jdk/src/java.desktop/share/classes/sun/java2d/marlin/DStroker.java
changeset 47126 188ef162f019
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/jdk/src/java.desktop/share/classes/sun/java2d/marlin/DStroker.java	Wed May 17 22:05:11 2017 +0200
@@ -0,0 +1,1325 @@
+/*
+ * Copyright (c) 2007, 2017, Oracle and/or its affiliates. All rights reserved.
+ * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
+ *
+ * This code is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License version 2 only, as
+ * published by the Free Software Foundation.  Oracle designates this
+ * particular file as subject to the "Classpath" exception as provided
+ * by Oracle in the LICENSE file that accompanied this code.
+ *
+ * This code is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+ * version 2 for more details (a copy is included in the LICENSE file that
+ * accompanied this code).
+ *
+ * You should have received a copy of the GNU General Public License version
+ * 2 along with this work; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+ *
+ * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
+ * or visit www.oracle.com if you need additional information or have any
+ * questions.
+ */
+
+package sun.java2d.marlin;
+
+import java.util.Arrays;
+
+// TODO: some of the arithmetic here is too verbose and prone to hard to
+// debug typos. We should consider making a small Point/Vector class that
+// has methods like plus(Point), minus(Point), dot(Point), cross(Point)and such
+final class DStroker implements DPathConsumer2D, MarlinConst {
+
+    private static final int MOVE_TO = 0;
+    private static final int DRAWING_OP_TO = 1; // ie. curve, line, or quad
+    private static final int CLOSE = 2;
+
+    /**
+     * Constant value for join style.
+     */
+    public static final int JOIN_MITER = 0;
+
+    /**
+     * Constant value for join style.
+     */
+    public static final int JOIN_ROUND = 1;
+
+    /**
+     * Constant value for join style.
+     */
+    public static final int JOIN_BEVEL = 2;
+
+    /**
+     * Constant value for end cap style.
+     */
+    public static final int CAP_BUTT = 0;
+
+    /**
+     * Constant value for end cap style.
+     */
+    public static final int CAP_ROUND = 1;
+
+    /**
+     * Constant value for end cap style.
+     */
+    public static final int CAP_SQUARE = 2;
+
+    // pisces used to use fixed point arithmetic with 16 decimal digits. I
+    // didn't want to change the values of the constant below when I converted
+    // it to floating point, so that's why the divisions by 2^16 are there.
+    private static final double ROUND_JOIN_THRESHOLD = 1000.0d/65536.0d;
+
+    private static final double C = 0.5522847498307933d;
+
+    private static final int MAX_N_CURVES = 11;
+
+    private DPathConsumer2D out;
+
+    private int capStyle;
+    private int joinStyle;
+
+    private double lineWidth2;
+    private double invHalfLineWidth2Sq;
+
+    private final double[] offset0 = new double[2];
+    private final double[] offset1 = new double[2];
+    private final double[] offset2 = new double[2];
+    private final double[] miter = new double[2];
+    private double miterLimitSq;
+
+    private int prev;
+
+    // The starting point of the path, and the slope there.
+    private double sx0, sy0, sdx, sdy;
+    // the current point and the slope there.
+    private double cx0, cy0, cdx, cdy; // c stands for current
+    // vectors that when added to (sx0,sy0) and (cx0,cy0) respectively yield the
+    // first and last points on the left parallel path. Since this path is
+    // parallel, it's slope at any point is parallel to the slope of the
+    // original path (thought they may have different directions), so these
+    // could be computed from sdx,sdy and cdx,cdy (and vice versa), but that
+    // would be error prone and hard to read, so we keep these anyway.
+    private double smx, smy, cmx, cmy;
+
+    private final PolyStack reverse;
+
+    // This is where the curve to be processed is put. We give it
+    // enough room to store all curves.
+    private final double[] middle = new double[MAX_N_CURVES * 6 + 2];
+    private final double[] lp = new double[8];
+    private final double[] rp = new double[8];
+    private final double[] subdivTs = new double[MAX_N_CURVES - 1];
+
+    // per-thread renderer context
+    final DRendererContext rdrCtx;
+
+    // dirty curve
+    final DCurve curve;
+
+    /**
+     * Constructs a <code>DStroker</code>.
+     * @param rdrCtx per-thread renderer context
+     */
+    DStroker(final DRendererContext rdrCtx) {
+        this.rdrCtx = rdrCtx;
+
+        this.reverse = new PolyStack(rdrCtx);
+        this.curve = rdrCtx.curve;
+    }
+
+    /**
+     * Inits the <code>DStroker</code>.
+     *
+     * @param pc2d an output <code>DPathConsumer2D</code>.
+     * @param lineWidth the desired line width in pixels
+     * @param capStyle the desired end cap style, one of
+     * <code>CAP_BUTT</code>, <code>CAP_ROUND</code> or
+     * <code>CAP_SQUARE</code>.
+     * @param joinStyle the desired line join style, one of
+     * <code>JOIN_MITER</code>, <code>JOIN_ROUND</code> or
+     * <code>JOIN_BEVEL</code>.
