GeometricTransformation

WLJS

Execution environment

wljs-graphics3d-threejs

Package

Supports dynamics

GeometricTransformation[object_, matrix3x3_List]

applies general matrix3x3 to each vertex of an object, i.e. replacing each point p by matrix3x3.p

GeometricTransformation[object_, vector3_List]

applies translation vector3 to each vertex of an object

GeometricTransformation[object_, {matrix3_List, vector3_List}]

applies transformation matrix and translation operation matrix3.p + vector3

info

object can be nested or group of graphics primitives as well

Examples

Graphics3D[
 GeometricTransformation[Sphere[], N@ShearingMatrix[2, {1,1,1}, {1,1,0}]]
 ]

tip

Numerical matrixes are usually faster. Use N to get pure numbers

Or more complicated one

Graphics3D[
 GeometricTransformation[Cuboid[{0, 0, 0}, {1.5, 1.5, .2}], 
  Table[{RotationMatrix[a, {0, 0, 1}], {Cos[a], Sin[a], a}}, {a, 0, 
    4 Pi, .2}]], Boxed -> False]

Dynamics

It fully supports dynamic updates. See example

cell 1

rot = RotationMatrix[45 Degree, {0, 0, 1}];
stair = GeometricTransformation[Cuboid[{0, 0, 0}, {1.5, 1.5, .2}], 
  Table[{RotationMatrix[a, {0, 0, 1}], {Cos[a], Sin[a], a}}, {a, 0, 
    4 Pi, .2}]];

    
Graphics3D[GeometricTransformation[stair, rot // Offload], Boxed -> False]

cell 2

EventHandler[InputRange[0, 180.0 Degree, 1.0 Degree], 
  Function[angle, rot = RotationMatrix[angle,{0, 0, 1}]]]

The result is following