Rotation

Geometric definition

A rotation is a transformation that turns a geometry around an axis by a certain angle. The angle can be defined in degrees or radians.

How to add

As often is possible in Rhino to use either RhinoCommons or RhinoScriptSynthax to add a point to the Rhino workspace. Here are the two methods:

RhinoCommons

import Rhino.Geometry as rg
import scriptcontext as sc
import math as m

# create a rectangle
rectangle = rg.Rectangle3d(rg.Plane.WorldXY, 10, 10)

# create a rotation transformation with RhinoCommon
angle_degrees = 45
angle_radians = m.radians(angle_degrees)
rotation = rg.Transform.Rotation(angle_radians,     # angle in radians
                                rg.Vector3d.ZAxis,  # rotation axis
                                rg.Point3d.Origin)  # rotation center

# transform the rectangle with RhinoCommon
rectangle.Transform(rotation)

# add the rectangle to the document
sc.doc.Objects.AddRectangle(rectangle)

RhinoScriptSynthax

import rhinoscriptsyntax as rs

# create a rectangle
rectangle_id = rs.AddRectangle(rs.WorldXYPlane(), 10, 10)

# create a rotation transformation
rotation = rs.XformRotation2(
    45,             # angle of rotation in degrees
    [0, 0, 1],      # axis of rotation
    [0, 0, 0]       # center of rotation
)

# transform the rectangle
rs.TransformObject(rectangle_id, rotation, copy=True)

Main methods and properties

Operators

Rotations as all the other transformations have a set of operators that can be used to perform to combine transformations (also different kinds, e.g.: translation with rotation). Here are the main ones:

xform_1 = rg.Transform.Rotation(m.radians(45), rg.Vector3d.ZAxis, rg.Point3d.Origin)
xform_2 = rg.Transform.Rotation(m.radians(45), rg.Vector3d.XAxis, rg.Point3d.Origin)

xform_3 = xform_2 * xform_1 # Will combine the two transformations

⚠️ Note that the order of the transformations is important. In the example above xform_1 will be applied first and xform_2 will be applied second. ⚠️

Properties

Rotations as all the other transformations have a set of properties that can be used to retrieve information about the transformation. Here are the main ones:

rotation = rg.Transform.Rotation(m.radians(45), rg.Vector3d.ZAxis, rg.Point3d.Origin)

rotation.IsIdentity # Will return True if the transformation is an identity transformation
rotation.IsZero # Will return True if the transformation is a zero transformation
rotation.IsValid # Will return True if the transformation is valid

🛠 Exercises

Starting file:

01: 🦏⬇️⬇️⬇️ Download the file here ⬇️⬇️⬇️🦏 01: 🐍⬇️⬇️⬇️ Download the script here ⬇️⬇️⬇️🐍

Solutions:

01: 🦏⬇️⬇️⬇️ Download the file here ⬇️⬇️⬇️🦏 01: 🐍⬇️⬇️⬇️ Download the script here ⬇️⬇️⬇️🐍