Page 25 | Table of Contents | Index | Page 27 |

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 |

ellipses.

An

are special cases of elliptical arcs.

An ellipse is specified in a manner that is easy to transform, and treats all ellipses on an equal

basis. An ellipse is specified by its center point and two vectors that describe a bounding

parallelogram of the ellipse. The bounding parallelogram is made by adding and subtracting the

vectors from the the center point in the following manner:

x coordinate | y coordinate | |

Center of Ellipse | x_{c} |
y_{c} |

Vectors | dx_{1}dx_{2} |
dy_{1}dy_{2} |

Corners of Parallelogram | x_{c} + dx_{1} + dx_{2}x_{c} + dx_{1} - dx_{2}x_{c} - dx_{1} - dx_{2}x_{c} - dx_{1} + dx_{2} |
y_{c} + dy_{1} + dy_{2}y_{c} + dy_{1} - dy_{2}y_{c} - dy_{1} - dy_{2}y_{c} - dy_{1} + dy_{2} |

Note that several different parallelograms specify the same ellipse. One parallelogram is bound

to be a rectangle|the vectors will be perpendicular and correspond to the semi-axes of the

ellipse.

The special case of an ellipse with its axes aligned with the coordinate axes can be obtained by

setting

The protocol class that corresponds to a mathematical ellipse. This is a subclass of

you want to create a new class that behaves like an ellipse, it should be a subclass of

Subclasses of

Page 25 | Table of Contents | Index | Page 27 |

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 |