From 6c8a62bbfea9ae40fa27ffe8b1756cec414d6db3 Mon Sep 17 00:00:00 2001 From: Tom Tromey Date: Tue, 26 Jul 2005 23:22:38 +0000 Subject: package.html, [...]: Removed. * gnu/java/net/protocol/ftp/package.html, gnu/javax/swing/text/html/package.html, gnu/javax/swing/text/html/parser/package.html, gnu/javax/swing/text/html/parser/models/package.html, gnu/javax/swing/text/html/parser/support/package.html, gnu/javax/swing/text/html/parser/support/low/package.html, gnu/xml/aelfred2/package.html, gnu/xml/dom/package.html, gnu/xml/pipeline/package.html, gnu/xml/transform/package.html, gnu/xml/util/package.html, java/awt/geom/doc-files/Area-1.png, java/awt/geom/doc-files/CubicCurve2D-1.png, java/awt/geom/doc-files/CubicCurve2D-2.png, java/awt/geom/doc-files/CubicCurve2D-3.png, java/awt/geom/doc-files/CubicCurve2D-4.png, java/awt/geom/doc-files/CubicCurve2D-5.png, java/awt/geom/doc-files/Ellipse-1.png, java/awt/geom/doc-files/FlatteningPathIterator-1.html, java/awt/geom/doc-files/GeneralPath-1.png, java/awt/geom/doc-files/QuadCurve2D-1.png, java/awt/geom/doc-files/QuadCurve2D-2.png, java/awt/geom/doc-files/QuadCurve2D-3.png, java/awt/geom/doc-files/QuadCurve2D-4.png, java/awt/geom/doc-files/QuadCurve2D-5.png, javax/imageio/package.html, javax/imageio/event/package.html, javax/imageio/metadata/package.html, javax/imageio/spi/package.html, javax/imageio/stream/package.html, javax/swing/border/doc-files/BevelBorder-1.png, javax/swing/border/doc-files/BevelBorder-2.png, javax/swing/border/doc-files/BevelBorder-3.png, javax/swing/border/doc-files/EmptyBorder-1.png, javax/swing/border/doc-files/EtchedBorder-1.png, javax/swing/border/doc-files/EtchedBorder-2.png, javax/swing/border/doc-files/LineBorder-1.png, javax/swing/border/doc-files/MatteBorder-1.png, javax/swing/border/doc-files/MatteBorder-2.png, javax/swing/border/doc-files/MatteBorder-3.png, javax/swing/border/doc-files/MatteBorder-4.png, javax/swing/border/doc-files/MatteBorder-5.png, javax/swing/border/doc-files/MatteBorder-6.png, javax/swing/border/doc-files/SoftBevelBorder-1.png, javax/swing/border/doc-files/SoftBevelBorder-2.png, javax/swing/border/doc-files/SoftBevelBorder-3.png, javax/swing/plaf/basic/doc-files/BasicBorders-1.png, javax/swing/plaf/basic/doc-files/BasicBorders-2.png, javax/swing/plaf/basic/doc-files/BasicBorders.ButtonBorder-1.png, javax/swing/plaf/basic/doc-files/BasicBorders.FieldBorder-1.png, javax/swing/plaf/basic/doc-files/BasicBorders.MarginBorder-1.png, javax/swing/plaf/basic/doc-files/BasicBorders.MenuBarBorder-1.png, javax/swing/plaf/basic/doc-files/BasicBorders.RadioButtonBorder-1.png, javax/swing/plaf/basic/doc-files/BasicBorders.SplitPaneBorder-1.png, javax/swing/plaf/basic/doc-files/BasicBorders.SplitPaneBorder-2.png, javax/swing/plaf/basic/doc-files/BasicBorders.SplitPaneDividerBorder-1.png, javax/swing/plaf/basic/doc-files/BasicBorders.ToggleButtonBorder-1.png, javax/swing/plaf/basic/doc-files/BasicGraphicsUtils-1.png, javax/swing/plaf/basic/doc-files/BasicGraphicsUtils-2.png, javax/swing/plaf/basic/doc-files/BasicGraphicsUtils-3.png, javax/swing/plaf/basic/doc-files/BasicGraphicsUtils-4.png, javax/swing/plaf/basic/doc-files/BasicGraphicsUtils-5.png, javax/swing/plaf/basic/doc-files/BasicGraphicsUtils-6.png, javax/swing/plaf/basic/doc-files/BasicGraphicsUtils-7.png, javax/swing/plaf/doc-files/ComponentUI-1.dia, javax/swing/plaf/doc-files/ComponentUI-1.png, javax/swing/plaf/doc-files/TreeUI-1.png, javax/xml/datatype/package.html, javax/xml/namespace/package.html, javax/xml/parsers/package.html, javax/xml/transform/package.html, javax/xml/transform/dom/package.html, javax/xml/transform/sax/package.html, javax/xml/transform/stream/package.html, javax/xml/validation/package.html, javax/xml/xpath/package.html: Removed. 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The GNU Implementation of FlatteningPathIterator

