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Documentation of class 'Point':

Class: Point

Inheritance
Description
Class protocol
Instance protocol

Inheritance:

   Object
   |
   +--Magnitude
      |
      +--ArithmeticValue
         |
         +--Point
            |
            +--Point3D

Package:: stx:libbasic

Category:: Graphics-Geometry

Version:: rev: 1.117 date: 2023/08/21 10:06:48; user: cg; file: Point.st directory: libbasic; module: stx stc-classLibrary: libbasic

Description:

I represent a point in 2D space. Or I can be used to represent
an extent (of a rectangle, for example), in which case my x-coordinate
represents the width, and y-coordinate the height of something.

The x and y coordinates are usually numbers.

[Instance variables:]

    x              <Number>        the x-coordinate of myself
    y              <Number>        the y-coordinate of myself

copyrightCOPYRIGHT (c) 1989 by Claus Gittinger
             All Rights Reserved

This software is furnished under a license and may be used
only in accordance with the terms of that license and with the
inclusion of the above copyright notice.   This software may not
be provided or otherwise made available to, or used by, any
other person.  No title to or ownership of the software is
hereby transferred.

create and return a new point given polar coordinates.
The angle is given in degrees.

OBSOLETE STX interface, use #r:theta:

** This is an obsolete interface - do not use it (it may vanish in future versions) **

r: distance degrees: angle

create and return a new point given polar coordinates.
The angle is given in degrees (ccw).
Added for Squeak compatibility

Usage example(s):

     Point r:100 degrees:90

r: distance theta: angleInRadians

create and return a new point given polar coordinates.
The angle is given in radians (ccw)

Usage example(s):

     Point r:100 theta:0
     Point r:100 theta:Float pi/2

readFrom: aStringOrStream onError: exceptionBlock

return the next Point from the (character-)stream aStream;
skipping all whitespace first; return the value of exceptionBlock,
if no point can be read.

Usage example(s):

     Point readFrom:'1.234 @ 5.678'
     Point readFrom:'( 1.234 @ 5.678 )'
     Point readFrom:'1'
     Point readFrom:'1' onError:[1@1]
     Point readFrom:'fooBar' onError:[0@0]

     Point readFrom:'( 10 × 20 )'   
     Point readFrom:'( 10 , 20 )'   
     Point readFrom:'( 10 ; 20 )'   
     Point readFrom:'( (10/2) × 20 )'   
     Point readFrom:'( (1/3) @ (1/2) )'

x: newX y: newY

create and return a new point with coordinates newX and newY

queries

isBuiltInClass: return true if this class is known by the run-time-system.
Here, true is returned for myself, false for subclasses.

Instance protocol:

Compatibility-Squeak

adhereTo: aRectangle

If the receiver lies outside aRectangle, return the nearest point on the boundary of the rectangle,
otherwise return self.

area

compute the area of a rectangle with myself taken as extent

asFloatPoint
( an extension from the stx:libcompat package )

Answer a new Point that is the receiver's x and y as floating-point numbers.

asLargerPowerOfTwo
( an extension from the stx:libcompat package )

return a point where both coordinates are rounded up to
the next larger power of two.
ATTN: it is not yet clear, what to do when a coordinate is already a powerOfTwo

Usage example(s):

     (10 @ 10) asLargerPowerOfTwo    
     (10 @ 10) asSmallerPowerOfTwo

asSmallerPowerOfTwo
( an extension from the stx:libcompat package )

return a point where both coordinates are rounded up to
the next smaller power of two.
ATTN: it is not yet clear, what to do when a coordinate is already a powerOfTwo

Usage example(s):

     (10 @ 10) asLargerPowerOfTwo    
     (10 @ 10) asSmallerPowerOfTwo   

     (16 @ 16) asLargerPowerOfTwo    
     (16 @ 16) asSmallerPowerOfTwo

maxDimension

Answer the larger of the two dimensions.

