FlatteningPathIterator.java: Entirely re-written.
2003-11-19 Sascha Brawer <brawer@dandelis.ch> * java/awt/geom/FlatteningPathIterator.java: Entirely re-written. * java/awt/geom/doc-files/FlatteningPathIterator-1.html: Describe how the implementation works. From-SVN: r73734
This commit is contained in:
Sascha Brawer
Michael Koch
parent
1f33554abb
commit
b6b8f69047
@ -1,3 +1,9 @@
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2003-11-19 Sascha Brawer <brawer@dandelis.ch>
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* java/awt/geom/FlatteningPathIterator.java: Entirely re-written.
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* java/awt/geom/doc-files/FlatteningPathIterator-1.html:
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Describe how the implementation works.
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2003-11-19 Michael Koch <konqueror@gmx.de>
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* java/net/Socket.java
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@ -1,5 +1,5 @@
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/* FlatteningPathIterator.java -- performs interpolation of curved paths
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Copyright (C) 2002 Free Software Foundation
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/* FlatteningPathIterator.java -- Approximates curves by straight lines
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Copyright (C) 2003 Free Software Foundation
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This file is part of GNU Classpath.
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@ -38,68 +38,542 @@ exception statement from your version. */
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package java.awt.geom;
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/**
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* This class can be used to perform the flattening required by the Shape
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* interface. It interpolates a curved path segment into a sequence of flat
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* ones within a certain flatness, up to a recursion limit.
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*
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* @author Eric Blake <ebb9@email.byu.edu>
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* @see Shape
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* @see RectangularShape#getPathIterator(AffineTransform, double)
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* @since 1.2
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* @status STUBS ONLY
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*/
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public class FlatteningPathIterator implements PathIterator
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{
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// The iterator we are applied to.
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private PathIterator subIterator;
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private double flatness;
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private int limit;
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import java.util.NoSuchElementException;
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/**
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* A PathIterator for approximating curved path segments by sequences
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* of straight lines. Instances of this class will only return
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* segments of type {@link PathIterator#SEG_MOVETO}, {@link
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* PathIterator#SEG_LINETO}, and {@link PathIterator#SEG_CLOSE}.
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*
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* <p>The accuracy of the approximation is determined by two
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* parameters:
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*
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* <ul><li>The <i>flatness</i> is a threshold value for deciding when
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* a curved segment is consided flat enough for being approximated by
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* a single straight line. Flatness is defined as the maximal distance
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* of a curve control point to the straight line that connects the
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* curve start and end. A lower flatness threshold means a closer
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* approximation. See {@link QuadCurve2D#getFlatness()} and {@link
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* CubicCurve2D#getFlatness()} for drawings which illustrate the
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* meaning of flatness.</li>
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*
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* <li>The <i>recursion limit</i> imposes an upper bound for how often
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* a curved segment gets subdivided. A limit of <i>n</i> means that
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* for each individual quadratic and cubic Bézier spline
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* segment, at most 2<sup><small><i>n</i></small></sup> {@link
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* PathIterator#SEG_LINETO} segments will be created.</li></ul>
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*
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* <p><b>Memory Efficiency:</b> The memory consumption grows linearly
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* with the recursion limit. Neither the <i>flatness</i> parameter nor
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* the number of segments in the flattened path will affect the memory
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* consumption.
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*
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* <p><b>Thread Safety:</b> Multiple threads can safely work on
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* separate instances of this class. However, multiple threads should
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* not concurrently access the same instance, as no synchronization is
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* performed.
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*
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* @see <a href="doc-files/FlatteningPathIterator-1.html"
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* >Implementation Note</a>
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*
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* @author Sascha Brawer (brawer@dandelis.ch)
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*
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* @since 1.2
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*/
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public class FlatteningPathIterator
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implements PathIterator
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{
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/**
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* The PathIterator whose curved segments are being approximated.
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*/
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private final PathIterator srcIter;
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/**
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* The square of the flatness threshold value, which determines when
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* a curve segment is considered flat enough that no further
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* subdivision is needed.
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*
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* <p>Calculating flatness actually produces the squared flatness
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* value. To avoid the relatively expensive calculation of a square
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* root for each curve segment, we perform all flatness comparisons
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* on squared values.
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*
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* @see QuadCurve2D#getFlatnessSq()
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* @see CubicCurve2D#getFlatnessSq()
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*/
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private final double flatnessSq;
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/**
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* The maximal number of subdivions that are performed to
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* approximate a quadratic or cubic curve segment.
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*/
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private final int recursionLimit;
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/**
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* A stack for holding the coordinates of subdivided segments.
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*
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* @see <a href="doc-files/FlatteningPathIterator-1.html"
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* >Implementation Note</a>
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*/
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private double[] stack;
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/**
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* The current stack size.