- -

Sascha -Brawer, November 2003

- -

This document describes the GNU implementation of the class -java.awt.geom.FlatteningPathIterator. It does -not describe how a programmer should use this class; please -refer to the generated API documentation for this purpose. Instead, it -is intended for maintenance programmers who want to understand the -implementation, for example because they want to extend the class or -fix a bug.

- - -

Data Structures

- -

The algorithm uses a stack. Its allocation is delayed to the time -when the source path iterator actually returns the first curved -segment (either SEG_QUADTO or SEG_CUBICTO). -If the input path does not contain any curved segments, the value of -the stack variable stays null. In this quite -common case, the memory consumption is minimal.

- -
stack
The variable stack is -a double array that holds the start, control and end -points of individual sub-segments.
- -
recLevel
The variable recLevel -holds how many recursive sub-divisions were needed to calculate a -segment. The original curve has recursion level 0. For each -sub-division, the corresponding recursion level is increased by -one.
- -
stackSize
Finally, the variable -stackSize indicates how many sub-segments are stored on -the stack.
- -

Algorithm

- -

The implementation separately processes each segment that the -base iterator returns.

- -

In the case of SEG_CLOSE, -SEG_MOVETO and SEG_LINETO segments, the -implementation simply hands the segment to the consumer, without actually -doing anything.

- -

Any SEG_QUADTO and SEG_CUBICTO segments -need to be flattened. Flattening is performed with a fixed-sized -stack, holding the coordinates of subdivided segments. When the base -iterator returns a SEG_QUADTO and -SEG_CUBICTO segments, it is recursively flattened as -follows:

- -
  1. Intialization: Allocate memory for the stack (unless a -sufficiently large stack has been allocated previously). Push the -original quadratic or cubic curve onto the stack. Mark that segment as -having a recLevel of zero.
    2. - -
  2. If the stack is empty, flattening the segment is complete, -and the next segment is fetched from the base iterator.
    3. - -
  3. If the stack is not empty, pop a curve segment from the -stack. - -
    • If its recLevel exceeds the recursion limit, - hand the current segment to the consumer.
      • - -
    • Calculate the squared flatness of the segment. If it smaller - than flatnessSq, hand the current segment to the - consumer.
      • - -
    • Otherwise, split the segment in two halves. Push the right - half onto the stack. Then, push the left half onto the stack. - Continue with step two.
    4. -
- -

The implementation is slightly complicated by the fact that -consumers pull the flattened segments from the -FlatteningPathIterator. This means that we actually -cannot “hand the curent segment over to the consumer.” -But the algorithm is easier to understand if one assumes a -push paradigm.

- - -

Example

- -

The following example shows how a -FlatteningPathIterator processes a -SEG_QUADTO segment. It is (arbitrarily) assumed that the -recursion limit was set to 2.

- -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ABCDEFGH
stack[0]——Sll.x—————
stack[1]——Sll.y—————
stack[2]——Cll.x—————
stack[3]——Cll.y—————
stack[4]—Sl.xEll.x - = Slr.xSlr.x—Srl.x——
stack[5]—Sl.yEll.x - = Slr.ySlr.y—Srl.y——
stack[6]—Cl.xClr.xClr.x—Crl.x——
stack[7]—Cl.yClr.yClr.y—Crl.y——
stack[8]S.xEl.x - = Sr.xElr.x - = Sr.xElr.x - = Sr.xSr.xErl.x - = Srr.xSrr.x—
stack[9]S.yEl.y - = Sr.yElr.y - = Sr.yElr.y - = Sr.ySr.yErl.y - = Srr.ySrr.y—
stack[10]C.xCr.xCr.xCr.xCr.xCrr.xCrr.x—
stack[11]C.yCr.yCr.yCr.yCr.yCrr.yCrr.y—
stack[12]E.xEr.xEr.xEr.xEr.xErr.xErr.x—
stack[13]E.yEr.yEr.yEr.yEr.yErr.yErr.x—
stackSize12321210
recLevel[2]——2—————
recLevel[1]—122—2——
recLevel[0]0111122—
-
- -
    - -
  1. The data structures are initialized as follows. - -
    • The segment’s end point E, control point -C, and start point S are pushed onto the stack.
      • - -
    • Currently, the curve in the stack would be approximated by one - single straight line segment (S – E). - Therefore, stackSize is set to 1.
      • - -
    • This single straight line segment is approximating the original - curve, which can be seen as the result of zero recursive - splits. Therefore, recLevel[0] is set to - zero.
    - -Column A shows the state after the initialization step.
    2. - -
  2. The algorithm proceeds by taking the topmost curve segment -(S – C – E) from the stack. - -
    • The recursion level of this segment (stored in - recLevel[0]) is zero, which is smaller than - the limit 2.
      • - -
    • The method java.awt.geom.QuadCurve2D.getFlatnessSq - is called to calculate the squared flatness.
      • - -
    • For the sake of argument, we assume that the squared flatness is - exceeding the threshold stored in flatnessSq. Thus, the - curve segment S – C – E gets - subdivided into a left and a right half, namely - Sl – Cl – - El and Sr – - Cr – Er. Both halves are - pushed onto the stack, so the left half is now on top. - -
       
