(10).resize([20]).bbox.size.inspect               # [20, 10, 10]
puts cube(10).resize([20], auto: true).bbox.size.inspect   # [20, 20, 20]

center

shape.center(axes = "xyz")

Moves the shape so the centre of its bounding box is at the origin on the axes named: a String or a Symbol of x, y and z (center(:xy)). A Sketch centres on x and y only. An Assembly moves as a whole. An empty shape has no box, and comes back as it is.

Returns: the receiver’s kind.

puts cube(10).center(:xy).bbox.min.inspect   # [-5, -5, 0]

align

shape.align(target, axes, my_align, target_align = my_align, offset = 0)

Moves the shape along axes so that its my_align side meets the target’s target_align side, offset beyond it. The sides are "min", "max" and "center"; the axes are letters of x, y and z. Each name is a String or a Symbol. The target is a Solid or a Sketch. An empty shape comes back as it is; an empty target has no side to meet.

Parameter	Type	Default	Description
target	Solid or Sketch	—	The shape to align to.
axes	String or Symbol	—	The axes to move along: :z, "xy".
my_align	String or Symbol	—	The shape’s side: min, max or center.
target_align	String or Symbol	my_align	The target’s side.
offset	Number	0	The distance beyond the target’s side.

Returns: the receiver’s kind.

Raises: ValueError for an empty target.

base = cube(x: 40, y: 40, z: 5)
knob = cylinder(d: 10, h: 8)
  .align(base, :z, :min, :max)          # on top of the base
  .align(base, :xy, :center)            # in its middle
puts knob.bbox.z_min                    # 5

transform

solid.transform([m00, m10, m20, m01, m11, m21, m02, m12, m22, tx, ty, tz])
sketch.transform([m00, m10, m01, m11, tx, ty])

Applies an affine matrix, given flat and column-major: the columns of the linear part, then the translation. A Solid takes 12 numbers, a Sketch 6.

Returns: the receiver’s kind.

Raises: ValueError for a singular matrix, which would flatten the shape, and for the wrong number of entries.

# x moves by y: a shear
sheared = cube(10).transform([1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0])
puts sheared.bbox.max.inspect   # [20, 10, 10]

repeat_linear

shape.repeat_linear(count, x, y, z)
shape.repeat_linear(count, [x, y, z])
shape.repeat_linear(count, x: 0, y: 0, z: 0)

count copies of the shape, each a step further along the offset, united. A count of 1 or less gives the shape itself. A Sketch steps in x and y.

Parameter	Type	Default	Description
count	Number	—	How many copies, the first in place; at most 10,000.
x, y, z	Number	0	The step from one copy to the next.

Returns: the receiver’s kind.

fins = cube([1, 20, 10]).repeat_linear(5, x: 4)
puts fins.bbox.size.inspect   # [17, 20, 10]

repeat_polar

shape.repeat_polar(count, angle = 360)

count copies of the shape turned about the z axis, united. Over a full turn the copies are spaced evenly, 360 / count apart. Over less, the first is in place and the last at angle. A count of 1 or less gives the shape itself.

Parameter	Type	Default	Description
count	Number	—	How many copies; at most 10,000.
angle	Number	360	The angle they spread over, in degrees. Also angle:.

Returns: the receiver’s kind.

bolt_holes = circle(r: 2).translate(20, 0).repeat_polar(6)
flange = (circle(r: 30) - circle(r: 10) - bolt_holes).extrude(5)