accessing

r: distance degrees: angle: initialize the new point given polar coordinates.
The angle is given in degrees (ccw).
Added for Squeak compatibility
r: distance theta: angleInRadians: initialize the new point given polar coordinates.
The angle is given in radians (ccw).
Added for Squeak compatibility
x: return the x coordinate
x: newX: set the x coordinate to be the argument, aNumber.
This is destructive (modifies the receiver, not a copy) and
should only be used if you know, that you are the exclusive owner
of the receiver.
x: newX y: newY: set both the x and y coordinates.
This is destructive (modifies the receiver, not a copy) and
should only be used if you know, that you are the exclusive owner
of the receiver.
y: return the y coordinate
y: newY: set the y coordinate to be the argument, aNumber.
This is destructive (modifies the receiver, not a copy) and
should only be used if you know, that you are the exclusive owner
of the receiver.
z ( an extension from the stx:libbasic2 package ): return the z coordinate - here zero

coercing & converting

coerce: anObject: convert the argument aNumber into an instance of the receiver's class and return it.
generality: return the generality value - see ArithmeticValue>>retry:coercing:

comparing

< aPointOrNumber

return true if the receiver is above and to the left
of the argument, aPointOrNumber

Usage example(s):

notice the funny result if one coordinate has the same value ...

     (3@3) < (4@4)     -> true
     (3@4) < (4@4)     -> false
     (4@3) < (4@4)     -> false

     (3@3) <= (4@4)    -> true
     (3@4) <= (4@4)    -> true
     (4@3) <= (4@4)    -> true
     (4@4) <= (4@4)    -> true

     (3@4) > (4@4)     -> false
     (4@4) >= (3@4)    -> true
     (4@4) > (3@4)     -> false

= aPointOrNumber

return true if the receiver represents the same point as
the argument, aPoint

> aPointOrNumber

return true if the receiver is below and to the right
of the argument, aPoint

hash

return a number for hashing

isLeftOrAbove: aPoint

return true if the receiver is above or to the left
of the argument, aPoint.
When sorting this enumerates points from left to right and top to bottom

max: aPoint

return the lower right corner of the rectangle uniquely defined by
the receiver and the argument, aPoint

min: aPoint

return the upper left corner of the rectangle uniquely defined by
the receiver and the argument, aPoint

converting

@ z ( an extension from the stx:libbasic2 package )

return a 3D coordinate from the receiver

Usage example(s):

     10 @ 20 @ 30
     (10 @ 20) @ 0

asComplex

Return a complex number whose real and imaginary components are the x and y
coordinates of the receiver.

asFloat

raises an error

asFraction

raises an error

asFractionalLayout
( an extension from the stx:libview2 package )

return a LayoutOrigin from the receiver,
treating the receiver coordinates as fractional parts
(i.e. relative to superview).

Usage example(s):

     (0@0.5) asFractionalLayout
     (0@0.5) asLayout
     (0@10) asLayout
     (0@10) asOffsetLayout

asFractionalLayoutWithOffset: aPoint

return a LayoutOrigin from the receiver,
treating the receiver coordinates as fractional parts
(i.e. relative to superview).

Usage example(s):

     (0@0.5) asFractionalLayoutWithOffset:(3@3)

asIntegerPoint

returns a point with truncated (towards zero)

Usage example(s):

     (1.5 @ 2.5) asIntegerPoint
     (-1.5 @ 2.5) asIntegerPoint

asLayout
( an extension from the stx:libview2 package )

return a LayoutOrigin from the receiver.
If the receiver coordinates are between 0 and 1, take
them as fractional parts (relative to superview).
Otherwise, treat them as absolute offsets.
Notice: in 10.5.x LayoutOrigin is not yet released.

Usage example(s):

     (0@0.5) asFractionalLayout
     (0@0.5) asLayout
     (0@10) asLayout
     (0@10) asOffsetLayout

asOffsetLayout
( an extension from the stx:libview2 package )

return a LayoutOrigin from the receiver,
treating the receiver coordinates as absolute offsets.