+     * @param miterLimit the desired miter limit
+     * @return this instance
+     */
+    DStroker init(DPathConsumer2D pc2d,
+              double lineWidth,
+              int capStyle,
+              int joinStyle,
+              double miterLimit)
+    {
+        this.out = pc2d;
+
+        this.lineWidth2 = lineWidth / 2.0d;
+        this.invHalfLineWidth2Sq = 1.0d / (2.0d * lineWidth2 * lineWidth2);
+        this.capStyle = capStyle;
+        this.joinStyle = joinStyle;
+
+        double limit = miterLimit * lineWidth2;
+        this.miterLimitSq = limit * limit;
+
+        this.prev = CLOSE;
+
+        rdrCtx.stroking = 1;
+
+        return this; // fluent API
+    }
+
+    /**
+     * Disposes this stroker:
+     * clean up before reusing this instance
+     */
+    void dispose() {
+        reverse.dispose();
+
+        if (DO_CLEAN_DIRTY) {
+            // Force zero-fill dirty arrays:
+            Arrays.fill(offset0, 0.0d);
+            Arrays.fill(offset1, 0.0d);
+            Arrays.fill(offset2, 0.0d);
+            Arrays.fill(miter, 0.0d);
+            Arrays.fill(middle, 0.0d);
+            Arrays.fill(lp, 0.0d);
+            Arrays.fill(rp, 0.0d);
+            Arrays.fill(subdivTs, 0.0d);
+        }
+    }
+
+    private static void computeOffset(final double lx, final double ly,
+                                      final double w, final double[] m)
+    {
+        double len = lx*lx + ly*ly;
+        if (len == 0.0d) {
+            m[0] = 0.0d;
+            m[1] = 0.0d;
+        } else {
+            len = Math.sqrt(len);
+            m[0] =  (ly * w) / len;
+            m[1] = -(lx * w) / len;
+        }
+    }
+
+    // Returns true if the vectors (dx1, dy1) and (dx2, dy2) are
+    // clockwise (if dx1,dy1 needs to be rotated clockwise to close
+    // the smallest angle between it and dx2,dy2).
+    // This is equivalent to detecting whether a point q is on the right side
+    // of a line passing through points p1, p2 where p2 = p1+(dx1,dy1) and
+    // q = p2+(dx2,dy2), which is the same as saying p1, p2, q are in a
+    // clockwise order.
+    // NOTE: "clockwise" here assumes coordinates with 0,0 at the bottom left.
+    private static boolean isCW(final double dx1, final double dy1,
+                                final double dx2, final double dy2)
+    {
+        return dx1 * dy2 <= dy1 * dx2;
+    }
+
+    private void drawRoundJoin(double x, double y,
+                               double omx, double omy, double mx, double my,
+                               boolean rev,
+                               double threshold)
+    {
+        if ((omx == 0.0d && omy == 0.0d) || (mx == 0.0d && my == 0.0d)) {
+            return;
+        }
+
+        double domx = omx - mx;
+        double domy = omy - my;
+        double len = domx*domx + domy*domy;
+        if (len < threshold) {
+            return;
+        }
+
+        if (rev) {
+            omx = -omx;
+            omy = -omy;
+            mx  = -mx;
+            my  = -my;
+        }
+        drawRoundJoin(x, y, omx, omy, mx, my, rev);
+    }
+
+    private void drawRoundJoin(double cx, double cy,
+                               double omx, double omy,
+                               double mx, double my,
+                               boolean rev)
+    {
+        // The sign of the dot product of mx,my and omx,omy is equal to the
+        // the sign of the cosine of ext
+        // (ext is the angle between omx,omy and mx,my).
+        final double cosext = omx * mx + omy * my;
+        // If it is >=0, we know that abs(ext) is <= 90 degrees, so we only
+        // need 1 curve to approximate the circle section that joins omx,omy
+        // and mx,my.
+        final int numCurves = (cosext >= 0.0d) ? 1 : 2;
+
+        switch (numCurves) {
+        case 1:
+            drawBezApproxForArc(cx, cy, omx, omy, mx, my, rev);
+            break;
+        case 2:
+            // we need to split the arc into 2 arcs spanning the same angle.
+            // The point we want will be one of the 2 intersections of the
+            // perpendicular bisector of the chord (omx,omy)->(mx,my) and the
+            // circle. We could find this by scaling the vector
+            // (omx+mx, omy+my)/2 so that it has length=lineWidth2 (and thus lies
+            // on the circle), but that can have numerical problems when the angle
+            // between omx,omy and mx,my is close to 180 degrees. So we compute a
+            // normal of (omx,omy)-(mx,my). This will be the direction of the
+            // perpendicular bisector. To get one of the intersections, we just scale
+            // this vector that its length is lineWidth2 (this works because the
+            // perpendicular bisector goes through the origin). This scaling doesn't
+            // have numerical problems because we know that lineWidth2 divided by
+            // this normal's length is at least 0.5 and at most sqrt(2)/2 (because
+            // we know the angle of the arc is > 90 degrees).
+            double nx = my - omy, ny = omx - mx;
+            double nlen = Math.sqrt(nx*nx + ny*ny);
+            double scale = lineWidth2/nlen;
+            double mmx = nx * scale, mmy = ny * scale;
+
+            // if (isCW(omx, omy, mx, my) != isCW(mmx, mmy, mx, my)) then we've
+            // computed the wrong intersection so we get the other one.
+            // The test above is equivalent to if (rev).
+            if (rev) {
+                mmx = -mmx;
+                mmy = -mmy;
+            }
+            drawBezApproxForArc(cx, cy, omx, omy, mmx, mmy, rev);
+            drawBezApproxForArc(cx, cy, mmx, mmy, mx, my, rev);
+            break;
+        default:
+        }
+    }
+
+    // the input arc defined by omx,omy and mx,my must span <= 90 degrees.
+    private void drawBezApproxForArc(final double cx, final double cy,
+                                     final double omx, final double omy,
+                                     final double mx, final double my,
+                                     boolean rev)
+    {
+        final double cosext2 = (omx * mx + omy * my) * invHalfLineWidth2Sq;
+
+        // check round off errors producing cos(ext) > 1 and a NaN below
+        // cos(ext) == 1 implies colinear segments and an empty join anyway
+        if (cosext2 >= 0.5d) {
+            // just return to avoid generating a flat curve:
+            return;
+        }
+
+        // cv is the length of P1-P0 and P2-P3 divided by the radius of the arc
+        // (so, cv assumes the arc has radius 1). P0, P1, P2, P3 are the points that
+        // define the bezier curve we're computing.
+        // It is computed using the constraints that P1-P0 and P3-P2 are parallel
+        // to the arc tangents at the endpoints, and that |P1-P0|=|P3-P2|.
