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Class: Geometric


Inheritance:

   Object
   |
   +--Geometric
      |
      +--Bezier
      |
      +--Circle
      |
      +--Curve
      |
      +--EllipticalArc
      |
      +--LineSegment
      |
      +--Polygon
      |
      +--Rectangle
      |
      +--Spline

Package:
stx:libbasic
Category:
Graphics-Geometry-Objects
Version:
rev: 1.37 date: 2017/02/22 17:58:25
user: cg
file: Geometric.st directory: libbasic
module: stx stc-classLibrary: libbasic
Author:
Claus Gittinger

Description:


Abstract superclass for geometric figures.
Concrete classes are (currently) Rectangle, Polygon and the classes
found in goodies/shape.

These are not graphical objects, but pure mathematical ones.
I.e. instances do not carry graphics attributes such as color, lineWidth etc.
However, they ``know'' how to display themself as stroked or possibly
filled picture on a graphicsContext (although, the GC's current
paint and lineStyles are used).

Use instances of (subclasses) of DisplayObject or 
of the GeometricWrapper classes for objects which keep the color 
and lineStyle information with them.

Notice: 
    ST/X does not use Geometric instances for drawing (yet).
    Except for Rectangle, Geometry and its subclasses exists mainly 
    for ST-80 compatibility and to provide a home when other (PD) 
    geometry classes are to be filed in.


Related information:

    Rectangle
    Polygon
    EllipticalArc
    Circle
    Spline
    Point
    LineSegment
    Curve
    Arrow
    ArrowedSpline
    GraphicsContext
    StrokingWrapper
    FillingWrapper

Class protocol:

helper functions
o  boundingRectangleForPoints: aSequencableCollectionOfPoints
given a bunch of point, compute the boundingRectangle
(i.e. the smallest rectangle which encloses all of those points)

initialization
o  initialize
setup class constants
usage example(s):
     Geometric initialize

queries
o  isAbstract
Return if this class is an abstract class.
True is returned here for myself only; false for subclasses.
Abstract subclasses must redefine this again.


Instance protocol:

converting
o  asFiller
return a wrapper which displays the receiver in its filled form

o  asRectangle
return the enclosing rectangle; same as #bounds

o  asStroker
return a wrapper which displays the receiver as stroked outline

o  asVisualComponent
return a wrapper on the receiver, which responds to VisualComponent messages.

displaying
o  ascentOn: aGC
displayOn: does not draw above baseline

o  displayFilledOn: aGC
display myself filled on a graphicsContext; the current graphics
attributes are used. Since we do not know how to do it, nothing is
drawn here.

** This method raises an error - it must be redefined in concrete classes **

o  displayOn: aGCOrStream
display myself on a graphicsContext; the current graphics
attributes are used. The default here is to display the outline.

o  displayStrokedOn: aGC
display my outline on a graphicsContext; the current graphics
attributes are used. Since we do not know how to do it, nothing is
drawn here.

** This method raises an error - it must be redefined in concrete classes **

queries
o  bounds
return the smallest enclosing rectangle.
This resends computeBounds, to allow caching of bounds in
case this computation is expensive.

o  computeBounds
return the smallest enclosing rectangle.

** This method raises an error - it must be redefined in concrete classes **

o  outlineIntersects: aRectangle
return true, if the receiver's image intersects
aRectangle, when drawn as an outline.
Here, all we can do is to ask the boundary rectangle;
subclasses should reimplement better checks.

o  regionIntersects: aRectangle
return true, if the receiver's image intersects
aRectangle, when drawn as a filled version.
Here, all we can do is to ask the boundary rectangle;
subclasses should reimplement better checks.

testing
o  canBeFilled
return true, if the receiver can be drawn as a filled geometric.
Return false here, since we don't know.

o  isBezier2Segment
return true, if the receiver is a quadratic bezier segment

o  isLineSegment
return true, if the receiver is a line segment

transformations
o  align: offset with: someCoordinate

o  alignBottomLeftWith: someCoordinate
return a copy of myself where its bottomLeft is aligned with someCoordinate

o  alignBottomRightWith: someCoordinate
return a copy of myself where its bottomRight is aligned with someCoordinate.
Same as alignCorner

o  alignCenterWith: someCoordinate
return a copy of myself where its center is aligned with someCoordinate.
Same as alignOrigin

o  alignCornerWith: someCoordinate
return a copy of myself where its corner is aligned with someCoordinate

o  alignOriginWith: someCoordinate
return a copy of myself where its origin is aligned with someCoordinate

o  alignTopLeftWith: someCoordinate
return a copy of myself where its topLeft is aligned with someCoordinate.
Same as alignOrigin

o  alignTopRightWith: someCoordinate
return a copy of myself where its topRight is aligned with someCoordinate.
Same as alignOrigin

o  scaledBy: scaleAmount
return a copy of the receiver, which is scaled by the argument,
a point or number

