Coordinate Systems	Coordinate Systems	Rect Objects

Point Objects

Point objects represent 2D points or vectors--depending on how you interpret them; their internal representation is identical.

While such points could be represented by Python tuples, this special object type requires less memory and overloads some arithmetic operators. A point object is represented by two C `float' numbers, one for each cartesian coordinate.

Point objects are immutable.

Constructors

There are two constructor functions:

Point(x, y)

Point(sequence)

Return a point object with the coordinates x and y. If called with one argument, the argument must be a sequence of two numbers. This form is called a PointSpec

Polar(r, phi)

Polar(phi)

Return a point object for the polar coordinates r and phi. If r is omitted, it defaults to 1.0.

Attributes

A point object has two (read only) attributes:

x

The X-coordinate of the point as a python float

y

The Y-coordinate of the point as a python float

Methods

A point object has these methods:

normalized()

Return a unit vector pointing in the same direction. If the point's length is 0, raise a ZeroDivisionError.

polar()

Return a tuple (r, phi) containing the polar coordinates of the point. phi is in the range -pi to pi. If r is 0, so is phi.

Operators

Point objects implement both the number and the sequence protocol for Python objects. This allows the following operations:

Number Protocol

+P

The same as P.

-P

The negated vector P. The same as

Point(-P.x, -P.y)

P1 + P2

The sum of the vectors P1 and P2. The same as

Point(P1.x + P2.x, P1.y + P2.y)

P1 - P2

The difference of the vectors P1 and P2. The same as

Point(P1.x - P2.x, P1.y - P2.y)

P1 * P2

The dot product of the vectors P1 and P2. The same as

P1.x * P2.x + P1.y * P2.y

NUMBER * P

P * NUMBER

The same as

Point(NUMBER * P.x, NUMBER * P.y)

P / NUMBER

The same as

Point(P.x / NUMBER, P.y / NUMBER)

abs(P)

The length of the vector P. The same as math.hypot(P.x, P.y).

Sequence Protocol

len(P)

Always returns 2.

P[i]

For i either 0 or 1, this is the same as P.x or P.y respectively. For other values of i raise an IndexError exception.

tuple(P)

Return the coordinates of P as a tuple (P.x, P.y).

x, y = P

Unpack the point P. Equivalent to x, y = tuple(P)

P, P1 and P2 are point objects, NUMBER is any number that can be converted to a float.

abs, tuple, len and math.hypot are the standard Python functions of that name.

Constants

NullPoint

This is Point(0, 0)

PointType

The point type object.

PointSpec

While point objects are the standard representation for a point, it is sometimes inconvenient (particularly if you are computing the individual coordinates separately) to create a point object just because a function requires that argument type. Therefore, some functions also accept a PointSpec instead.

An argument that is supposed to be a PointSpec can be either a point object or any sequence of two numbers. Here, number means any object that can be converted to a `double' in C. You could use e. g. a tuple of floats or ints instead of a point object.

Coordinate Systems	Coordinate Systems	Rect Objects