Graphics Reference
In-Depth Information
Inline Exercise 12.1:
Without looking at the code, consider whether you can
find a more efficient way to invert an affine transformation on
R
2
than by invert-
ing its 3
3 matrix. Hint: The bottom row of the matrix is always
001
.
×
For each kind of transformation, the default constructor generates the identity
transformation. (The constructor for
MatrixTransformation2
is
protected
,as
only the derived classes are supposed to ever create a
MatrixTransformation
.)
In general, though, transformations are constructed by static methods with
mnemonic names. For the
AffineTransformation2
class, for instance, there are
eight static methods (all
public static AffineTransform2
) that construct trans-
formations.
1
2
3
4
5
6
7
8
9
10
RotateXY(double angle)
Translate(Vector v)
Translate(Point p, Point q)
AxisScale(double x_amount, double y_amount)
RotateAboutPoint(Point p, double angle)
PointsToPoints(Point p1, Point p2, Point p3,Point q1, Point q2, Point q3)
PointAndVectorsToPointAndVectors(Point p1, Vector v1, Vector v2,
Point q1, Vector w1, Vector w2)
PointsAndVectorToPointsAndVector(Point p1, Point p2, Vector v1,
Point q1, Point q2, Vector w1)
The naming convention is straightforward: “From” comes before “to” so that
Translate(Point p, Point q)
creates a translation that sends
p
to
q
, and within a collection of arguments, points
come before vectors so that in
PointAndVectorsToPointAndVectors
the point
p1
is sent to the point
q1
, the vector
v1
is sent to the vector
w1
, and the
vector
v2
is sent to the vector
w2
. The method name tells you that there is one point
and more than one vector; since an affine transformation of the plane is determined
by its values on three points, or one point and two vectors, or two points and one
vector, you know that the arguments must be one point and two vectors.
Methods that produce particular familiar transformations—translations, rota-
tions, axis-aligned scales—have names indicating these. While the names are
sometimes cumbersome, they are also expressive; it's easy to understand code
that uses them.
Most of the transformations are easy to implement. For instance, we first imple-
mented the
