3.5 The Transformations Used by CLIM

3.5.4 CLIM Transformation Functions

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.

Arguments:

transformation

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.

Arguments:

transformation dx dy

Arguments:

transformation sx sy&optionalorigin

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.

Arguments:

transformation dx dy

Arguments:

transformation sx sy&optional origin

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.

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))) 

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.

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.

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.

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.

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.

Arguments:

(medium&optional x y)&bodybody

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.

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.

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