Transform Menu

The Transform menu commands apply geometric transformations to figures in your sketches, allowing you to create translations, rotations, dilations, reflections, tessellations, scale models, kaleidoscopes, fractals, and much more. These commands include four basic transformations: Translate (to slide), Rotate (to turn), Dilate (to shrink or enlarge) Reflect (to flip).

In addition to the object or objects that they transform—the transformational pre-image—each type of transformation involves certain parameters: objects or values upon which the transformation is based. For instance, a rotation requires both an angle and a center about which to rotate. The Mark commands—Mark Center, Mark Mirror, Mark Angle, Mark Ratio, Mark Vector, and Mark Distance—let you specify objects in your sketch to act as dynamic parameters for your transformations.

These parameters may be either geometric objects or geometric quantities. For example, a rotation is defined by two parameters: a center and an angle. The center is a geometric point about which objects rotate. The angle is a geometric quantity that determines how far objects rotate about the center.

The Transform menu provides a flexible set of commands that allow you to specify a rich variety of transformations using either fixed or dynamic transformational parameters. For instance, you can rotate a triangle by a fixed angle of 45° about some center point, or you might rotate by a dynamic parameter such as angle ABC. (This is a “dynamic” parameter in the sense that if you then drag A, B, or C, the rotated image changes dynamically to the new angle ABC.)

In general, follow these steps to construct the transformed image of one or more objects:

Once you mark a parameter, Sketchpad remembers that mark even after you change the selections. If you’ve already marked a parameter for one transformation, you don’t need to mark it again to use the same parameter for a second transformation.

1. Mark any parameters that determine dynamic aspects of your transformation by selecting objects to define those parameters and choosing the appropriate Mark commands (for example, Mark Center to mark a selected point as the center of rotation).

2. Select the object(s) you wish to transform. (Mathematically, this is the pre-image of your transformation.)

3. Choose the appropriate transformation command from the Transform menu (for example, Rotate).

4. In the resulting dialog box, enter any fixed parameters you wish to use in your transformation (for example, type 45°) then leave the dialog box.

Sketchpad constructs the image of your selection according to the transformation and parameters you’ve specified.

Finally, the Iterate command allows you to create in a single step multiple transformed images such as the spiral shown above, or any figure resulting from a transformation or construction repeated many times. Iteration can even be used to create complex images such as tessellations and fractals.

Subtopics:
Mark Commands
Mark Center
Mark Mirror
Mark Angle
Mark Ratio/Mark Segment Ratio/Mark Scale Factor
Mark Vector
Mark Distance
Translate
Rotate
How To Construct an Angle of Fixed Measure
Dilate
Reflect
Iterate