The following functions create transformation objects that can be used, for instance, in a call to compose-transformations . The transformation constructors do not capture any of their inputs. The constructors all create objects that are subclasses of transformation .

make-translation-transformation [Function]

Arguments: translation-x translation-y

Summary: A translation is a transformation that preserves the length, angle, and orientation of all geometric entities.

make-translation-transformation
returns a transformation that translates all points by *
translation-x*
in the *
x*
direction and *
translation-y*
in the *
y*
direction. *
translation-x*
and *
translation-y*
must be real numbers.

make-rotation-transformation [Function]

Arguments: angle ```
&optional
```

origin

make-rotation-transformation* [Function]

Arguments: angle ```
&optional
```

origin-x origin-y

Summary: A rotation is a transformation that preserves the length and angles of all geometric entities. Rotations also preserve one point (the origin) and the distance of all entities from that point.

make-rotation-transformation
returns a transformation that rotates all points by *
angle*
(which is a real number indicating an angle in radians) around the point *
origin*
. If *
origin*
is supplied it must be a point; if not supplied, it defaults to (0, 0). *
origin-x*
and *
origin-y*
must be real numbers.

make-scaling-transformation [Function]

Arguments: scale-x scale-y ```
&optional
```

origin

make-scaling-transformation* [Function]

Arguments: scale-x scale-y ```
&optional
```

origin-x origin-y

Summary: As discussed previously, there is no single definition of a scaling transformation.
make-scaling-transformation
returns a transformation that multiplies the *
x*
-coordinate distance of every point from *
origin*
by *
scale-x*
and the *
y*
-coordinate distance of every point from *
origin*
by *
scale-y*
. *
scale-x*
and *
scale-y*
must be real numbers. If *
origin*
is supplied it must be a point; if not supplied, it defaults to (0, 0). *
origin-x*
and *
origin-y*
must be real numbers.

make-reflection-transformation [Function]

make-reflection-transformation* [Function]

Summary: A reflection is a transformation that preserves lengths and magnitudes of angles, but changes the sign (or "handedness") of angles. If you think of the drawing plane on a transparent sheet of paper, a reflection is a transformation that "turns the paper over."

make-reflection-transformation
returns a transformation that reflects every point through the line passing through the points *
point1*
and *
point2*
(or through the positions*
(x1, y1)*
and *
(x2, y2)*
in the case of the spread version).

make-transformation [Function]

Arguments: m*
xx*
m*
xy*
m*
yx*
m*
yy*
t*
x*
t*
y*

Summary: Returns a general transformation whose effect is:

where *
x*
and *
y*
are the coordinates of a point before the transformation and
and
are the coordinates of the corresponding point after.

All of the arguments to make-transformation must be real numbers.

make-3-point-transformation [Function]

Arguments: point-1 point-2 point-3 point-1-image point-2-image point-3-image

Summary: Returns a transformation that takes points *
point-1*
into *
point-1-image*
, *
point-2*
into *
point-2-image*
, and *
point-3*
into *
point-3-image*
. Three non-collinear points and their images under the transformation are enough to specify any affine transformation.

If *
point-1*
, *
point-2*
, and *
point-3*
are collinear, the
transformation-underspecified
error will be signaled. If *
point-1-image*
, *
point-2-image*
, and *
point-3-image*
are collinear, the resulting transformation will be singular (that is, will have no inverse), but this is not an error.

make-3-point-transformation* [Function]

Arguments: x1 y1 x2 y2 x3 y3 x1-image y1-image x2-image y2-image x3-image y3-image

Summary: Returns a transformation that takes the points at the positions (*
x1*
,*
y1*
) into (*
x1-image*
,*
y1-image*
), (*
x2*
,*
y2*
) into (*
x2-image*
,*
y2-image*
) and (*
x3*
,*
y3*
) into (*
x3-image*
,*
y3-image*
). Three non-collinear points and their images under the transformation are enough to specify any affine transformation.

If the positions *
(x1, y1)*
, *
(x2, y2)*
, and *
(x3, y3)*
are collinear, the
transformation-underspecified
error will be signaled. If (*
x1-image*
,*
y1-image*
), (*
x2-image*
,*
y2-image*
), and (*
x3-image*
,*
y3-image*
) are collinear, the resulting transformation will be singular, but this is not an error.

This is the spread version of make-3-point-transformation .

CommonLisp Interface Manager 2.0 User's Guide - 18 Mar 2005