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*
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* @see <a href="doc-files/FlatteningPathIterator-1.html"
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* >Implementation Note</a>
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*/
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private int stackSize;
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/**
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* The number of recursions that were performed to arrive at
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* a segment on the stack.
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*
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* @see <a href="doc-files/FlatteningPathIterator-1.html"
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* >Implementation Note</a>
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*/
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private int[] recLevel;
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private final double[] scratch = new double[6];
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/**
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* The segment type of the last segment that was returned by
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* the source iterator.
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*/
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private int srcSegType;
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/**
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* The current <i>x</i> position of the source iterator.
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*/
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private double srcPosX;
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/**
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* The current <i>y</i> position of the source iterator.
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*/
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private double srcPosY;
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/**
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* A flag that indicates when this path iterator has finished its
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* iteration over path segments.
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*/
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private boolean done;
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/**
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* Constructs a new PathIterator for approximating an input
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* PathIterator with straight lines. The approximation works by
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* recursive subdivisons, until the specified flatness threshold is
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* not exceeded.
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*
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* <p>There will not be more than 10 nested recursion steps, which
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* means that a single <code>SEG_QUADTO</code> or
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* <code>SEG_CUBICTO</code> segment is approximated by at most
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* 2<sup><small>10</small></sup> = 1024 straight lines.
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*/
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public FlatteningPathIterator(PathIterator src, double flatness)
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{
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this(src, flatness, 10);
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}
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public FlatteningPathIterator(PathIterator src, double flatness, int limit)
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/**
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* Constructs a new PathIterator for approximating an input
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* PathIterator with straight lines. The approximation works by
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* recursive subdivisons, until the specified flatness threshold is
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* not exceeded. Additionally, the number of recursions is also
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* bound by the specified recursion limit.
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*/
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public FlatteningPathIterator(PathIterator src, double flatness,
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int limit)
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{
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subIterator = src;
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this.flatness = flatness;
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this.limit = limit;
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if (flatness < 0 || limit < 0)
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throw new IllegalArgumentException();
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srcIter = src;
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flatnessSq = flatness * flatness;
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recursionLimit = limit;
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fetchSegment();
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}
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/**
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* Returns the maximally acceptable flatness.
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*
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* @see QuadCurve2D#getFlatness()
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* @see CubicCurve2D#getFlatness()
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*/
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public double getFlatness()
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{
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return flatness;
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return Math.sqrt(flatnessSq);
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}
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/**
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* Returns the maximum number of recursive curve subdivisions.
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*/
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public int getRecursionLimit()
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{
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return limit;
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return recursionLimit;
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}
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// Documentation will be copied from PathIterator.
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public int getWindingRule()
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{
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return subIterator.getWindingRule();
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return srcIter.getWindingRule();
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}
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// Documentation will be copied from PathIterator.
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public boolean isDone()
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{
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return subIterator.isDone();
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return done;
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}
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// Documentation will be copied from PathIterator.
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public void next()
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{
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throw new Error("not implemented");
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if (stackSize > 0)
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{
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--stackSize;
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if (stackSize > 0)
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{
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switch (srcSegType)
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{
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case PathIterator.SEG_QUADTO:
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subdivideQuadratic();
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return;
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case PathIterator.SEG_CUBICTO:
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subdivideCubic();
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return;
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default:
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throw new IllegalStateException();
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}
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}
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}
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srcIter.next();
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fetchSegment();
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}
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// Documentation will be copied from PathIterator.
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public int currentSegment(double[] coords)
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{
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throw new Error("not implemented");
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if (done)
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throw new NoSuchElementException();
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switch (srcSegType)
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{
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case PathIterator.SEG_CLOSE:
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return srcSegType;
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case PathIterator.SEG_MOVETO:
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case PathIterator.SEG_LINETO:
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coords[0] = srcPosX;
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coords[1] = srcPosY;
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return srcSegType;
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case PathIterator.SEG_QUADTO:
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if (stackSize == 0)
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{
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coords[0] = srcPosX;
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coords[1] = srcPosY;
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}
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else
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{
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int sp = stack.length - 4 * stackSize;
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coords[0] = stack[sp + 2];
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coords[1] = stack[sp + 3];
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}
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return PathIterator.SEG_LINETO;
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case PathIterator.SEG_CUBICTO:
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if (stackSize == 0)
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{
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coords[0] = srcPosX;
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coords[1] = srcPosY;
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}
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else
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{
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int sp = stack.length - 6 * stackSize;
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coords[0] = stack[sp + 4];
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coords[1] = stack[sp + 5];
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}
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return PathIterator.SEG_LINETO;
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}
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throw new IllegalStateException();
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}
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// Documentation will be copied from PathIterator.
