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, 30
A, B, C, D, E



CHAPTER 3. REGIONS


Figure 3.4: Different vectors may specify the same ellipse.


3.2.5 Ellipses and Elliptical Arcs

An ellipse is an area that is the outline and interior of an ellipse. Circles are special cases of
ellipses.

An elliptical arc is a path consisting of all or a portion of the outline of an ellipse. Circular arcs
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 xc yc
Vectors dx1
dx2
dy1
dy2
Corners of Parallelogram xc + dx1 + dx2
xc + dx1 - dx2
xc - dx1 - dx2
xc - dx1 + dx2
yc + dy1 + dy2
yc + dy1 - dy2
yc - dy1 - dy2
yc - dy1 + dy2

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 dx2 = dy1 = 0 or dx1 = dy2 = 0.

=> ellipse [Protocol Class]
The protocol class that corresponds to a mathematical ellipse. This is a subclass of area. If
you want to create a new class that behaves like an ellipse, it should be a subclass of ellipse.
Subclasses of ellipse must obey the ellipse protocol.

=> ellipsep object [Function]


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, 30
A, B, C, D, E