compose-transformations [Generic Function]

Arguments: transformation1 transformation2

Summary: Returns a transformation that is the mathematical composition of its arguments. Composition is in right-to-left order; that is, the resulting transformation represents the effects of applying the transformation * transformation2* followed by the transformation * transformation1* .

invert-transformation [Generic Function]

Summary: Returns a transformation that is the inverse of the transformation * transformation* . The result of composing a transformation with its inverse is equal to the identity transformation.

If * transformation* is singular, invert-transformation will signal the singulartransformation error, with a named restart that is invoked with a transformation and makes invert-transformation return that transformation. This is to allow a drawing application, for example, to use a generalized inverse to transform a region through a singular transformation.

Note that with finite-precision arithmetic there are several low-level conditions that might occur during the attempt to invert a singular or "almost singular" transformation. (These include computation of a zero determinant, floating-point underflow during computation of the determinant, or floating-point overflow during subsequent multiplication.) invert-transformation signals the singular-transformation error for all of these cases.

compose-translation-with-transformation [Function]

Arguments: transformation dx dy

compose-scaling-with-transformation [Function]

Arguments: transformation sx sy` &optional`

origin

compose-rotation-with-transformation [Function]

Arguments: transformation angle` &optional`

origin

Summary: These functions create a new transformation by composing the transformation * transformation* with a given translation, scaling, or rotation, respectively. The order of composition is that the translation, scaling, or rotation "transformation" is first, followed by * transformation* .

* dx* and * dy* are as for make-translation-transformation . * sx* and * sy* are as for make-scaling-transformation . * angle* and * origin* are as for make-rotationtransformation .

Note that these functions could be implemented by using the various constructors. They are provided because it is common to build up a transformation as a series of simple transformations.

compose-transformation-with-translation [Function]

Arguments: transformation dx dy

compose-transformation-with-scaling [Function]

Arguments: transformation sx sy` &optional`

origin

compose-transformation-with-rotation [Function]

Arguments: transformation angle` &optional`

origin

Summary: These functions create a new transformation by composing a given translation, scaling, or rotation, respectively, with the transformation * transformation* . The order of composition is * transformation* first, followed by the translation, scaling, or rotation "transformation."

* dx* and * dy* are as for make-translation-transformation . * sx* and * sy* are as for make-scaling-transformation . * angle* and * origin* are as for make-rotationtransformation .

Note that these functions could be implemented by using the various constructors and compose-transformations . They are provided because it is common to build up a transformation as a series of simple transformations.

The following three functions are no different than using with-drawing-options with the :transformation keyword argument supplied. However, they are sufficiently useful that they are provided as a convenience to programmers.

In order to preserve referential transparency, these three forms apply the translation, rotation, or scaling transformation first, then the rest of the transformation from` (medium-transformation`

` medium`

` )`

. That is, the following two forms would return the same transformation (assuming that the medium's transformation in the second example is the identity transformation):

(compose-transformations

(make-translation-transformation`dx`

`dy`

)

` (make-rotation-transformation ``angle`

))

(with-translation (`medium`

`dx`

`dy`

)

(with-rotation (`medium`

`angle`

)

` (medium-transformation ``medium`

)))

with-translation [Macro]

Arguments: (medium dx dy)` &body`

body

Summary: Establishes a translation on the medium * medium* that translates by * dx* in the * x* direction and * dy* in the * y* direction, and then executes * body* with that transformation in effect.

* dx* and * dy* are as for make-translation-transformation .

The * medium* argument is not evaluated, and must be a symbol that is bound to a sheet or medium. If * medium* is t , *standard-output* is used. * body* may have zero or more declarations as its first forms.

with-scaling [Macro]

Arguments: (medium sx` &optional`

sy origin)` &body`

body

Summary: Establishes a scaling transformation on the medium * medium* that scales by * sx* in the * x* direction and * sy* in the * y* direction, and then executes * body* with that transformation in effect. If * sy* is not supplied, it defaults to * sx* . If * origin* is supplied, the scaling is about that point; if it is not supplied, it defaults to (0, 0).

* sx* and * sy* are as for make-scaling-transformation .

The * medium* argument is not evaluated, and must be a symbol that is bound to a sheet or medium. If * medium* is t , *standard-output* is used. * body* may have zero or more declarations as its first forms.

with-rotation [Macro]

Arguments: (medium angle` &optional`

origin)` &body`

body

Summary: Establishes a rotation on the medium * medium* that rotates by * angle* , and then executes * body* with that transformation in effect. If * origin* is supplied, the rotation is about that point; if it is not supplied, it defaults to (0, 0).

* angle* and * origin* are as for make-rotation-transformation .

The * medium* argument is not evaluated, and must be a symbol that is bound to a sheet or medium. If * medium* is t , *standard-output* is used. * body* may have zero or more declarations as its first forms.

These two functions also compose a transformation into the current transformation of a stream, but have more complex behavior.

with-local-coordinates [Macro]

Arguments: (medium` &optional`

x y)` &body`

body

Summary: Binds the dynamic environment to establish a local coordinate system on the medium * medium* with the origin of the new coordinate system at the position * (x, y)* . The "directionality" of the coordinate system is otherwise unchanged. * x* and * y* are real numbers, and both default to 0.

* medium* argument is not evaluated, and must be a symbol that is bound to a sheet or medium. If * medium* is t , *standard-output* is used. * body* may have zero or more declarations as its first forms.

with-first-quadrant-coordinates [Macro]

Arguments: (medium` &optional`

x y)` &body`

body

Summary: Binds the dynamic environment to establish a local coordinate system on the medium * medium* with the positive * x* axis extending to the right and the positive * y* axis extending upward, with the origin of the new coordinate system at the position * (x, y)* . * x* and * y* are real numbers, and both default to 0.

* medium* argument is not evaluated, and must be a symbol that is bound to a sheet or medium. If * medium* is t , *standard-output* is used. * body* may have zero or more declarations as its first forms.

Common Lisp Interface Manager 2.0 User Guide - 14 Dec 2001