3.1.6 Transformations

Geometrical transformations can be applied to elementary entities, or to copies of elementary entities (using the Duplicata command: see below). The syntax of the transformation commands is:

transform:

Dilate { { expression-list }, expression } { transform-list }

Scales all elementary entities in transform-list by a factor expression. The expression-list should contain three expressions giving the X, Y and Z direction of the homothetic transformation.

Rotate { { expression-list }, { expression-list }, expression } { transform-list }

Rotates all elementary entities in transform-list by an angle of expression radians. The first expression-list should contain three expressions giving the X, Y and Z direction of the rotation axis; the second expression-list should contain three expressions giving the X, Y and Z components of any point on this axis.

Symmetry { expression-list } { transform-list }

Transforms all elementary entities symmetrically to a plane. The expression-list should contain four expressions giving the coefficients of the plane's equation.

Translate { expression-list } { transform-list }

Translates all elementary entities in transform-list. The expression-list should contain three expressions giving the X, Y and Z components of the translation vector.

Boundary { transform-list }

(Not a transformation per-se.) Returns the boundary of the elementary entities in transform-list.

with

transform-list: 
  Point | Line | Surface { expression-list }; … |
  Duplicata { Point | Line | Surface { expression-list }; … } |
  transform