Geometric subclass:#Curve

	instanceVariableNames:'startPoint middlePoint endPoint'

!Curve class methodsFor:'documentation'!

    A Curve is a conic section determined by three points

    that interpolates the first and the third and is tangent to the angle formed

    by the three points at the first and third points.

        Rectangle Polygon EllipticalArc Circle Spline Point LineSegment

examples

"

  filled & unfilled:

                                                                        [exBegin]

    |v c|

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

    c := Curve start:(20@20) middle:(80@80) end:(20@80).

    v paint:Color blue.

    c displayFilledOn:v.

    v paint:Color red.

    c displayStrokedOn:v.

                                                                        [exEnd]

  with a grid (for demonstration):

                                                                        [exBegin]

    |v c|

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

    v lineStyle:#dashed.

    v displayLineFrom:(20@0) to:(20@200).

    v displayLineFrom:(180@0) to:(180@200).

    v displayLineFrom:(0@20) to:(200@20).

    v displayLineFrom:(0@80) to:(200@80).

    v lineStyle:#solid.

    c := Curve start:(20@20) middle:(180@80) end:(20@80).

    v paint:Color blue.

    c displayFilledOn:v.

    v paint:Color red.

    c displayStrokedOn:v.

    v paint:(Color black).

    v displayLineFrom:(20@20) to:(180@80).

    v displayLineFrom:(20@80) to:(180@80).

                                                                        [exEnd]

"

!Curve class methodsFor:'instance creation'!

from:startPoint to:endPoint through:middlePoint

    "return a new curve, passing through the three given points"

    ^ self new start:startPoint middle:middlePoint end:endPoint

    "Created: 8.5.1996 / 21:16:39 / cg"

!

start:startPoint middle:middlePoint end:endPoint

    "return a new curve, passing through the three given points"

    ^ self new start:startPoint middle:middlePoint end:endPoint

    "Created: 8.5.1996 / 21:19:30 / cg"

! !

!Curve methodsFor:'accessing'!

    "Created: 8.5.1996 / 21:08:35 / cg"

    "Created: 8.5.1996 / 21:08:44 / cg"

start:p1 middle:p2 end:p3

    "set the startPoint, middlePoint and the endPoint"

    middlePoint := p2.

    endPoint := p3.

    "Created: 8.5.1996 / 21:09:40 / cg"

!Curve methodsFor:'displaying'!

    "draw the receiver as a filled curve in a graphicsContext, aGC"

    aGC fillPolygon:self computeLines

    "Created: 8.5.1996 / 21:24:15 / cg"

    "Modified: 8.5.1996 / 21:25:33 / cg"

    "draw the receiver as a unfilled curve in a graphicsContext, aGC"

    aGC displayPolygon:self computeLines

    "Modified: 8.5.1996 / 21:25:35 / cg"

!Curve methodsFor:'helpers'!

computeLines

    "compute the lines which approxiamte this curve"

    |lines pa pb 

     numberOfSegments "{ Class: SmallInteger }"|

    lines := OrderedCollection new.

    "/ Compute the number of line segments used to approximate the curve.

    pa := middlePoint - startPoint.

    pb := endPoint - middlePoint.

    numberOfSegments := 5 max:pa x abs + pa y abs + pb x abs + pb y abs // 20.

    "/ Add all of the points necessary for the path.

    lines add:startPoint.

    1 to:numberOfSegments do:[:seg | 

        lines add:

                ((pa * seg // numberOfSegments + startPoint) * (numberOfSegments - seg)

                + ((pb * (seg - 1) // numberOfSegments + middlePoint) * (seg - 1)))

                // (numberOfSegments - 1)

    ].

    lines add:endPoint.

    ^ lines

    "Created: 8.5.1996 / 21:23:29 / cg"

! !

!Curve methodsFor:'queries'!

    |min max|

    min := (startPoint min: endPoint) min: middlePoint.

    max := (startPoint max: endPoint) max: middlePoint.

    ^ min corner:max

     (Curve from:10@10 to:50@100 through:50@50) bounds   

     (Curve from:10@10 to:50@100 through:100@50) bounds 

    "Modified: 8.5.1996 / 21:18:50 / cg"

!Curve class methodsFor:'documentation'!

    ^ '$Header: /cvs/stx/stx/libbasic2/LineSegment.st,v 1.2 1996-05-08 19:32:21 cg Exp $'