+        double cv = ((4.0d / 3.0d) * Math.sqrt(0.5d - cosext2) /
+                            (1.0d + Math.sqrt(cosext2 + 0.5d)));
+        // if clockwise, we need to negate cv.
+        if (rev) { // rev is equivalent to isCW(omx, omy, mx, my)
+            cv = -cv;
+        }
+        final double x1 = cx + omx;
+        final double y1 = cy + omy;
+        final double x2 = x1 - cv * omy;
+        final double y2 = y1 + cv * omx;
+
+        final double x4 = cx + mx;
+        final double y4 = cy + my;
+        final double x3 = x4 + cv * my;
+        final double y3 = y4 - cv * mx;
+
+        emitCurveTo(x1, y1, x2, y2, x3, y3, x4, y4, rev);
+    }
+
+    private void drawRoundCap(double cx, double cy, double mx, double my) {
+        final double Cmx = C * mx;
+        final double Cmy = C * my;
+        emitCurveTo(cx + mx - Cmy, cy + my + Cmx,
+                    cx - my + Cmx, cy + mx + Cmy,
+                    cx - my,       cy + mx);
+        emitCurveTo(cx - my - Cmx, cy + mx - Cmy,
+                    cx - mx - Cmy, cy - my + Cmx,
+                    cx - mx,       cy - my);
+    }
+
+    // Return the intersection point of the lines (x0, y0) -> (x1, y1)
+    // and (x0p, y0p) -> (x1p, y1p) in m[off] and m[off+1]
+    private static void computeMiter(final double x0, final double y0,
+                                     final double x1, final double y1,
+                                     final double x0p, final double y0p,
+                                     final double x1p, final double y1p,
+                                     final double[] m, int off)
+    {
+        double x10 = x1 - x0;
+        double y10 = y1 - y0;
+        double x10p = x1p - x0p;
+        double y10p = y1p - y0p;
+
+        // if this is 0, the lines are parallel. If they go in the
+        // same direction, there is no intersection so m[off] and
+        // m[off+1] will contain infinity, so no miter will be drawn.
+        // If they go in the same direction that means that the start of the
+        // current segment and the end of the previous segment have the same
+        // tangent, in which case this method won't even be involved in
+        // miter drawing because it won't be called by drawMiter (because
+        // (mx == omx && my == omy) will be true, and drawMiter will return
+        // immediately).
+        double den = x10*y10p - x10p*y10;
+        double t = x10p*(y0-y0p) - y10p*(x0-x0p);
+        t /= den;
+        m[off++] = x0 + t*x10;
+        m[off]   = y0 + t*y10;
+    }
+
+    // Return the intersection point of the lines (x0, y0) -> (x1, y1)
+    // and (x0p, y0p) -> (x1p, y1p) in m[off] and m[off+1]
+    private static void safeComputeMiter(final double x0, final double y0,
+                                         final double x1, final double y1,
+                                         final double x0p, final double y0p,
+                                         final double x1p, final double y1p,
+                                         final double[] m, int off)
+    {
+        double x10 = x1 - x0;
+        double y10 = y1 - y0;
+        double x10p = x1p - x0p;
+        double y10p = y1p - y0p;
+
+        // if this is 0, the lines are parallel. If they go in the
+        // same direction, there is no intersection so m[off] and
+        // m[off+1] will contain infinity, so no miter will be drawn.
+        // If they go in the same direction that means that the start of the
+        // current segment and the end of the previous segment have the same
+        // tangent, in which case this method won't even be involved in
+        // miter drawing because it won't be called by drawMiter (because
+        // (mx == omx && my == omy) will be true, and drawMiter will return
+        // immediately).
+        double den = x10*y10p - x10p*y10;
+        if (den == 0.0d) {
+            m[off++] = (x0 + x0p) / 2.0d;
+            m[off]   = (y0 + y0p) / 2.0d;
+            return;
+        }
+        double t = x10p*(y0-y0p) - y10p*(x0-x0p);
+        t /= den;
+        m[off++] = x0 + t*x10;
+        m[off] = y0 + t*y10;
+    }
+
+    private void drawMiter(final double pdx, final double pdy,
+                           final double x0, final double y0,
+                           final double dx, final double dy,
+                           double omx, double omy, double mx, double my,
+                           boolean rev)
+    {
+        if ((mx == omx && my == omy) ||
+            (pdx == 0.0d && pdy == 0.0d) ||
+            (dx == 0.0d && dy == 0.0d))
+        {
+            return;
+        }
+
+        if (rev) {
+            omx = -omx;
+            omy = -omy;
+            mx  = -mx;
+            my  = -my;
+        }
+
+        computeMiter((x0 - pdx) + omx, (y0 - pdy) + omy, x0 + omx, y0 + omy,
+                     (dx + x0) + mx, (dy + y0) + my, x0 + mx, y0 + my,
+                     miter, 0);
+
+        final double miterX = miter[0];
+        final double miterY = miter[1];
+        double lenSq = (miterX-x0)*(miterX-x0) + (miterY-y0)*(miterY-y0);
+
+        // If the lines are parallel, lenSq will be either NaN or +inf
+        // (actually, I'm not sure if the latter is possible. The important
+        // thing is that -inf is not possible, because lenSq is a square).
+        // For both of those values, the comparison below will fail and
+        // no miter will be drawn, which is correct.
