Point2¶
import introcs
Points have position, but they do not have magnitude or direction. Use the class
Vector2
if you want direction. Points support basic point arithmetic via the
operators. However, pay close attention to how we handle typing. For example, the
difference between two points is a vector (as it should be). But points may freely
convert to vectors and vice versa.
Constructor¶

class
introcs.
Point2
([x, [y]])¶ An instance is a point in 2D space.
All attribute values are 0.0 by default.
 Parameters
x (
int
orfloat
) – initial x valuey (
int
orfloat
) – initial y value
Attributes¶

Point2.
x
¶ The x coordinate
Invariant: Value must be an
int
orfloat
.

Point2.
y
¶ The y coordinate
Invariant: Value must be an
int
orfloat
.
Immutable Methods¶
Immutable methods return a new object and do not modify the original.

Point2.
toVector
()¶  Returns
The
Vector2
object equivalent to this point Return type
Vector2

Point2.
midpoint
(other)¶ Computes the midpoint between self and
other
.This method treats
self
andother
as a line segment, so they must both be points. Parameters
other (
Point2
) – the other end of the line segment Returns
the midpoint between this point and
other
 Return type
Point2

Point2.
distance
(other)¶ Computes the Euclidean between two points
 Parameters
other (
Point2
) – value to compare against Returns
the Euclidean distance from this point to
other
 Return type
float

Point2.
distance2
(other)¶ Computes the squared Euclidean between two points
This method is slightly faster than
distance()
. Parameters
other (
Point2
) – value to compare against Returns
the squared Euclidean distance from this point to
other
 Return type
float

Point2.
under
(other)¶ Compares
self
toother
under the domination partial orderWe say that one point dominates another is all components of the first are greater than or equal to the components of the second. This is a partial order, not a total one.
 Parameters
other (
Vector2
) – The object to check Returns
True if
other
dominatesself
; False otherwise Return type
bool

Point2.
over
(other)¶ Compares
self
toother
under the domination partial orderWe say that one point dominates another is all components of the first are greater than or equal to the components of the second. This is a partial order, not a total one.
 Parameters
other (
Vector2
) – The object to check Returns
True if
self
dominatesother
; False otherwise Return type
bool

Point2.
isZero
()¶ Determines whether or not this object is ‘close enough’ to the origin.
This method uses
allclose()
to test whether the coordinates are “close enough”. It does not require exact equality for floats. Returns
True if this object is ‘close enough’ to the origin; False otherwise
 Return type
bool

Point2.
interpolant
(other, alpha)¶ Interpolates this object with another, producing a new object
The resulting value is:
alpha*self+(1alpha)*other
according to the rules of addition and scalar multiplication.
 Parameters
other (
Vector2
) – object to interpolate withalpha (
int
orfloat
) – scalar to interpolate by
 Returns
the interpolation of this object and
other
viaalpha
. Return type
Vector2

Point2.
copy
()¶  Returns
A copy of this point
 Return type
Vector2

Point2.
list
()¶  Returns
A python list with the contents of this point.
 Return type
list
Mutable Methods¶
Mutable methods modify the underlying object.

Point2.
interpolate
(other, alpha)¶ Interpolates this object with another in place
This method will modify the attributes of this oject. The new attributes will be equivalent to:
alpha*self+(1alpha)*other
according to the rules of addition and scalar multiplication.
This method returns this object for chaining.
 Parameters
other (
Vector2
) – object to interpolate withalpha (
int
orfloat
) – scalar to interpolate by
 Returns
This object, newly modified

Point2.
clamp
(low, high)¶ Clamps this point to the range [
low
,high
].Any value in this tuple less than
low
is set tolow
. Any value greater thanhigh
is set tohigh
.This method returns this object for chaining.
 Parameters
low (
int
orfloat
) – The low range of the clamphigh (
int
orfloat
) – The high range of the clamp
 Returns
This object, newly modified
 Return type
Vector2
Operators¶
Operators redefine the meaning of the basic operations. For example:: p + q
is
the same as p.__add__(q)
. This allows us to treat points like regular numbers.
For the sake of brevity, we have not listed all operators – only the most important
ones. The equivalences are as follows:
p == q > p.__eq__(q)
p < q > p.__lt__(q)
p + q > p.__add__(q)
p  q > p.__sub__(q)
p * q > p.__mul__(q)
q * p > p.__rmul__(q)
p / q > p.__truediv__(q)
q / p > p.__rtruediv__(q)

Point2.
__eq__
(other)¶ Compares this point with
other
This method uses
allclose()
to test whether the coordinates are “close enough”. It does not require exact equality for floats. Equivalence also requires type equivalence. Parameters
other (
any
) – The object to check Returns
True if
self
andother
are equivalent Return type
bool

Point2.
__lt__
(other)¶ Compares the lexicographic ordering of
self
andother
.Lexicographic ordering checks the xcoordinate first, and then y.
 Parameters
other (
Vector2
) – The object to check Returns
True if
self
is lexicographic kess thanother
 Return type
float

Point2.
__add__
(other)¶ Performs a context dependent addition of this point and
other
.If
other
is a point, the result is the vector from this position toother
(soother
is the head). If it is a vector, it is the point at the head of the vector when it is anchored at this point. Parameters
other (
Point2
orVector2
) – object to add Returns
the sum of this object and
other
. Return type
Point2
orVector2

Point2.
__sub__
(other)¶ Performs a context dependent subtraction of this point and
other
.If
other
is a point, the result is the vector fromother
to this position (soother
is the tail). If it is a vector, it is the point at the tail of the vector whose head is at this point. Parameters
other (
Point2
orVector2
) – object to subtract Returns
the difference of this object and
other
. Return type
Point2
orVector2

Point2.
__mul__
(value)¶ Multiples this object by a scalar,
Vector2
, or aMatrix
, producing a new object.The exact effect is determined by the type of value. If
value
is a scalar, the result is standard scalar multiplication. If it is a point, then the result is pointwise multiplication. Finally, if is a matrix, then we use the matrix to transform the object. We treat matrix transformation as multiplication on the right to make inplace multiplication easier. SeeMatrix
doe more Parameters
value (
int
,float
,Vector2
orMatrix
) – value to multiply by Returns
the altered object
 Return type
Vector2

Point2.
__rmul__
(value)¶ Multiplies this object by a scalar or
Vector2
on the left.The exact effect is determined by the type of value. If
value
is a scalar, the result is standard scalar multiplication. If it is a 2d tuple, then the result is pointwise multiplication. We do not allow matrix multiplication on the left. Parameters
value (
int
,float
, orVector2
) – The value to multiply by Returns
the scalar multiple of
self
andscalar
 Return type
Vector2

Point2.
__truediv__
(value)¶ Divides this object by a scalar or a
Vector2
on the right, producting a new object.The exact effect is determined by the type of value. If
value
is a scalar, the result is standard scalar division. If it is aVector2
, then the result is pointwise division.The value returned has the same type as
self
(so ifself
is an instance of a subclass, it uses that object instead of the original class. The contents of this object are not altered. Parameters
value (
int
,float
, orVector2
) – The value to multiply by Returns
the division of
self
byvalue
 Return type
Vector2

Point2.
__rtruediv__
(value)¶ Divides a scalar or
Vector2
by this object.Dividing by a point means pointwise reciprocation, followed by multiplication.
 Parameters
value (
int
,float
, orVector2
) – The value to divide Returns
the division of
value
byself
 Return type