Linear Algebra & Analytic Geometry

[bomastudio]

Hi Guys, I have an agony-problem with a 3D rotation.
Suppose to have a face placed generically in space, with its normal vector

v = [vx,vy,vz]

How you could rotate this face in order to put is for example in the XY plane (or anywhere else)?

[TIG]

First you have to decide the point that anchors the proposed rotation...
Perhaps pt=face.bounds.center, or pt=ORIGIN ? but you choose...
Then decide the axis of rotation.
Perhaps axis=Y_AXIS ? [or X_ or Z_ etc]
From the face you can extract normal=face.normal to get its current orientation.
So angle=normal.angle_between(axis)
Now make a:
transformation=Geom::Transformation.rotation(pt, axis, angle)
Or -angle depending on the desired result ?
Then apply that to the geometry:
face.parent.entities.transform_entities(transformation, face)
The face should now be transformed as you hoped.
But of course, if it's connected to other geometry it could skew other things unexpectedly.
Remember you can use groups/components to separate geometry...

[MSP_Greg]

Try the following --

module SUMath
  def self.transVector2Vector (vStart, vEnd)
    v1 = vStart.normalize
    v2 = vEnd.normalize
    return Geom;;Transformation.new if v1.samedirection?(v2)
    v3 = v2.cross(v1)
    v4 = v3.cross(v1)
    c = v2.dot(v1)
    s = v2.dot(v4.normalize)

    m1 = Geom;;Transformation.axes( [0,0,0], v1, v4, v3)
    m2 = Geom;;Transformation.axes( [0,0,0], [c,s,0], [-s,c,0], [0,0,1] )
    mT = m1 * m2 * m1.inverse
  end

  def self.rotateFace(s_vector_end)
    vector_end = s_vector_end.split(",").collect { |i| i.to_f }
    entities = Sketchup.active_model.entities
    faces = entities.grep(Sketchup;;Face)
    face = faces[0]
    face_normal = face.normal
    t = transVector2Vector(face_normal, vector_end)
    entities.transform_entities(t, face)
    par = face.normal.samedirection?(vector_end)
    puts "face.normal.samedirection?([#{s_vector_end}]) = #{par}"
  end
end

# load module thru console
# type SUMath.rotateFace("0,0,1") into console, or use whatever vector,
# you can type repeatedly.  Best to have just one face in the model...

Greg

[MSP_Greg]

@bomastudio said:

Hi Guys, I have an agony-problem with a 3D rotation.

The transform that TIG suggested (rotation) works for your need. The docs on transformations aren’t very clear, especially for people who aren’t familiar with 3D transforms or linear algebra. They’re also a little quirky, as the trans.to_a method returns a matrix that is the transpose of what I would expect. FWIW, I had a lot of linear algebra (long time ago)...

Anyway, the rotation method returns a transformation based on a rotation in a plane, which is defined by the ‘axis’ parameter, which should be the normal to the plane of rotation.

If the start and end vectors are parallel, they do not define a unique plane, hence, both my original ‘linear algebra’ algorithm and the rotation method fail. The code below accounts for that –

Greg

module SUMath
  def self.transVector2Vector(vStart, vEnd, pt = nil)
    ptRot = pt || [0,0,0]

    if vStart.samedirection?(vEnd)
      # return identity transformation, vectors are in the same direction
      Geom;;Transformation.new 
    elsif vStart.parallel?(vEnd)
      #return 180 transformation, vStart and vEnd in opposite direction
      Geom;;Transformation.axes(ptRot, [-1,0,0], [0,-1,0], [0,0,-1] )
    else
      # return rotation transform based on vStart and vEnd
      # vCross is normal to plane of rotation
      vCross = vStart.cross(vEnd)
      ang = vStart.angle_between(vEnd)
      Geom;;Transformation.rotation(ptRot, vCross, ang)
    end
  end

  def self.rotateFace(face, vector_end, pt = nil)
    # for demo purposes, the next 2 statements chose an arbitrary face
    # if no face passed
    unless face
      entities = Sketchup.active_model.entities
      faces = entities.grep(Sketchup;;Face)
      face = faces[0]
    end

    face_normal = face.normal
    t = transVector2Vector(face_normal, vector_end, pt)
    entities.transform_entities(t, face)

    # below is just for a demo confirmation
    sd = face.normal.samedirection?(vector_end)
    sVEnd = "[#{vector_end.join(",")}]"
    puts "face.normal.samedirection?(#{sVEnd}) = #{sd}"
  end
end
# load module thru console
# type SUMath.rotateFace(nil, [0,0,1]) into console with whatever vector
# you want, it can be typed as often as you'd like.
# As a demo, best done with one face in the model