Usage example(s):

     (0@0.5) asFractionalLayout
     (0@0.5) asLayout
     (0@10) asLayout
     (0@10) asOffsetLayout

asPoint

return the receiver as Point - this is the receiver

asRectangle

return a zero-width rectangle consisting of origin
and corner being the receiver

Usage example(s):

     (0@10) asRectangle

corner: aPoint

return a rectangle whose origin is self and corner is aPoint

extent: aPoint

return a rectangle whose origin is self and extent is aPoint

fromLiteralArrayEncoding: encoding

read my values from an encoding.
The encoding is supposed to be of the form: (Point xValue yValue)

Usage example(s):

     Point new fromLiteralArrayEncoding:#(Point 10 20)

literalArrayEncoding

encode myself as an array, from which a copy of the receiver
can be reconstructed with #decodeAsLiteralArray.
The encoding is: (Point xValue yValue)

Usage example(s):

     Point new fromLiteralArrayEncoding:#(Point 10 20)
     (10@20) literalArrayEncoding

rectangleRelativeTo: aRectangle preferred: prefRectHolder

compute a displayRectangle, treating the receiver like a
layoutorigin. This allows point to be used interchangable with
LayoutOrigins.

Usage example(s):

     consider the case, where a view has a preferred extent of 50@50
     and is to be positioned in its superview which has size 100@100.
     For absolute origin:
	 (10@20) rectangleRelativeTo:(0@0 corner:100@100) preferred:(0@0 corner:50@50)

     for relative origin:
	 (0.5@0.5) rectangleRelativeTo:(0@0 corner:100@100) preferred:(0@0 corner:50@50)

destructive transformations

scaleBy: aScale: scale the receiver, by replacing coordinates by the product
of the receiver's coordinates and the scale (a Point or Number).
This is destructive (modifies the receiver, not a copy) and
should only be used if you know, that you are the exclusive owner
of the receiver.
translateBy: anOffset: translate the receiver, by replacing coordinates by the sum
of the receiver's coordinated and the scale (a Point or Number).
This is destructive (modifies the receiver, not a copy) and
should only be used if you know, that you are the exclusive owner
of the receiver.

double dispatching

differenceFromPoint: aPoint: return the difference from aPoint - self.
(not used with points, but with subclass instances)
productFromPoint: aPoint: return the product of aPoint * self.
(not used with points, but with subclass instances)
quotientFromPoint: aPoint: return the quotient of aPoint / self.
(not used with points, but with subclass instances)
sumFromPoint: aPoint: return the sum of aPoint + self.
(not used with points, but with subclass instances)

inspecting

inspectorValueStringInListFor: anInspector
( an extension from the stx:libtool package ): returns a string to be shown in the inspector's list

interpolating

interpolateTo: end at: amountDone

Interpolate between the instance and end after the specified amount has been done (0 - 1).
i.e. given a line segment deom the receiver to end,
return the coordinate of a point which is amountDone (a fraction) along the line

Usage example(s):

     (10@10) interpolateTo:(20@20) at:0.5
     (10@10) interpolateTo:(20@20) at:0.3
     (0@0) interpolateTo:(0@20) at:0.5

     (0@0) interpolateTo:(0@20) at:0    => 0@0        => the start point
     (0@0) interpolateTo:(0@20) at:1    => 0@20       => the end point
     (0@0) interpolateTo:(0@20) at:0.5  => 0.0@10.0   => the center point

     (0@0) interpolateTo:(20@20) at:0.5 => 10.0@10.0  => the center point

misc

abs

return a new point with my coordinates taken from the absolute values.

ceiling

return a new point with my coordinates truncated towards positive infinity.
Return the receiver if its coordinates are already integral.

Usage example(s):

     (1.5 @ 2.6) ceiling    => 2@3
     (1.5 @ -2.6) ceiling   => 2@-2
     (-1.5 @ -2.6) ceiling  => -1@-2
     (1 @ 2) ceiling        => 1@2

floor

return a new point with my coordinates truncated towards negative infinity.
Return the receiver if its coordinates are already integral.

Usage example(s):

     (1.5 @ 2.6) floor    => 1@2
     (1.5 @ -2.6) floor   => 1@-3
     (-1.5 @ -2.6) floor  => -2@-3
     (1.5 @ 2.4) floor    => 1@2
     (1 @ 2) floor        => 1@2

quadrant

return the number of the quadrant containing the receiver.
quadrants are named as follows:

^ 2 | 3
Y ------
1 | 0

X >

Q: what is to be returned if any coordinate is 0 ?