+        if (lenSq < miterLimitSq) {
+            emitLineTo(miterX, miterY, rev);
+        }
+    }
+
+    @Override
+    public void moveTo(double x0, double y0) {
+        if (prev == DRAWING_OP_TO) {
+            finish();
+        }
+        this.sx0 = this.cx0 = x0;
+        this.sy0 = this.cy0 = y0;
+        this.cdx = this.sdx = 1.0d;
+        this.cdy = this.sdy = 0.0d;
+        this.prev = MOVE_TO;
+    }
+
+    @Override
+    public void lineTo(double x1, double y1) {
+        double dx = x1 - cx0;
+        double dy = y1 - cy0;
+        if (dx == 0.0d && dy == 0.0d) {
+            dx = 1.0d;
+        }
+        computeOffset(dx, dy, lineWidth2, offset0);
+        final double mx = offset0[0];
+        final double my = offset0[1];
+
+        drawJoin(cdx, cdy, cx0, cy0, dx, dy, cmx, cmy, mx, my);
+
+        emitLineTo(cx0 + mx, cy0 + my);
+        emitLineTo( x1 + mx,  y1 + my);
+
+        emitLineToRev(cx0 - mx, cy0 - my);
+        emitLineToRev( x1 - mx,  y1 - my);
+
+        this.cmx = mx;
+        this.cmy = my;
+        this.cdx = dx;
+        this.cdy = dy;
+        this.cx0 = x1;
+        this.cy0 = y1;
+        this.prev = DRAWING_OP_TO;
+    }
+
+    @Override
+    public void closePath() {
+        if (prev != DRAWING_OP_TO) {
+            if (prev == CLOSE) {
+                return;
+            }
+            emitMoveTo(cx0, cy0 - lineWidth2);
+            this.cmx = this.smx = 0.0d;
+            this.cmy = this.smy = -lineWidth2;
+            this.cdx = this.sdx = 1.0d;
+            this.cdy = this.sdy = 0.0d;
+            finish();
+            return;
+        }
+
+        if (cx0 != sx0 || cy0 != sy0) {
+            lineTo(sx0, sy0);
+        }
+
+        drawJoin(cdx, cdy, cx0, cy0, sdx, sdy, cmx, cmy, smx, smy);
+
+        emitLineTo(sx0 + smx, sy0 + smy);
+
+        emitMoveTo(sx0 - smx, sy0 - smy);
+        emitReverse();
+
+        this.prev = CLOSE;
+        emitClose();
+    }
+
+    private void emitReverse() {
+        reverse.popAll(out);
+    }
+
+    @Override
+    public void pathDone() {
+        if (prev == DRAWING_OP_TO) {
+            finish();
+        }
+
+        out.pathDone();
+
+        // this shouldn't matter since this object won't be used
+        // after the call to this method.
+        this.prev = CLOSE;
+
+        // Dispose this instance:
+        dispose();
+    }
+
+    private void finish() {
+        if (capStyle == CAP_ROUND) {
+            drawRoundCap(cx0, cy0, cmx, cmy);
+        } else if (capStyle == CAP_SQUARE) {
+            emitLineTo(cx0 - cmy + cmx, cy0 + cmx + cmy);
+            emitLineTo(cx0 - cmy - cmx, cy0 + cmx - cmy);
+        }
+
+        emitReverse();
+
+        if (capStyle == CAP_ROUND) {
+            drawRoundCap(sx0, sy0, -smx, -smy);
+        } else if (capStyle == CAP_SQUARE) {
+            emitLineTo(sx0 + smy - smx, sy0 - smx - smy);
+            emitLineTo(sx0 + smy + smx, sy0 - smx + smy);
+        }
+
+        emitClose();
+    }
+
+    private void emitMoveTo(final double x0, final double y0) {
+        out.moveTo(x0, y0);
+    }
+
+    private void emitLineTo(final double x1, final double y1) {
+        out.lineTo(x1, y1);
+    }
+
+    private void emitLineToRev(final double x1, final double y1) {
+        reverse.pushLine(x1, y1);
+    }
+
+    private void emitLineTo(final double x1, final double y1,
+                            final boolean rev)
+    {
+        if (rev) {
+            emitLineToRev(x1, y1);
+        } else {
+            emitLineTo(x1, y1);
+        }
+    }
+
+    private void emitQuadTo(final double x1, final double y1,
+                            final double x2, final double y2)
+    {
+        out.quadTo(x1, y1, x2, y2);
+    }
+
+    private void emitQuadToRev(final double x0, final double y0,
+                               final double x1, final double y1)
+    {
+        reverse.pushQuad(x0, y0, x1, y1);
+    }
+
+    private void emitCurveTo(final double x1, final double y1,
+                             final double x2, final double y2,
+                             final double x3, final double y3)
+    {
+        out.curveTo(x1, y1, x2, y2, x3, y3);
+    }
+
+    private void emitCurveToRev(final double x0, final double y0,
+                                final double x1, final double y1,
+                                final double x2, final double y2)
+    {
+        reverse.pushCubic(x0, y0, x1, y1, x2, y2);
+    }
+
+    private void emitCurveTo(final double x0, final double y0,
+                             final double x1, final double y1,
+                             final double x2, final double y2,
+                             final double x3, final double y3, final boolean rev)
+    {
+        if (rev) {
+            reverse.pushCubic(x0, y0, x1, y1, x2, y2);
+        } else {
+            out.curveTo(x1, y1, x2, y2, x3, y3);
+        }
+    }
+
+    private void emitClose() {
+        out.closePath();
+    }
+
+    private void drawJoin(double pdx, double pdy,
+                          double x0, double y0,
+                          double dx, double dy,
+                          double omx, double omy,
+                          double mx, double my)
+    {
+        if (prev != DRAWING_OP_TO) {
+            emitMoveTo(x0 + mx, y0 + my);
+            this.sdx = dx;
+            this.sdy = dy;
+            this.smx = mx;
+            this.smy = my;
+        } else {
+            boolean cw = isCW(pdx, pdy, dx, dy);
+            if (joinStyle == JOIN_MITER) {
+                drawMiter(pdx, pdy, x0, y0, dx, dy, omx, omy, mx, my, cw);
+            } else if (joinStyle == JOIN_ROUND) {
+                drawRoundJoin(x0, y0,
+                              omx, omy,
+                              mx, my, cw,
+                              ROUND_JOIN_THRESHOLD);
+            }
+            emitLineTo(x0, y0, !cw);
+        }
+        prev = DRAWING_OP_TO;
+    }
+
+    private static boolean within(final double x1, final double y1,
+                                  final double x2, final double y2,
+                                  final double ERR)
+    {
+        assert ERR > 0 : "";
+        // compare taxicab distance. ERR will always be small, so using
+        // true distance won't give much benefit
+        return (DHelpers.within(x1, x2, ERR) &&  // we want to avoid calling Math.abs
+                DHelpers.within(y1, y2, ERR)); // this is just as good.
