Page 36 | Table of Contents | Index | Page 38 |

Chapters | |||

1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30A, B, C, D, E |

There is no single definition of a scaling transformation. Transformations that preserve all angles

and multiply all lengths by the same factor (preserving the "shape" of all entities) are certainly

scaling transformations. However, scaling is also used to refer to transformations that scale

distances in the

tance of every point from

point; if not supplied it defaults to (0

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".

the line passing through the

(

Returns a general transformation whose effect is:

wherex^{t}=m_{xx}x+m_{xy}y+t_{x}y^{t}=m_{yx}x+m_{yy}y+t_{y}

coordinates of the corresponding point after.

All of the arguments to

image

Returns a transformation that takes

image

transformation are enough to specify any affine transformation.

If

signalled. If

formation will be singular (that is, will have no inverse) but this is not an error.

image y3-image

Returns a transformation that takes the points at the positions (

(

Page 36 | Table of Contents | Index | Page 38 |

Chapters | |||

1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30A, B, C, D, E |