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public int currentSegment(float[] coords)
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{
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throw new Error("not implemented");
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if (done)
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throw new NoSuchElementException();
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switch (srcSegType)
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{
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case PathIterator.SEG_CLOSE:
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return srcSegType;
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case PathIterator.SEG_MOVETO:
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case PathIterator.SEG_LINETO:
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coords[0] = (float) srcPosX;
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coords[1] = (float) srcPosY;
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return srcSegType;
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case PathIterator.SEG_QUADTO:
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if (stackSize == 0)
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{
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coords[0] = (float) srcPosX;
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coords[1] = (float) srcPosY;
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}
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else
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{
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int sp = stack.length - 4 * stackSize;
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coords[0] = (float) stack[sp + 2];
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coords[1] = (float) stack[sp + 3];
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}
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return PathIterator.SEG_LINETO;
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case PathIterator.SEG_CUBICTO:
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if (stackSize == 0)
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{
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coords[0] = (float) srcPosX;
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coords[1] = (float) srcPosY;
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}
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else
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{
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int sp = stack.length - 6 * stackSize;
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coords[0] = (float) stack[sp + 4];
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coords[1] = (float) stack[sp + 5];
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}
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return PathIterator.SEG_LINETO;
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}
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throw new IllegalStateException();
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}
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} // class FlatteningPathIterator
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/**
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* Fetches the next segment from the source iterator.
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*/
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private void fetchSegment()
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{
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int sp;
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if (srcIter.isDone())
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{
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done = true;
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return;
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}
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srcSegType = srcIter.currentSegment(scratch);
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switch (srcSegType)
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{
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case PathIterator.SEG_CLOSE:
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return;
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case PathIterator.SEG_MOVETO:
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case PathIterator.SEG_LINETO:
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srcPosX = scratch[0];
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srcPosY = scratch[1];
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return;
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case PathIterator.SEG_QUADTO:
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if (recursionLimit == 0)
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{
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srcPosX = scratch[2];
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srcPosY = scratch[3];
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stackSize = 0;
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return;
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}
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sp = 4 * recursionLimit;
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stackSize = 1;
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if (stack == null)
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{
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stack = new double[sp + /* 4 + 2 */ 6];
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recLevel = new int[recursionLimit + 1];
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}
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recLevel[0] = 0;
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stack[sp] = srcPosX; // P1.x
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stack[sp + 1] = srcPosY; // P1.y
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stack[sp + 2] = scratch[0]; // C.x
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stack[sp + 3] = scratch[1]; // C.y
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srcPosX = stack[sp + 4] = scratch[2]; // P2.x
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srcPosY = stack[sp + 5] = scratch[3]; // P2.y
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subdivideQuadratic();
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break;
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case PathIterator.SEG_CUBICTO:
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if (recursionLimit == 0)
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{
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srcPosX = scratch[4];
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srcPosY = scratch[5];
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stackSize = 0;
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return;
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}
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sp = 6 * recursionLimit;
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stackSize = 1;
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if ((stack == null) || (stack.length < sp + 8))
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{
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stack = new double[sp + /* 6 + 2 */ 8];
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recLevel = new int[recursionLimit + 1];
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}
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recLevel[0] = 0;
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stack[sp] = srcPosX; // P1.x
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stack[sp + 1] = srcPosY; // P1.y
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stack[sp + 2] = scratch[0]; // C1.x
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stack[sp + 3] = scratch[1]; // C1.y
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stack[sp + 4] = scratch[2]; // C2.x
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stack[sp + 5] = scratch[3]; // C2.y
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srcPosX = stack[sp + 6] = scratch[4]; // P2.x
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srcPosY = stack[sp + 7] = scratch[5]; // P2.y
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subdivideCubic();
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return;
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}
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}
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/**
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* Repeatedly subdivides the quadratic curve segment that is on top
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* of the stack. The iteration terminates when the recursion limit
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* has been reached, or when the resulting segment is flat enough.
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*/
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private void subdivideQuadratic()
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{
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int sp;
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int level;
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sp = stack.length - 4 * stackSize - 2;
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level = recLevel[stackSize - 1];
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while ((level < recursionLimit)
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&& (QuadCurve2D.getFlatnessSq(stack, sp) >= flatnessSq))
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{
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recLevel[stackSize] = recLevel[stackSize - 1] = ++level;
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QuadCurve2D.subdivide(stack, sp, stack, sp - 4, stack, sp);
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++stackSize;
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sp -= 4;
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}
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}
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/**
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* Repeatedly subdivides the cubic curve segment that is on top
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* of the stack. The iteration terminates when the recursion limit
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* has been reached, or when the resulting segment is flat enough.
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*/
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private void subdivideCubic()
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{
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int sp;
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int level;
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sp = stack.length - 6 * stackSize - 2;
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level = recLevel[stackSize - 1];
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while ((level < recursionLimit)
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&& (CubicCurve2D.getFlatnessSq(stack, sp) >= flatnessSq))
|
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{
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recLevel[stackSize] = recLevel[stackSize - 1] = ++level;
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CubicCurve2D.subdivide(stack, sp, stack, sp - 6, stack, sp);
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++stackSize;
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sp -= 6;
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}
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}
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||||
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/* These routines were useful for debugging. Since they would
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* just bloat the implementation, they are commented out.
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*
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*
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||||
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private static String segToString(int segType, double[] d, int offset)
|
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{
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String s;
|
||||
|
||||
switch (segType)
|
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{
|
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case PathIterator.SEG_CLOSE:
|
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return "SEG_CLOSE";
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||||
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||||
case PathIterator.SEG_MOVETO:
|
||||
return "SEG_MOVETO (" + d[offset] + ", " + d[offset + 1] + ")";
|
||||
|
||||
case PathIterator.SEG_LINETO:
|
||||
return "SEG_LINETO (" + d[offset] + ", " + d[offset + 1] + ")";
|
||||
|
||||
case PathIterator.SEG_QUADTO:
|
||||
return "SEG_QUADTO (" + d[offset] + ", " + d[offset + 1]
|
||||
+ ") (" + d[offset + 2] + ", " + d[offset + 3] + ")";
|
||||
|
||||
case PathIterator.SEG_CUBICTO:
|
||||
return "SEG_CUBICTO (" + d[offset] + ", " + d[offset + 1]
|
||||
+ ") (" + d[offset + 2] + ", " + d[offset + 3]
|
||||
+ ") (" + d[offset + 4] + ", " + d[offset + 5] + ")";
|
||||
}
|
||||
|
||||
throw new IllegalStateException();
|
||||
}
|
||||
|
||||
|
||||
private void dumpQuadraticStack(String msg)
|
||||
{
|
||||
int sp = stack.length - 4 * stackSize - 2;
|
||||
int i = 0;
|
||||
System.err.print(" " + msg + ":");
|
||||
while (sp < stack.length)
|
||||
{
|
||||
System.err.print(" (" + stack[sp] + ", " + stack[sp+1] + ")");
|
||||
if (i < recLevel.length)
|
||||
System.out.print("/" + recLevel[i++]);
|
||||
if (sp + 3 < stack.length)
|
||||
System.err.print(" [" + stack[sp+2] + ", " + stack[sp+3] + "]");
|
||||
sp += 4;
|
||||
}
|
||||
System.err.println();
|
||||
}
|
||||
|
||||
|
||||
private void dumpCubicStack(String msg)
|
||||
{
|
||||
int sp = stack.length - 6 * stackSize - 2;
|
||||
int i = 0;
|
||||
System.err.print(" " + msg + ":");
|
||||
while (sp < stack.length)
|
||||
{
|
||||
System.err.print(" (" + stack[sp] + ", " + stack[sp+1] + ")");
|
||||
if (i < recLevel.length)
|
||||
System.out.print("/" + recLevel[i++]);
|
||||
if (sp + 3 < stack.length)
|
||||
{
|
||||
System.err.print(" [" + stack[sp+2] + ", " + stack[sp+3] + "]");
|
||||
System.err.print(" [" + stack[sp+4] + ", " + stack[sp+5] + "]");
|
||||
}
|
||||
sp += 6;
|
||||
}
|
||||
System.err.println();
|
||||
}
|
||||
|
||||
*
|
||||
*
|
||||
*/
|
||||
}
|
||||
|
||||
481
libjava/java/awt/geom/doc-files/FlatteningPathIterator-1.html
Normal file
481
libjava/java/awt/geom/doc-files/FlatteningPathIterator-1.html
Normal file
@ -0,0 +1,481 @@
|
||||
<?xml version="1.0" encoding="US-ASCII"?>
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
|
||||
<head>
|
||||
<title>The GNU Implementation of java.awt.geom.FlatteningPathIterator</title>
|
||||
<meta name="author" content="Sascha Brawer" />
|
||||
<style type="text/css"><!--
|
||||
td { white-space: nowrap; }
|
||||
li { margin: 2mm 0; }
|
||||
--></style>
|
||||
</head>
|
||||
<body>
|
||||
|
||||
<h1>The GNU Implementation of FlatteningPathIterator</h1>
|
||||
|
||||
<p><i><a href="http://www.dandelis.ch/people/brawer/">Sascha
|
||||
Brawer</a>, November 2003</i></p>
|
||||
|
||||
<p>This document describes the GNU implementation of the class
|
||||
<code>java.awt.geom.FlatteningPathIterator</code>. It does
|
||||
<em>not</em> 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.</p>
|
||||
|
||||
|
||||
<h2>Data Structures</h2>
|
||||
|
||||
<p>The algorithm uses a stack. Its allocation is delayed to the time
|
||||
when the source path iterator actually returns the first curved
|
||||
segment (either <code>SEG_QUADTO</code> or <code>SEG_CUBICTO</code>).
|
||||
If the input path does not contain any curved segments, the value of
|
||||
the <code>stack</code> variable stays <code>null</code>. In this quite
|
||||
common case, the memory consumption is minimal.</p>
|
||||
|
||||
<dl><dt><code>stack</code></dt><dd>The variable <code>stack</code> is
|
||||
a <code>double</code> array that holds the start, control and end
|
||||
points of individual sub-segments.</dd>
|
||||
|
||||
<dt><code>recLevel</code></dt><dd>The variable <code>recLevel</code>
|
||||
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.</dd>
|
||||
|
||||
<dt><code>stackSize</code></dt><dd>Finally, the variable
|
||||
<code>stackSize</code> indicates how many sub-segments are stored on
|
||||
the stack.</dd></dl>
|
||||
|
||||
<h2>Algorithm</h2>
|
||||
|
||||
<p>The implementation separately processes each segment that the
|
||||
base iterator returns.</p>
|
||||
|
||||
<p>In the case of <code>SEG_CLOSE</code>,
|
||||
<code>SEG_MOVETO</code> and <code>SEG_LINETO</code> segments, the
|
||||
implementation simply hands the segment to the consumer, without actually
|
||||
doing anything.</p>
|
||||
|
||||
<p>Any <code>SEG_QUADTO</code> and <code>SEG_CUBICTO</code> 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 <code>SEG_QUADTO</code> and
|
||||
<code>SEG_CUBICTO</code> segments, it is recursively flattened as
|
||||
follows:</p>
|
||||
|
||||
<ol><li>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 <code>recLevel</code> of zero.</li>
|
||||
|
||||
<li>If the stack is empty, flattening the segment is complete,
|
||||
and the next segment is fetched from the base iterator.</li>
|
||||
|
||||
<li>If the stack is not empty, pop a curve segment from the
|
||||
stack.
|
||||
|
||||
<ul><li>If its <code>recLevel</code> exceeds the recursion limit,
|
||||
hand the current segment to the consumer.</li>
|
||||
|
||||
<li>Calculate the squared flatness of the segment. If it smaller
|
||||
than <code>flatnessSq</code>, hand the current segment to the
|
||||
consumer.</li>
|
||||
|
||||
<li>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.</li></ul></li>
|
||||
</ol>
|
||||
|
||||
<p>The implementation is slightly complicated by the fact that
|
||||
consumers <em>pull</em> the flattened segments from the
|
||||
<code>FlatteningPathIterator</code>. 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
|
||||
<em>push</em> paradigm.</p>
|
||||
|
||||
|
||||
<h2>Example</h2>
|
||||
|
||||
<p>The following example shows how a
|
||||
<code>FlatteningPathIterator</code> processes a
|
||||
<code>SEG_QUADTO</code> segment. It is (arbitrarily) assumed that the
|
||||
recursion limit was set to 2.</p>
|
||||
|
||||
<blockquote>
|
||||
<table border="1" cellspacing="0" cellpadding="8">
|
||||
<tr align="center" valign="baseline">
|
||||
<th></th><th>A</th><th>B</th><th>C</th>
|
||||
<th>D</th><th>E</th><th>F</th><th>G</th><th>H</th>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[0]</code></th>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td><i>S<sub>ll</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[1]</code></th>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td><i>S<sub>ll</sub>.y</i></td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[2]</code></th>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td><i>C<sub>ll</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[3]</code></th>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td><i>C<sub>ll</sub>.y</i></td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[4]</code></th>
|
||||
<td>—</td>
|
||||
<td><i>S<sub>l</sub>.x</i></td>
|
||||
<td><i>E<sub>ll</sub>.x</i>
|
||||
= <i>S<sub>lr</sub>.x</i></td>
|
||||
<td><i>S<sub>lr</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
<td><i>S<sub>rl</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[5]</code></th>
|
||||
<td>—</td>
|
||||
<td><i>S<sub>l</sub>.y</i></td>
|
||||
<td><i>E<sub>ll</sub>.x</i>
|
||||
= <i>S<sub>lr</sub>.y</i></td>
|
||||
<td><i>S<sub>lr</sub>.y</i></td>
|
||||
<td>—</td>
|
||||
<td><i>S<sub>rl</sub>.y</i></td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[6]</code></th>
|
||||
<td>—</td>
|
||||
<td><i>C<sub>l</sub>.x</i></td>
|
||||
<td><i>C<sub>lr</sub>.x</i></td>
|
||||
<td><i>C<sub>lr</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
<td><i>C<sub>rl</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[7]</code></th>
|
||||
<td>—</td>
|
||||
<td><i>C<sub>l</sub>.y</i></td>
|
||||
<td><i>C<sub>lr</sub>.y</i></td>
|
||||
<td><i>C<sub>lr</sub>.y</i></td>
|
||||
<td>—</td>
|
||||
<td><i>C<sub>rl</sub>.y</i></td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[8]</code></th>
|
||||
<td><i>S.x</i></td>
|
||||
<td><i>E<sub>l</sub>.x</i>
|
||||
= <i>S<sub>r</sub>.x</i></td>
|
||||
<td><i>E<sub>lr</sub>.x</i>
|
||||
= <i>S<sub>r</sub>.x</i></td>
|
||||
<td><i>E<sub>lr</sub>.x</i>
|
||||
= <i>S<sub>r</sub>.x</i></td>
|
||||
<td><i>S<sub>r</sub>.x</i></td>
|
||||
<td><i>E<sub>rl</sub>.x</i>
|
||||
= <i>S<sub>rr</sub>.x</i></td>
|
||||
<td><i>S<sub>rr</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[9]</code></th>
|
||||
<td><i>S.y</i></td>
|
||||
<td><i>E<sub>l</sub>.y</i>
|
||||
= <i>S<sub>r</sub>.y</i></td>
|
||||
<td><i>E<sub>lr</sub>.y</i>
|
||||
= <i>S<sub>r</sub>.y</i></td>
|
||||
<td><i>E<sub>lr</sub>.y</i>
|
||||
= <i>S<sub>r</sub>.y</i></td>
|
||||
<td><i>S<sub>r</sub>.y</i></td>
|
||||
<td><i>E<sub>rl</sub>.y</i>
|
||||
= <i>S<sub>rr</sub>.y</i></td>
|
||||
<td><i>S<sub>rr</sub>.y</i></td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[10]</code></th>
|
||||
<td><i>C.x</i></td>
|
||||
<td><i>C<sub>r</sub>.x</i></td>
|
||||
<td><i>C<sub>r</sub>.x</i></td>
|
||||
<td><i>C<sub>r</sub>.x</i></td>
|
||||
<td><i>C<sub>r</sub>.x</i></td>
|
||||
<td><i>C<sub>rr</sub>.x</i></td>
|
||||
<td><i>C<sub>rr</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[11]</code></th>
|
||||
<td><i>C.y</i></td>
|
||||
<td><i>C<sub>r</sub>.y</i></td>
|
||||
<td><i>C<sub>r</sub>.y</i></td>
|
||||
<td><i>C<sub>r</sub>.y</i></td>
|
||||
<td><i>C<sub>r</sub>.y</i></td>
|
||||
<td><i>C<sub>rr</sub>.y</i></td>
|
||||
<td><i>C<sub>rr</sub>.y</i></td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[12]</code></th>
|
||||
<td><i>E.x</i></td>
|
||||
<td><i>E<sub>r</sub>.x</i></td>
|
||||
<td><i>E<sub>r</sub>.x</i></td>
|
||||
<td><i>E<sub>r</sub>.x</i></td>
|
||||
<td><i>E<sub>r</sub>.x</i></td>
|
||||
<td><i>E<sub>rr</sub>.x</i></td>
|
||||
<td><i>E<sub>rr</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stack[13]</code></th>
|
||||
<td><i>E.y</i></td>
|
||||
<td><i>E<sub>r</sub>.y</i></td>
|
||||
<td><i>E<sub>r</sub>.y</i></td>
|
||||
<td><i>E<sub>r</sub>.y</i></td>
|
||||
<td><i>E<sub>r</sub>.y</i></td>
|
||||
<td><i>E<sub>rr</sub>.y</i></td>
|
||||
<td><i>E<sub>rr</sub>.x</i></td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>stackSize</code></th>
|
||||
<td>1</td>
|
||||
<td>2</td>
|
||||
<td>3</td>
|
||||
<td>2</td>
|
||||
<td>1</td>
|
||||
<td>2</td>
|
||||
<td>1</td>
|
||||
<td>0</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>recLevel[2]</code></th>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>2</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>recLevel[1]</code></th>
|
||||
<td>—</td>
|
||||
<td>1</td>
|
||||
<td>2</td>
|
||||
<td>2</td>
|
||||
<td>—</td>
|
||||
<td>2</td>
|
||||
<td>—</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
<tr align="center" valign="baseline">
|
||||
<th><code>recLevel[0]</code></th>
|
||||
<td>0</td>
|
||||
<td>1</td>
|
||||
<td>1</td>
|
||||
<td>1</td>
|
||||
<td>1</td>
|
||||
<td>2</td>
|
||||
<td>2</td>
|
||||
<td>—</td>
|
||||
</tr>
|
||||
</table>
|
||||
</blockquote>
|
||||
|
||||
<ol>
|
||||
|
||||
<li>The data structures are initialized as follows.
|
||||
|
||||
<ul><li>The segment’s end point <i>E</i>, control point
|
||||
<i>C</i>, and start point <i>S</i> are pushed onto the stack.</li>
|
||||
|
||||
<li>Currently, the curve in the stack would be approximated by one
|
||||
single straight line segment (<i>S</i> – <i>E</i>).
|
||||
Therefore, <code>stackSize</code> is set to 1.</li>
|
||||
|
||||
<li>This single straight line segment is approximating the original
|
||||
curve, which can be seen as the result of zero recursive
|
||||
splits. Therefore, <code>recLevel[0]</code> is set to
|
||||
zero.</li></ul>
|
||||
|
||||
Column A shows the state after the initialization step.</li>
|
||||
|
||||
<li>The algorithm proceeds by taking the topmost curve segment
|
||||
(<i>S</i> – <i>C</i> – <i>E</i>) from the stack.
|
||||
|
||||
<ul><li>The recursion level of this segment (stored in
|
||||
<code>recLevel[0]</code>) is zero, which is smaller than
|
||||
the limit 2.</li>
|
||||
|
||||
<li>The method <code>java.awt.geom.QuadCurve2D.getFlatnessSq</code>
|
||||
is called to calculate the squared flatness.</li>
|
||||
|
||||
<li>For the sake of argument, we assume that the squared flatness is
|
||||
exceeding the threshold stored in <code>flatnessSq</code>. Thus, the
|
||||
curve segment <i>S</i> – <i>C</i> – <i>E</i> gets
|
||||
subdivided into a left and a right half, namely
|
||||
<i>S<sub>l</sub></i> – <i>C<sub>l</sub></i> –
|
||||
<i>E<sub>l</sub></i> and <i>S<sub>r</sub></i> –
|
||||
<i>C<sub>r</sub></i> – <i>E<sub>r</sub></i>. Both halves are
|
||||
pushed onto the stack, so the left half is now on top.
|
||||
|
||||
<br /> <br />The left half starts at the same point
|
||||
as the original curve, so <i>S<sub>l</sub></i> has the same
|
||||
coordinates as <i>S</i>. Similarly, the end point of the right
|
||||
half and of the original curve are identical
|
||||
(<i>E<sub>r</sub></i> = <i>E</i>). More interestingly, the left
|
||||
half ends where the right half starts. Because
|
||||
<i>E<sub>l</sub></i> = <i>S<sub>r</sub></i>, their coordinates need
|
||||
to be stored only once, which amounts to saving 16 bytes (two
|
||||
<code>double</code> values) for each iteration.</li></ul>
|
||||
|
||||
Column B shows the state after the first iteration.</li>
|
||||
|
||||
<li>Again, the topmost curve segment (<i>S<sub>l</sub></i>
|
||||
– <i>C<sub>l</sub></i> – <i>E<sub>l</sub></i>) is
|
||||
taken from the stack.
|
||||
|
||||
<ul><li>The recursion level of this segment (stored in
|
||||
<code>recLevel[1]</code>) is 1, which is smaller than
|
||||
the limit 2.</li>
|
||||
|
||||
<li>The method <code>java.awt.geom.QuadCurve2D.getFlatnessSq</code>
|
||||
is called to calculate the squared flatness.</li>
|
||||
|
||||
<li>Assuming that the segment is still not considered
|
||||
flat enough, it gets subdivided into a left
|
||||
(<i>S<sub>ll</sub></i> – <i>C<sub>ll</sub></i> –
|
||||
<i>E<sub>ll</sub></i>) and a right (<i>S<sub>lr</sub></i>
|
||||
– <i>C<sub>lr</sub></i> – <i>E<sub>lr</sub></i>)
|
||||
half.</li></ul>
|
||||
|
||||
Column C shows the state after the second iteration.</li>
|
||||
|
||||
<li>The topmost curve segment (<i>S<sub>ll</sub></i> –
|
||||
<i>C<sub>ll</sub></i> – <i>E<sub>ll</sub></i>) is popped from
|
||||
the stack.
|
||||
|
||||
<ul><li>The recursion level of this segment (stored in
|
||||
<code>recLevel[2]</code>) is 2, which is <em>not</em> smaller than
|
||||
the limit 2. Therefore, a <code>SEG_LINETO</code> (from
|
||||
<i>S<sub>ll</sub></i> to <i>E<sub>ll</sub></i>) is passed to the
|
||||
consumer.</li></ul>
|
||||
|
||||
The new state is shown in column D.</li>
|
||||
|
||||
|
||||
<li>The topmost curve segment (<i>S<sub>lr</sub></i> –
|
||||
<i>C<sub>lr</sub></i> – <i>E<sub>lr</sub></i>) is popped from
|
||||
the stack.
|
||||
|
||||
<ul><li>The recursion level of this segment (stored in
|
||||
<code>recLevel[1]</code>) is 2, which is <em>not</em> smaller than
|
||||
the limit 2. Therefore, a <code>SEG_LINETO</code> (from
|
||||
<i>S<sub>lr</sub></i> to <i>E<sub>lr</sub></i>) is passed to the
|
||||
consumer.</li></ul>
|
||||
|
||||
The new state is shown in column E.</li>
|
||||
|
||||
<li>The algorithm proceeds by taking the topmost curve segment
|
||||
(<i>S<sub>r</sub></i> – <i>C<sub>r</sub></i> –
|
||||
<i>E<sub>r</sub></i>) from the stack.
|
||||
|
||||
<ul><li>The recursion level of this segment (stored in
|
||||
<code>recLevel[0]</code>) is 1, which is smaller than
|
||||
the limit 2.</li>
|
||||
|
||||
<li>The method <code>java.awt.geom.QuadCurve2D.getFlatnessSq</code>
|
||||
is called to calculate the squared flatness.</li>
|
||||
|
||||
<li>For the sake of argument, we again assume that the squared
|
||||
flatness is exceeding the threshold stored in
|
||||
<code>flatnessSq</code>. Thus, the curve segment
|
||||
(<i>S<sub>r</sub></i> – <i>C<sub>r</sub></i> –
|
||||
<i>E<sub>r</sub></i>) is subdivided into a left and a right half,
|
||||
namely
|
||||
<i>S<sub>rl</sub></i> – <i>C<sub>rl</sub></i> –
|
||||
<i>E<sub>rl</sub></i> and <i>S<sub>rr</sub></i> –
|
||||
<i>C<sub>rr</sub></i> – <i>E<sub>rr</sub></i>. Both halves
|
||||
are pushed onto the stack.</li></ul>
|
||||
|
||||
The new state is shown in column F.</li>
|
||||
|
||||
<li>The topmost curve segment (<i>S<sub>rl</sub></i> –
|
||||
<i>C<sub>rl</sub></i> – <i>E<sub>rl</sub></i>) is popped from
|
||||
the stack.
|
||||
|
||||
<ul><li>The recursion level of this segment (stored in
|
||||
<code>recLevel[2]</code>) is 2, which is <em>not</em> smaller than
|
||||
the limit 2. Therefore, a <code>SEG_LINETO</code> (from
|
||||
<i>S<sub>rl</sub></i> to <i>E<sub>rl</sub></i>) is passed to the
|
||||
consumer.</li></ul>
|
||||
|
||||
The new state is shown in column G.</li>
|
||||
|
||||
<li>The topmost curve segment (<i>S<sub>rr</sub></i> –
|
||||
<i>C<sub>rr</sub></i> – <i>E<sub>rr</sub></i>) is popped from
|
||||
the stack.
|
||||
|
||||
<ul><li>The recursion level of this segment (stored in
|
||||
<code>recLevel[2]</code>) is 2, which is <em>not</em> smaller than
|
||||
the limit 2. Therefore, a <code>SEG_LINETO</code> (from
|
||||
<i>S<sub>rr</sub></i> to <i>E<sub>rr</sub></i>) is passed to the
|
||||
consumer.</li></ul>
|
||||
|
||||
The new state is shown in column H.</li>
|
||||
|
||||
<li>The stack is now empty. The FlatteningPathIterator will fetch the
|
||||
next segment from the base iterator, and process it.</li>
|
||||
|
||||
</ol>
|
||||
|
||||
<p>In order to split the most recently pushed segment, the
|
||||
<code>subdivideQuadratic()</code> method passes <code>stack</code>
|
||||
directly to
|
||||
<code>QuadCurve2D.subdivide(double[],int,double[],int,double[],int)</code>.
|
||||
Because the stack grows towards the beginning of the array, no data
|
||||
needs to be copied around: <code>subdivide</code> will directly store
|
||||
the result into the stack, which will have the contents shown to the
|
||||
right.</p>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
Loading…
Reference in New Issue
Block a user