      The left half starts at the same point - as the original curve, so Sl has the same - coordinates as S. Similarly, the end point of the right - half and of the original curve are identical - (Er = E). More interestingly, the left - half ends where the right half starts. Because - El = Sr, their coordinates need - to be stored only once, which amounts to saving 16 bytes (two - double values) for each iteration.
    - -Column B shows the state after the first iteration.
    3. - -
  3. Again, the topmost curve segment (Sl -– Cl – El) is -taken from the stack. - -
    • The recursion level of this segment (stored in - recLevel[1]) is 1, which is smaller than - the limit 2.
      • - -
    • The method java.awt.geom.QuadCurve2D.getFlatnessSq - is called to calculate the squared flatness.
      • - -
    • Assuming that the segment is still not considered - flat enough, it gets subdivided into a left - (Sll – Cll – - Ell) and a right (Slr - – Clr – Elr) - half.
    - -Column C shows the state after the second iteration.
    4. - -
  4. The topmost curve segment (Sll – -Cll – Ell) is popped from -the stack. - -
    • The recursion level of this segment (stored in - recLevel[2]) is 2, which is not smaller than - the limit 2. Therefore, a SEG_LINETO (from - Sll to Ell) is passed to the - consumer.
    - - The new state is shown in column D.
    5. - - -
  5. The topmost curve segment (Slr – -Clr – Elr) is popped from -the stack. - -
    • The recursion level of this segment (stored in - recLevel[1]) is 2, which is not smaller than - the limit 2. Therefore, a SEG_LINETO (from - Slr to Elr) is passed to the - consumer.
    - - The new state is shown in column E.
    6. - -
  6. The algorithm proceeds by taking the topmost curve segment -(Sr – Cr – -Er) from the stack. - -
    • The recursion level of this segment (stored in - recLevel[0]) is 1, which is smaller than - the limit 2.
      • - -
    • The method java.awt.geom.QuadCurve2D.getFlatnessSq - is called to calculate the squared flatness.
      • - -
    • For the sake of argument, we again assume that the squared - flatness is exceeding the threshold stored in - flatnessSq. Thus, the curve segment - (Sr – Cr – - Er) is subdivided into a left and a right half, - namely - Srl – Crl – - Erl and Srr – - Crr – Err. Both halves - are pushed onto the stack.
    - - The new state is shown in column F.
    7. - -
  7. The topmost curve segment (Srl – -Crl – Erl) is popped from -the stack. - -
    • The recursion level of this segment (stored in - recLevel[2]) is 2, which is not smaller than - the limit 2. Therefore, a SEG_LINETO (from - Srl to Erl) is passed to the - consumer.
    - - The new state is shown in column G.
    8. - -
  8. The topmost curve segment (Srr – -Crr – Err) is popped from -the stack. - -
    • The recursion level of this segment (stored in - recLevel[2]) is 2, which is not smaller than - the limit 2. Therefore, a SEG_LINETO (from - Srr to Err) is passed to the - consumer.
    - - The new state is shown in column H.
    9. - -
  9. The stack is now empty. The FlatteningPathIterator will fetch the -next segment from the base iterator, and process it.
    10. - -
- -

In order to split the most recently pushed segment, the -subdivideQuadratic() method passes stack -directly to -QuadCurve2D.subdivide(double[],int,double[],int,double[],int). -Because the stack grows towards the beginning of the array, no data -needs to be copied around: subdivide will directly store -the result into the stack, which will have the contents shown to the -right.

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