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	x_c	y_c
Vectors	dx₁ dx₂	dy₁ dy₂
Corners of Parallelogram	x_c + dx₁ + dx₂ x_c + dx₁ - dx₂ x_c - dx₁ - dx₂ x_c - dx₁ + dx₂	y_c + dy₁ + dy₂ y_c + dy₁ - dy₂ y_c - dy₁ - dy₂ y_c - 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