Usage example(s):

     (1@1) quadrant
     (-1@1) quadrant
     (-1@-1) quadrant
     (1@-1) quadrant
     (0@0) quadrant

quadrantContaining: aPoint

return the number of the quadrant containing aPoint placing
the receiver at the origin, where the quadrants are numbered as
follows:
^ 2 | 3
Y ------
1 | 0

X >
This can be used for polygon operations (see Foley for examples).

Usage example(s):

      (10 @ 10) quadrantContaining:(15 @ 15)
      (10 @ 10) quadrantContaining:(5 @ 5)
      (10 @ 10) quadrantContaining:(5 @ 15)
      (10 @ 10) quadrantContaining:(15 @ 5)

rounded

return a new point with my coordinates rounded to the next integer.
Return the receiver if its coordinates are already integral.

Usage example(s):

     (1.5 @ 2.6) rounded   => 2@3
     (1.5 @ 2.4) rounded   => 2@2
     (1 @ 2) rounded       => 1@2

truncateTo: aNumber

return a new point with my coordinates truncated towards zero to the next
multiple of aNumber.
Bad name: should be called truncatedTo: because it returns a new instance

Usage example(s):

     (10 @ 10) truncateTo:2         => 10@10
     (10.5 @ 10.5) truncateTo:2     => 10@10
     (10.5 @ 12.5) truncateTo:2     => 10@12
     (-10.5 @ 12.5) truncateTo:2    => -10@12
     (-10.5 @ -12.5) truncateTo:2   => -10@-12
     (-10.5 @ -13.5) truncateTo:2   => -10@-12
     (-10.5 @ -13.9) truncateTo:2   => -10@-12

truncated

return a new point with my coordinates truncated as integer.
Return the receiver if its coordinates are already integral.

Usage example(s):

     (10 @ 10) truncated         => 10@10
     (10.5 @ 10.5) truncated     => 10@10
     (10.5 @ 12.5) truncated     => 10@12
     (-10.5 @ 12.5) truncated    => -10@12
     (-10.5 @ -12.5) truncated   => -10@-12

point functions

crossProduct: aPoint

Return a number that is the cross product of the receiver and the
argument, aPoint.

dist: aPoint

return the distance between aPoint and the receiver.

dotProduct: aPoint

return a number that is the dot product of the receiver and
the argument, aPoint. That is, the two points are
multiplied and the coordinates of the result summed.

fourNeighbors

Modified (format): / 17-07-2017 / 14:20:40 / cg

grid: gridPoint

return a new point with coordinates grided (i.e. rounded to the
nearest point on the grid)

nearestIntegerPointOnLineFrom: point1 to: point2

return the closest integer point to the receiver on the line
determined by (point1, point2)--much faster than the more
accurate version if the receiver and arguments are integer points.
This method was found in the Manchester goody library.

Usage example(s):

     120@40 nearestIntegerPointOnLineFrom: 30@120 to: 100@120
     0@0 nearestIntegerPointOnLineFrom: 10@10 to: 100@100

nearestPointIn: aPointCollection

return the point from aPointCollection which is
closest to the receiver.

Usage example(s):

     120@40 nearestPointIn:{10@40 . 20@40 . 150@40}            => 150@40
     120@40 nearestPointIn:{10@40 . 20@40 . 150@40 . 130@50}   => 130@50

normalized

interpreting myself as the endPoint of a 0@0 based vector,
return the endPoint of the corresponding normalized vector.
(that is the endPoint of a vector with the same direction but length 1)

Usage example(s):

     (10 @ 10) normalized
     (1 @ 1) normalized
     (10 @ 0) normalized
     (0 @ 10) normalized
     (-10 @ 0) normalized
     (0 @ -10) normalized
     (0 @ 0) normalized

transposed

return a new point with x and y coordinates exchanged

polar coordinates

angle

return the receiver's angle (in degrees) in a polar coordinate system.
(i.e. the angle of a vector from 0@0 to the receiver).
OBSOLETE ST/X interface; use theta for ST-80 compatibility.