** This method raises an error - it must be redefined in concrete classes **

o  translatedBy: scaleAmount
return a copy of the receiver, which is translated by the argument,
a point or number

** This method raises an error - it must be redefined in concrete classes **


Examples:


line segment:
  |v l|

  v := (View extent:100@100) openAndWait.

  l := LineSegment from:10@10 to:90@90. 

  v paint:Color red.
  l displayStrokedOn:v.

  l start:90@10 end:10@90.
  v paint:Color blue.
  l displayStrokedOn:v.
rectangle, unfilled:
  |v r|

  v := (View extent:100@100) openAndWait.

  r := Rectangle origin:10@10 corner:90@90. 

  v paint:Color red.
  r displayStrokedOn:v.
circle; filled and unfilled:
  |v c|

  v := (View extent:200@100) openAndWait.

  c := Circle boundingBox:(10@10 corner:90@90). 

  v paint:Color blue.
  c displayFilledOn:v.

  c center:150@50.
  v paint:Color red.
  c displayStrokedOn:v.

circle & rectangle; both filled:
  |v c|

  v := (View extent:100@100) openAndWait.

  c := Circle center:50@50 radius:40. 

  v paint:Color red.
  c asRectangle displayFilledOn:v.

  v paint:Color blue.
  c displayFilledOn:v.

elliptical arcs; filled & unfilled:
  |v e|

  v := (View extent:200@100) openAndWait.

  e := EllipticalArc 
          boundingBox:(10@10 corner:190@90)
          startAngle:0
          endAngle:270. 

  v paint:Color blue.
  e displayFilledOn:v.

  v paint:Color red.
  e displayStrokedOn:v.

polygon; filled & unfilled:
  |v p|

  v := (View extent:100@100) openAndWait.

  p := Polygon vertices:
              (Array with:(10@10)
                     with:(90@90)
                     with:(10@90)).

  v paint:Color blue.
  p displayFilledOn:v.

  v paint:Color red.
  p displayStrokedOn:v.
circles; filled & unfilled:
  |v c|

  v := View new openAndWait.

  c := Circle center:50@50 radius:40.

  c displayFilledOn:v.
  50 to:1 by:-1 do:[:r |
      c radius:r.
      v paint:(Color grey:(r * 2)).
      c displayStrokedOn:v.
  ].
  1 to:50 do:[:r |
      c radius:r.
      v paint:(Color grey:100-(r * 2)).
      c displayStrokedOn:v.
  ]

arcs; filled:
  |v ell|

  v := View new openAndWait.

  ell := EllipticalArc
              boundingBox:(10@10 corner:90@90) 
              startAngle:0
              sweepAngle:0.

  #(45 90 135 180 225 270 315 360) keysAndValuesDo:[:index :angle |
      index odd ifTrue:[
          v paint:Color white
      ] ifFalse:[
          v paint:Color black
      ].
      ell sweepAngle:angle.
      ell displayFilledOn:v.
      Delay waitForSeconds:0.5.
  ].

arcs; filled:
  |v ell|

  v := View new openAndWait.

  ell := EllipticalArc
              boundingBox:(10@10 corner:90@90) 
              startAngle:0
              sweepAngle:45.

  #(45 90 135 180 225 270 315 360) 
  with:#( 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1)
  do:[:angle :grey |
      ell startAngle:angle-45.
      v paint:(ColorValue red:grey green:0 blue:0).
      ell displayFilledOn:v.
  ].

spline; filled & unfilled:
  |v p|

  v := (View extent:100@100) openAndWait.

  p := Spline controlPoints:
              (Array with:(20@20)
                     with:(80@80)
                     with:(20@80)).

  v paint:Color blue.
  p displayFilledOn:v.

  v paint:Color red.
  p displayStrokedOn:v.
closed spline; filled & unfilled:
  |v p|

  v := (View extent:100@100) openAndWait.

  p := Spline controlPoints:
              (Array with:(20@20)
                     with:(80@80)
                     with:(20@80)
                     with:(20@20)).

  v paint:Color blue.
  p displayFilledOn:v.

  v paint:Color red.
  p displayStrokedOn:v.


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