+    }
+
+    private void getLineOffsets(double x1, double y1,
+                                double x2, double y2,
+                                double[] left, double[] right) {
+        computeOffset(x2 - x1, y2 - y1, lineWidth2, offset0);
+        final double mx = offset0[0];
+        final double my = offset0[1];
+        left[0] = x1 + mx;
+        left[1] = y1 + my;
+        left[2] = x2 + mx;
+        left[3] = y2 + my;
+        right[0] = x1 - mx;
+        right[1] = y1 - my;
+        right[2] = x2 - mx;
+        right[3] = y2 - my;
+    }
+
+    private int computeOffsetCubic(double[] pts, final int off,
+                                   double[] leftOff, double[] rightOff)
+    {
+        // if p1=p2 or p3=p4 it means that the derivative at the endpoint
+        // vanishes, which creates problems with computeOffset. Usually
+        // this happens when this stroker object is trying to widen
+        // a curve with a cusp. What happens is that curveTo splits
+        // the input curve at the cusp, and passes it to this function.
+        // because of inaccuracies in the splitting, we consider points
+        // equal if they're very close to each other.
+        final double x1 = pts[off + 0], y1 = pts[off + 1];
+        final double x2 = pts[off + 2], y2 = pts[off + 3];
+        final double x3 = pts[off + 4], y3 = pts[off + 5];
+        final double x4 = pts[off + 6], y4 = pts[off + 7];
+
+        double dx4 = x4 - x3;
+        double dy4 = y4 - y3;
+        double dx1 = x2 - x1;
+        double dy1 = y2 - y1;
+
+        // if p1 == p2 && p3 == p4: draw line from p1->p4, unless p1 == p4,
+        // in which case ignore if p1 == p2
+        final boolean p1eqp2 = within(x1, y1, x2, y2, 6.0d * Math.ulp(y2));
+        final boolean p3eqp4 = within(x3, y3, x4, y4, 6.0d * Math.ulp(y4));
+        if (p1eqp2 && p3eqp4) {
+            getLineOffsets(x1, y1, x4, y4, leftOff, rightOff);
+            return 4;
+        } else if (p1eqp2) {
+            dx1 = x3 - x1;
+            dy1 = y3 - y1;
+        } else if (p3eqp4) {
+            dx4 = x4 - x2;
+            dy4 = y4 - y2;
+        }
+
+        // if p2-p1 and p4-p3 are parallel, that must mean this curve is a line
+        double dotsq = (dx1 * dx4 + dy1 * dy4);
+        dotsq *= dotsq;
+        double l1sq = dx1 * dx1 + dy1 * dy1, l4sq = dx4 * dx4 + dy4 * dy4;
+        if (DHelpers.within(dotsq, l1sq * l4sq, 4.0d * Math.ulp(dotsq))) {
+            getLineOffsets(x1, y1, x4, y4, leftOff, rightOff);
+            return 4;
+        }
+
+//      What we're trying to do in this function is to approximate an ideal
+//      offset curve (call it I) of the input curve B using a bezier curve Bp.
+//      The constraints I use to get the equations are:
+//
+//      1. The computed curve Bp should go through I(0) and I(1). These are
+//      x1p, y1p, x4p, y4p, which are p1p and p4p. We still need to find
+//      4 variables: the x and y components of p2p and p3p (i.e. x2p, y2p, x3p, y3p).
+//
+//      2. Bp should have slope equal in absolute value to I at the endpoints. So,
+//      (by the way, the operator || in the comments below means "aligned with".
+//      It is defined on vectors, so when we say I'(0) || Bp'(0) we mean that
+//      vectors I'(0) and Bp'(0) are aligned, which is the same as saying
+//      that the tangent lines of I and Bp at 0 are parallel. Mathematically
+//      this means (I'(t) || Bp'(t)) <==> (I'(t) = c * Bp'(t)) where c is some
+//      nonzero constant.)
+//      I'(0) || Bp'(0) and I'(1) || Bp'(1). Obviously, I'(0) || B'(0) and
+//      I'(1) || B'(1); therefore, Bp'(0) || B'(0) and Bp'(1) || B'(1).
+//      We know that Bp'(0) || (p2p-p1p) and Bp'(1) || (p4p-p3p) and the same
+//      is true for any bezier curve; therefore, we get the equations
+//          (1) p2p = c1 * (p2-p1) + p1p
+//          (2) p3p = c2 * (p4-p3) + p4p
+//      We know p1p, p4p, p2, p1, p3, and p4; therefore, this reduces the number
+//      of unknowns from 4 to 2 (i.e. just c1 and c2).
+//      To eliminate these 2 unknowns we use the following constraint:
+//
+//      3. Bp(0.5) == I(0.5). Bp(0.5)=(x,y) and I(0.5)=(xi,yi), and I should note
+//      that I(0.5) is *the only* reason for computing dxm,dym. This gives us
+//          (3) Bp(0.5) = (p1p + 3 * (p2p + p3p) + p4p)/8, which is equivalent to
+//          (4) p2p + p3p = (Bp(0.5)*8 - p1p - p4p) / 3
+//      We can substitute (1) and (2) from above into (4) and we get:
+//          (5) c1*(p2-p1) + c2*(p4-p3) = (Bp(0.5)*8 - p1p - p4p)/3 - p1p - p4p
+//      which is equivalent to
+//          (6) c1*(p2-p1) + c2*(p4-p3) = (4/3) * (Bp(0.5) * 2 - p1p - p4p)
+//
+//      The right side of this is a 2D vector, and we know I(0.5), which gives us
+//      Bp(0.5), which gives us the value of the right side.
+//      The left side is just a matrix vector multiplication in disguise. It is
+//
+//      [x2-x1, x4-x3][c1]
+//      [y2-y1, y4-y3][c2]
+//      which, is equal to
+//      [dx1, dx4][c1]
+//      [dy1, dy4][c2]
+//      At this point we are left with a simple linear system and we solve it by
+//      getting the inverse of the matrix above. Then we use [c1,c2] to compute
+//      p2p and p3p.
+
+        double x = (x1 + 3.0d * (x2 + x3) + x4) / 8.0d;
+        double y = (y1 + 3.0d * (y2 + y3) + y4) / 8.0d;
+        // (dxm,dym) is some tangent of B at t=0.5. This means it's equal to
+        // c*B'(0.5) for some constant c.
+        double dxm = x3 + x4 - x1 - x2, dym = y3 + y4 - y1 - y2;
+
+        // this computes the offsets at t=0, 0.5, 1, using the property that
+        // for any bezier curve the vectors p2-p1 and p4-p3 are parallel to
+        // the (dx/dt, dy/dt) vectors at the endpoints.
+        computeOffset(dx1, dy1, lineWidth2, offset0);
+        computeOffset(dxm, dym, lineWidth2, offset1);
+        computeOffset(dx4, dy4, lineWidth2, offset2);
+        double x1p = x1 + offset0[0]; // start
+        double y1p = y1 + offset0[1]; // point
+        double xi  = x  + offset1[0]; // interpolation
+        double yi  = y  + offset1[1]; // point
+        double x4p = x4 + offset2[0]; // end
+        double y4p = y4 + offset2[1]; // point
+
+        double invdet43 = 4.0d / (3.0d * (dx1 * dy4 - dy1 * dx4));
+
+        double two_pi_m_p1_m_p4x = 2.0d * xi - x1p - x4p;
+        double two_pi_m_p1_m_p4y = 2.0d * yi - y1p - y4p;
+        double c1 = invdet43 * (dy4 * two_pi_m_p1_m_p4x - dx4 * two_pi_m_p1_m_p4y);
+        double c2 = invdet43 * (dx1 * two_pi_m_p1_m_p4y - dy1 * two_pi_m_p1_m_p4x);
+
+        double x2p, y2p, x3p, y3p;
+        x2p = x1p + c1*dx1;
+        y2p = y1p + c1*dy1;
+        x3p = x4p + c2*dx4;
+        y3p = y4p + c2*dy4;
+
+        leftOff[0] = x1p; leftOff[1] = y1p;
+        leftOff[2] = x2p; leftOff[3] = y2p;
+        leftOff[4] = x3p; leftOff[5] = y3p;
+        leftOff[6] = x4p; leftOff[7] = y4p;
+
+        x1p = x1 - offset0[0]; y1p = y1 - offset0[1];
+        xi = xi - 2.0d * offset1[0]; yi = yi - 2.0d * offset1[1];
+        x4p = x4 - offset2[0]; y4p = y4 - offset2[1];
+
+        two_pi_m_p1_m_p4x = 2.0d * xi - x1p - x4p;
+        two_pi_m_p1_m_p4y = 2.0d * yi - y1p - y4p;
+        c1 = invdet43 * (dy4 * two_pi_m_p1_m_p4x - dx4 * two_pi_m_p1_m_p4y);
+        c2 = invdet43 * (dx1 * two_pi_m_p1_m_p4y - dy1 * two_pi_m_p1_m_p4x);
+
+        x2p = x1p + c1*dx1;
+        y2p = y1p + c1*dy1;
+        x3p = x4p + c2*dx4;
+        y3p = y4p + c2*dy4;
+
+        rightOff[0] = x1p; rightOff[1] = y1p;
+        rightOff[2] = x2p; rightOff[3] = y2p;
+        rightOff[4] = x3p; rightOff[5] = y3p;
+        rightOff[6] = x4p; rightOff[7] = y4p;
+        return 8;
+    }
+
+    // compute offset curves using bezier spline through t=0.5 (i.e.
+    // ComputedCurve(0.5) == IdealParallelCurve(0.5))
+    // return the kind of curve in the right and left arrays.
+    private int computeOffsetQuad(double[] pts, final int off,
+                                  double[] leftOff, double[] rightOff)
+    {
+        final double x1 = pts[off + 0], y1 = pts[off + 1];
+        final double x2 = pts[off + 2], y2 = pts[off + 3];
+        final double x3 = pts[off + 4], y3 = pts[off + 5];
+
+        final double dx3 = x3 - x2;
+        final double dy3 = y3 - y2;
+        final double dx1 = x2 - x1;
+        final double dy1 = y2 - y1;
+
+        // if p1=p2 or p3=p4 it means that the derivative at the endpoint
+        // vanishes, which creates problems with computeOffset. Usually
+        // this happens when this stroker object is trying to widen
+        // a curve with a cusp. What happens is that curveTo splits
+        // the input curve at the cusp, and passes it to this function.
+        // because of inaccuracies in the splitting, we consider points
+        // equal if they're very close to each other.
+
+        // if p1 == p2 && p3 == p4: draw line from p1->p4, unless p1 == p4,
+        // in which case ignore.