** This is an obsolete interface - do not use it (it may vanish in future versions) **

degrees

return the receiver's angle (in degrees) in a polar coordinate system.
(i.e. the angle of a vector from 0@0 to the receiver).
The angle is counted counter-clock-wise, starting with 0 for a horizontal
line (i.e. 0@0 -> 100@0 has an angle of 0 and 0@0 -> 0@100 has an angle of 90).
Added for Squeak compatibility.

Usage example(s):

     (1@1) degrees
     (2@1) degrees

r

return the receiver's radius in a polar coordinate system.
I.e. the length of a vector from 0@0 to the receiver

Usage example(s):

((x*x) + (y*y)) sqrt

Usage example(s):

     (1@1) r    -> 1.4142135623731
     (2@1) r    -> 2.23606797749979
     (2@0) r    -> 2.0
     (0@2) r    -> 2.0
     (-2@-2) r  -> 2.82842712474619
     (2@2) r    -> 2.82842712474619

theta

return the receiver's angle (in radians) in a polar coordinate system.
(i.e. the angle of a vector from 0@0 to the receiver)

Usage example(s):

     (1@1) theta
     (2@1) theta
     (-2@1) theta
     (-2@-1) theta
     (0@-1) theta

printing & storing

printOn: aStream: append a printed representation of the receiver to aStream
storeOn: aStream: append my storeString to aStream

testing

isFinite: return true, if the receiver is a finite point
I.e. both coordinates are not NaN and not +/-INF
isInfinite: return true, if the receiver has an infinite coordinate
isPoint: return true, if the receiver is some kind of point

transformations

* scale

Return a new Point that is the coordinate product of the
receiver and scale (which is a Point or Number).
See also cross- and dot products

+ translation

Return a new Point that is the sum of the
receiver and translation (which is a Point or Number).

Usage example(s):

     (10 @ 20) + (5 @ 10)     => 15@30
     (10 @ 20) + (5 @ 5)      => 15@25
     (10 @ 20) + 5            => 15@25
     (10 @ 20) + (5 + 10i)    => 15@30

- translation

Return a new Point that is the difference of the
receiver and translation (which is a Point or Number).

Usage example(s):

     (10 @ 20) - (5 @ 10)     => 5@10
     (10 @ 20) - (5 @ 5)      => 5@15
     (10 @ 20) - 5            => 5@15
     (10 @ 20) - (5 + 10i)    => 5@10

Usage example(s):

Modified (comment): / 02-07-2022 / 14:00:20 / cg

/ scale

Return a new Point that is the integer quotient of the
receiver and scale (which is a Point or Number).

// scale

Return a new Point that is the quotient of the
receiver and scale (which is a Point or Number).

negated

return a new point with my coordinates negated
i.e. the receiver mirrored at the origin

Usage example(s):

	(1 @ 1) negated

reciprocal

return a new point where the coordinates are
the reciproce of mine

rotateBy: angle about: center

Return a new point, generated by rotating the receiver
counterClockWise by some angle in radians around the given center point.
Even though Point.theta is measured CW,
this rotates with the more conventional CCW interpretation of angle.
CG: bad naming: should be named 'rotatedBy:', as this is non-destructive

Usage example(s):

     (10@10) rotateBy:Float pi about:0@0
     (10@0) rotateBy:Float pi about:0@0

rotatedBy: angle about: center

Return a new point, generated by rotating the receiver
counterClockWise by some angle in radians around the given center point.
Even though Point theta is measured CW,
this rotates with the more conventional CCW interpretation of angle

scaledBy: aScale

return a new Point that is the product of the
receiver and scale (which is a Point or Number).

transformedBy: aMatrix

return a new point which is me transformed by aMatrix

translatedBy: anOffset

return a copy of the receiver which is translated (i.e. moved)
by anOffset, aPoint or Number.
(i.e. receiver + anOffset).

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Smalltalk/X Webserver

Documentation of class 'Point':

Class: Point

Inheritance:

Description:

copyright

Class protocol:

Instance protocol: