Class: Geometric

• Inheritance
• Description
• Class protocol
  • helper functions
  • initialization
  • queries
• Instance protocol
  • converting
  • destructive transformations
  • displaying
  • helper functions
  • inspecting
  • queries
  • testing
  • transformations
• Examples

Inheritance:

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

Package:

stx:libbasic

Category:

Graphics-Geometry-Objects

Version:

rev: 1.55 date: 2022/07/02 15:03:21

user: cg

file: Geometric.st directory: libbasic

module: stx stc-classLibrary: libbasic

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.

copyright
COPYRIGHT (c) 1995 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.

Class protocol:

 boundingRectangleForPoints: aSequencableCollectionOfPoints

given a bunch of point, compute the boundingRectangle
(i.e. the smallest rectangle which encloses all of those points)

 matrixToRotateBy: alpha

return a rotationmatrix;
the angle is interpreted as counter-clockwise (same as in Point >> rotateBy:)

TODO: cache to avoid recreating matrixes all the time

Usage example(s):

self matrixToRotateBy:0 self matrixToRotateBy:(90 degreesToRadians) self matrixToRotateBy:(180 degreesToRadians) self matrixToRotateBy:(270 degreesToRadians)

 matrixToScaleBy: aPointOrNumber

return a scaling matrix - simple
TODO: cache to avoid recreating matrixes all the time

Usage example(s):

self matrixToScaleBy:1 self matrixToScaleBy:2 (10@10 corner:20@20) scaledBy:2 (10@10 corner:20@20) transformedBy:(Geometric matrixToScaleBy:2)

 matrixToTranslateBy: aPointOrNumber

return a translation matrix - simple
TODO: cache to avoid recreating matrixes all the time

 initialize

setup class constants

Usage example(s):

Geometric initialize

 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:

 asFiller

return a wrapper which displays the receiver in its filled form

Usage example(s):

|v r| v := View new. v extent:200@200. v openAndWaitUntilVisible. r := Rectangle origin:10@10 corner:100@100. r asFiller displayOn:v.

 asFiller: fillColor

return a wrapper which displays the receiver filled with fillColor

Usage example(s):

|v r| v := View new. v extent:200@200. v openAndWaitUntilVisible. r := Rectangle origin:10@10 corner:100@100. (r asFiller:Color red) displayOn:v.

 asRectangle

return the enclosing rectangle; same as #bounds

 asStroker

return a wrapper which displays the receiver as stroked outline

 asStroker: lineColor

return a wrapper which displays the receiver drawn with strokeColor

Usage example(s):

|v r| v := View new. v extent:200@200. v openAndWaitUntilVisible. r := Rectangle origin:10@10 corner:100@100. (r asStroker:Color red) displayOn:v.

 asVisualComponent

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

 scaleBy: scale

scale the receiver rectangle by scale (a Number or Point).
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. (use scaledBy: if in doubt)

** This method must be redefined in concrete classes (subclassResponsibility) **

 translateBy: amount

translate (i.e. move) the receiver rectangle
by amount, a Point or Number (keeping extent unchanged).
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. (use translatedBy: if in doubt)

** This method must be redefined in concrete classes (subclassResponsibility) **

 ascentOn: aGC

displayOn: does not draw above baseline

 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 must be redefined in concrete classes (subclassResponsibility) **

 displayOn: aGCOrStream

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

Usage example(s):

|v r| v := View new. v extent:200@200. v openAndWaitUntilVisible. r := Rectangle origin:10@10 corner:100@100. r displayOn:v.

 displayOn: aGC x: x y: y

display myself on a graphicsContext at some coordinate;
the current graphics attributes are used.
The default here is to display the outline.

Usage example(s):

|v r| v := View new. v extent:200@200. v openAndWaitUntilVisible. r := Rectangle origin:10@10 corner:100@100. r displayOn:v at:20@30.

 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 must be redefined in concrete classes (subclassResponsibility) **

 matrixToScaleBy: aPointOrNumber

return a scaling matrix - simple
TODO: cache to avoid recreating matrixes all the time

Usage example(s):

self matrixToScaleBy:1 self matrixToScaleBy:2 (10@10 corner:20@20) scaledBy:2 (20@20) extent: (20@20) (10@10 corner:20@20) transformedBy:(Geometric matrixToScaleBy:2)

 inspector2TabDisplayObject

(comment from inherited method)
a tab, showing the receiver as display object

 bounds

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

 computeBounds

return the smallest enclosing rectangle.