+        final boolean p1eqp2 = within(x1, y1, x2, y2, 6.0d * Math.ulp(y2));
+        final boolean p2eqp3 = within(x2, y2, x3, y3, 6.0d * Math.ulp(y3));
+        if (p1eqp2 || p2eqp3) {
+            getLineOffsets(x1, y1, x3, y3, leftOff, rightOff);
+            return 4;
+        }
+
+        // if p2-p1 and p4-p3 are parallel, that must mean this curve is a line
+        double dotsq = (dx1 * dx3 + dy1 * dy3);
+        dotsq *= dotsq;
+        double l1sq = dx1 * dx1 + dy1 * dy1, l3sq = dx3 * dx3 + dy3 * dy3;
+        if (DHelpers.within(dotsq, l1sq * l3sq, 4.0d * Math.ulp(dotsq))) {
+            getLineOffsets(x1, y1, x3, y3, leftOff, rightOff);
+            return 4;
+        }
+
+        // this computes the offsets at t=0, 0.5, 1, using the property that
+        // for any bezier curve the vectors p2-p1 and p4-p3 are parallel to
+        // the (dx/dt, dy/dt) vectors at the endpoints.
+        computeOffset(dx1, dy1, lineWidth2, offset0);
+        computeOffset(dx3, dy3, lineWidth2, offset1);
+
+        double x1p = x1 + offset0[0]; // start
+        double y1p = y1 + offset0[1]; // point
+        double x3p = x3 + offset1[0]; // end
+        double y3p = y3 + offset1[1]; // point
+        safeComputeMiter(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, leftOff, 2);
+        leftOff[0] = x1p; leftOff[1] = y1p;
+        leftOff[4] = x3p; leftOff[5] = y3p;
+
+        x1p = x1 - offset0[0]; y1p = y1 - offset0[1];
+        x3p = x3 - offset1[0]; y3p = y3 - offset1[1];
+        safeComputeMiter(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, rightOff, 2);
+        rightOff[0] = x1p; rightOff[1] = y1p;
+        rightOff[4] = x3p; rightOff[5] = y3p;
+        return 6;
+    }
+
+    // finds values of t where the curve in pts should be subdivided in order
+    // to get good offset curves a distance of w away from the middle curve.
+    // Stores the points in ts, and returns how many of them there were.
+    private static int findSubdivPoints(final DCurve c, double[] pts, double[] ts,
+                                        final int type, final double w)
+    {
+        final double x12 = pts[2] - pts[0];
+        final double y12 = pts[3] - pts[1];
+        // if the curve is already parallel to either axis we gain nothing
+        // from rotating it.
+        if (y12 != 0.0d && x12 != 0.0d) {
+            // we rotate it so that the first vector in the control polygon is
+            // parallel to the x-axis. This will ensure that rotated quarter
+            // circles won't be subdivided.
+            final double hypot = Math.sqrt(x12 * x12 + y12 * y12);
+            final double cos = x12 / hypot;
+            final double sin = y12 / hypot;
+            final double x1 = cos * pts[0] + sin * pts[1];
+            final double y1 = cos * pts[1] - sin * pts[0];
+            final double x2 = cos * pts[2] + sin * pts[3];
+            final double y2 = cos * pts[3] - sin * pts[2];
+            final double x3 = cos * pts[4] + sin * pts[5];
+            final double y3 = cos * pts[5] - sin * pts[4];
+
+            switch(type) {
+            case 8:
+                final double x4 = cos * pts[6] + sin * pts[7];
+                final double y4 = cos * pts[7] - sin * pts[6];
+                c.set(x1, y1, x2, y2, x3, y3, x4, y4);
+                break;
+            case 6:
+                c.set(x1, y1, x2, y2, x3, y3);
+                break;
+            default:
+            }
+        } else {
+            c.set(pts, type);
+        }
+
+        int ret = 0;
+        // we subdivide at values of t such that the remaining rotated
+        // curves are monotonic in x and y.
+        ret += c.dxRoots(ts, ret);
+        ret += c.dyRoots(ts, ret);
+        // subdivide at inflection points.
+        if (type == 8) {
+            // quadratic curves can't have inflection points
+            ret += c.infPoints(ts, ret);
+        }
+
+        // now we must subdivide at points where one of the offset curves will have
+        // a cusp. This happens at ts where the radius of curvature is equal to w.
+        ret += c.rootsOfROCMinusW(ts, ret, w, 0.0001d);
+
+        ret = DHelpers.filterOutNotInAB(ts, 0, ret, 0.0001d, 0.9999d);
+        DHelpers.isort(ts, 0, ret);
+        return ret;
+    }
+
+    @Override public void curveTo(double x1, double y1,
+                                  double x2, double y2,
+                                  double x3, double y3)
+    {
+        final double[] mid = middle;
+
+        mid[0] = cx0; mid[1] = cy0;
+        mid[2] = x1;  mid[3] = y1;
+        mid[4] = x2;  mid[5] = y2;
+        mid[6] = x3;  mid[7] = y3;
+
+        // need these so we can update the state at the end of this method
+        final double xf = mid[6], yf = mid[7];
+        double dxs = mid[2] - mid[0];
+        double dys = mid[3] - mid[1];
+        double dxf = mid[6] - mid[4];
+        double dyf = mid[7] - mid[5];
+
+        boolean p1eqp2 = (dxs == 0.0d && dys == 0.0d);
+        boolean p3eqp4 = (dxf == 0.0d && dyf == 0.0d);
+        if (p1eqp2) {
+            dxs = mid[4] - mid[0];
+            dys = mid[5] - mid[1];
+            if (dxs == 0.0d && dys == 0.0d) {
+                dxs = mid[6] - mid[0];
+                dys = mid[7] - mid[1];
+            }
+        }
+        if (p3eqp4) {
+            dxf = mid[6] - mid[2];
+            dyf = mid[7] - mid[3];
+            if (dxf == 0.0d && dyf == 0.0d) {
+                dxf = mid[6] - mid[0];
+                dyf = mid[7] - mid[1];
+            }
+        }
+        if (dxs == 0.0d && dys == 0.0d) {
+            // this happens if the "curve" is just a point
+            lineTo(mid[0], mid[1]);
+            return;
+        }
+
+        // if these vectors are too small, normalize them, to avoid future
+        // precision problems.
