A
Matrix
is an object that represents an affine transformation,
which is a 2D coordinate transformation that preserves parallel lines.
Matrices are commonly used to transform points that a Yoix program works
with into points that describe a physical location in an object, like a
Canvas,
Frame,
Image,
or
JFrame,
that can be drawn on your screen, and in that context we often say the
matrix maps "user space" into "device space".
A
Matrix
defines the numbers that describe the affine transformation and a collection
of built-ins, many with names borrowed from PostScript, that use or modify
the matrix.
The fields in a
Matrix
are:
| concat |
A
Builtin
that multiplies this matrix by another matrix and replaces this matrix by
the result.
| | concatmatrix |
A
Builtin
that multiplies this matrix by another matrix and returns the result.
| | currentmatrix |
A
Builtin
that returns a writable copy of this matrix.
| | dividematrix |
A
Builtin
that divides this matrix by another matrix and returns the result.
| | dtransform |
A
Builtin
that transforms a displacement using this matrix and returns the result.
| | identmatrix |
A
Builtin
that replaces this matrix with the identity matrix.
| | idtransform |
A
Builtin
that transforms a displacement using the inverse of this matrix
and returns the result.
| | initmatrix |
A
Builtin
that changes this matrix so it represents the default Yoix coordinate system.
| | invertmatrix |
A
Builtin
that returns the inverse of this matrix.
| | itransform |
A
Builtin
that transforms a point using the inverse of this matrix and returns
the result.
| | rotate |
A
Builtin
that changes this matrix so it applies a rotation about the origin
to transformed points.
| | scale |
A
Builtin
that changes this matrix so it applies horizontal and vertical scaling
to transformed points.
| | setmatrix |
A
Builtin
that replaces this matrix with a copy of another matrix.
| | shear |
A
Builtin
that changes this matrix so it applies horizontal and vertical shearing
to transformed points.
| | shx |
A
double
that represents the horizontal shearing associated with this matrix,
which is
0
by default.
| | shy |
A
double
that represents the vertical shearing associated with this matrix,
which is
0
by default.
| | sx |
A
double
that represents the horizontal scaling associated with this matrix,
which is
1
by default.
| | sy |
A
double
that represents the vertical scaling associated with this matrix,
which is
1
by default.
| | transform |
A
Builtin
that transforms a point using this matrix and returns the result.
| | translate |
A
Builtin
that changes this matrix so it applies horizontal and vertical translation
to transformed points.
| | tx |
A
double
that represents the horizontal translation associated with this matrix,
which is
0
by default.
| | ty |
A
double
that represents a vertical translation associated with this matrix,
which is
0
by default.
|
Several permanent fields have not been documented and should not be
used in Yoix applications.
In addition, we should point out that most applications make changes
to a matrix using built-ins, like
rotate,
scale,
and
translate,
rather than by explicitly setting individual components.
The read-only matrix
VM.screen.defaultmatrix
describes the default Yoix coordinate system, which has its origin
in the upper left corner of an object
(e.g., a
Canvas,
Frame,
Image,
JFrame,
or your entire screen), positive x to the right, positive y down,
and a resolution of 72 dots per inch.
It is a consistent coordinate system that is used to describe the position
and size of components that appear on your screen, the location of
mouse events, the initial coordinate system associated with
Graphics
objects, and much more.
In other words, ask for a frame that has a width of 720 and your program
gets a 10 inch wide frame no matter where it runs.
Add a
mousePressed
event handler to the frame and the location of mouse pressed events
in the frame are reported in the default Yoix coordinate system.
The default values assigned to
sx,
sy,
shx,
shy,
tx,
and
ty
mean that a new matrix created without an initializer starts out
as the identity matrix.
However the matrix stored in the
CTM
field associated with a
Graphics
or
Path
object, or the one created by the declaration
Matrix mtx = VM.screen.defaultmatrix.currentmatrix();
start out as writable copies of
VM.screen.defaultmatrix.
| |
| Example: |
The program,
import yoix.*.*;
Triangle(Graphics graphics, double sx, double sy) {
Matrix mtx;
graphics { // "named block"
mtx = currentmatrix();
scale(sx, sy);
moveto(72, 72);
rlineto(72, 0);
rlineto(0, 72);
closepath();
setmatrix(mtx);
fill();
}
}
JFrame f = {
Color background = Color.white;
paint(Rectangle rect) {
Triangle(graphics, 2, 1);
Triangle(graphics, 1, 3);
}
};
f.visible = TRUE;
defines a simple function that draws triangles that vary in shape and
position based on arguments that are used to scale the matrix that is
controlling the drawing.
We used
currentmatrix
and
setmatrix
to save and restore the original matrix, which is changed by
scale,
to illustrate their use and to emphasize, by the placement of
setmatrix,
that the scaled matrix is automatically used as components, like lines,
are added to the path but it is not used when
fill
is called to draw the path.
This is a simple example, but there is plenty to learn, so experiment by
moving
setmatrix,
removing
closepath,
replacing
fill
with
stroke
(pay close attention to the width of lines), and using
gsave
and
grestore
instead of
currentmatrix
and
setmatrix.
Pay careful attention to line widths when you try
stroke
instead of
fill,
because the matrix will make a subtle difference.
| | |
| See Also: |
Font,
Graphics,
Path
|
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