** This method must be redefined in concrete classes (subclassResponsibility) **

 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.

 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.

 canBeFilled

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

 isBezier2Segment

return true, if the receiver is a quadratic bezier segment

 isGeometric

return true, if the receiver is a geometric object

 isLineSegment

return true, if the receiver is a line segment

 align: offset with: someCoordinate

return a new geometric object which is translated (i.e. moved)
such that the point offset in mySelf is placed on someCoordinate.

 alignBottomLeftWith: someCoordinate

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

Usage example(s):

|r1 r2 r3 v| r1 := 0@0 corner:10@10. r2 := 100@100 corner:200@200. r3 := r1 copy alignBottomLeftWith:r2 corner. v := (View extent:300@300) openAndWaitUntilVisible. r2 displayOn:v. r3 displayOn:v.

 alignBottomRightWith: someCoordinate

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

Usage example(s):

|r1 r2 r3 v| r1 := 0@0 corner:10@10. r2 := 100@100 corner:200@200. r3 := r1 copy alignBottomRightWith:r2 corner. v := (View extent:300@300) openAndWaitUntilVisible. r2 displayOn:v. r3 displayOn:v.

 alignCenterWith: someCoordinate

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

Usage example(s):

|r1 r2 r3 v| r1 := 0@0 corner:10@10. r2 := 100@100 corner:200@200. r3 := r1 copy alignCenterWith:r2 corner. v := (View extent:300@300) openAndWaitUntilVisible. r2 displayOn:v. r3 displayOn:v.

 alignCornerWith: someCoordinate

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

Usage example(s):

|r1 r2 r3 v| r1 := 0@0 corner:10@10. r2 := 100@100 corner:200@200. r3 := r1 copy alignCornerWith:r2 corner. v := (View extent:300@300) openAndWaitUntilVisible. r2 displayOn:v. r3 displayOn:v.

 alignOriginWith: someCoordinate

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

Usage example(s):

|r1 r2 r3 v| r1 := 0@0 corner:10@10. r2 := 100@100 corner:200@200. r3 := r1 copy alignOriginWith:r2 corner. v := (View extent:300@300) openAndWaitUntilVisible. r2 displayOn:v. r3 displayOn:v.

 alignTopLeftWith: someCoordinate

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

Usage example(s):

|r1 r2 r3 v| r1 := 0@0 corner:10@10. r2 := 100@100 corner:200@200. r3 := r1 copy alignTopLeftWith:r2 corner. v := (View extent:300@300) openAndWaitUntilVisible. r2 displayOn:v. r3 displayOn:v.

 alignTopRightWith: someCoordinate

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

Usage example(s):

|r1 r2 r3 v| r1 := 0@0 corner:10@10. r2 := 100@100 corner:200@200. r3 := r1 copy alignTopRightWith:r2 corner. v := (View extent:300@300) openAndWaitUntilVisible. r2 displayOn:v. r3 displayOn:v.

 rotatedBy: angle about: rotationCenter

return a copy of the receiver, which is rotated around rotationCenter
by an angle (radians) around rotationCenter (which may be located outside);
the angle is interpreted as counter-clockwise (same as in Point >> rotatedBy:)

Usage example(s):

(Rectangle origin:10@10 corner:50@50) rotatedBy:(Float pi) around:0@0 (Rectangle origin:10@10 corner:50@50) rotatedBy:(Float pi) around:10@10

 roundedToNearestIntegerPoint

return a copy of the receiver, where all points are rounded to ly on the nearest integer coordinate

** This method must be redefined in concrete classes (subclassResponsibility) **

 scaledBy: aPointOrNumber

return a copy of the receiver, which is scaled by the argument, a point or number

 transformedBy: aMatrix

return a copy of the receiver, which is transformed using aMatrix

** This method must be redefined in concrete classes (subclassResponsibility) **

 translatedBy: amount

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

Examples:

  |v l|

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

  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.

  |v r|

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

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

  v paint:Color red.
  r displayStrokedOn:v.

  |v c|

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

  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.

  |v c|

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

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

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

  v paint:Color blue.
  c displayFilledOn:v.

  |v e|

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

  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.

  |v p|

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

  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.

  |v c|

  v := View new openAndWaitUntilVisible.

  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.
  ]

  |v ell|

  v := View new openAndWaitUntilVisible.

  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.
  ].

  |v ell|

  v := View new openAndWaitUntilVisible.

  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.
  ].

  |v p|

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

  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.

  |v p|

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

  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.