+        if (Math.abs(dxs) < 0.1d && Math.abs(dys) < 0.1d) {
+            double len = Math.sqrt(dxs*dxs + dys*dys);
+            dxs /= len;
+            dys /= len;
+        }
+        if (Math.abs(dxf) < 0.1d && Math.abs(dyf) < 0.1d) {
+            double len = Math.sqrt(dxf*dxf + dyf*dyf);
+            dxf /= len;
+            dyf /= len;
+        }
+
+        computeOffset(dxs, dys, lineWidth2, offset0);
+        drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, offset0[0], offset0[1]);
+
+        final int nSplits = findSubdivPoints(curve, mid, subdivTs, 8, lineWidth2);
+
+        double prevT = 0.0d;
+        for (int i = 0, off = 0; i < nSplits; i++, off += 6) {
+            final double t = subdivTs[i];
+            DHelpers.subdivideCubicAt((t - prevT) / (1.0d - prevT),
+                                     mid, off, mid, off, mid, off + 6);
+            prevT = t;
+        }
+
+        final double[] l = lp;
+        final double[] r = rp;
+
+        int kind = 0;
+        for (int i = 0, off = 0; i <= nSplits; i++, off += 6) {
+            kind = computeOffsetCubic(mid, off, l, r);
+
+            emitLineTo(l[0], l[1]);
+
+            switch(kind) {
+            case 8:
+                emitCurveTo(l[2], l[3], l[4], l[5], l[6], l[7]);
+                emitCurveToRev(r[0], r[1], r[2], r[3], r[4], r[5]);
+                break;
+            case 4:
+                emitLineTo(l[2], l[3]);
+                emitLineToRev(r[0], r[1]);
+                break;
+            default:
+            }
+            emitLineToRev(r[kind - 2], r[kind - 1]);
+        }
+
+        this.cmx = (l[kind - 2] - r[kind - 2]) / 2.0d;
+        this.cmy = (l[kind - 1] - r[kind - 1]) / 2.0d;
+        this.cdx = dxf;
+        this.cdy = dyf;
+        this.cx0 = xf;
+        this.cy0 = yf;
+        this.prev = DRAWING_OP_TO;
+    }
+
+    @Override public void quadTo(double x1, double y1, double x2, double y2) {
+        final double[] mid = middle;
+
+        mid[0] = cx0; mid[1] = cy0;
+        mid[2] = x1;  mid[3] = y1;
+        mid[4] = x2;  mid[5] = y2;
+
+        // need these so we can update the state at the end of this method
+        final double xf = mid[4], yf = mid[5];
+        double dxs = mid[2] - mid[0];
+        double dys = mid[3] - mid[1];
+        double dxf = mid[4] - mid[2];
+        double dyf = mid[5] - mid[3];
+        if ((dxs == 0.0d && dys == 0.0d) || (dxf == 0.0d && dyf == 0.0d)) {
+            dxs = dxf = mid[4] - mid[0];
+            dys = dyf = mid[5] - mid[1];
+        }
+        if (dxs == 0.0d && dys == 0.0d) {
+            // this happens if the "curve" is just a point
+            lineTo(mid[0], mid[1]);
+            return;
+        }
+        // if these vectors are too small, normalize them, to avoid future
+        // precision problems.
+        if (Math.abs(dxs) < 0.1d && Math.abs(dys) < 0.1d) {
+            double len = Math.sqrt(dxs*dxs + dys*dys);
+            dxs /= len;
+            dys /= len;
+        }
+        if (Math.abs(dxf) < 0.1d && Math.abs(dyf) < 0.1d) {
+            double len = Math.sqrt(dxf*dxf + dyf*dyf);
+            dxf /= len;
+            dyf /= len;
+        }
+
+        computeOffset(dxs, dys, lineWidth2, offset0);
+        drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, offset0[0], offset0[1]);
+
+        int nSplits = findSubdivPoints(curve, mid, subdivTs, 6, lineWidth2);
+
+        double prevt = 0.0d;
+        for (int i = 0, off = 0; i < nSplits; i++, off += 4) {
+            final double t = subdivTs[i];
+            DHelpers.subdivideQuadAt((t - prevt) / (1.0d - prevt),
+                                    mid, off, mid, off, mid, off + 4);
+            prevt = t;
+        }
+
+        final double[] l = lp;
+        final double[] r = rp;
+
+        int kind = 0;
+        for (int i = 0, off = 0; i <= nSplits; i++, off += 4) {
+            kind = computeOffsetQuad(mid, off, l, r);
+
+            emitLineTo(l[0], l[1]);
+
+            switch(kind) {
+            case 6:
+                emitQuadTo(l[2], l[3], l[4], l[5]);
+                emitQuadToRev(r[0], r[1], r[2], r[3]);
+                break;
+            case 4:
+                emitLineTo(l[2], l[3]);
+                emitLineToRev(r[0], r[1]);
+                break;
+            default:
+            }
+            emitLineToRev(r[kind - 2], r[kind - 1]);
+        }
+
+        this.cmx = (l[kind - 2] - r[kind - 2]) / 2.0d;
+        this.cmy = (l[kind - 1] - r[kind - 1]) / 2.0d;
+        this.cdx = dxf;
+        this.cdy = dyf;
+        this.cx0 = xf;
+        this.cy0 = yf;
+        this.prev = DRAWING_OP_TO;
+    }
+
+    @Override public long getNativeConsumer() {
+        throw new InternalError("Stroker doesn't use a native consumer");
+    }
+
+    // a stack of polynomial curves where each curve shares endpoints with
+    // adjacent ones.
+    static final class PolyStack {
+        private static final byte TYPE_LINETO  = (byte) 0;
+        private static final byte TYPE_QUADTO  = (byte) 1;
+        private static final byte TYPE_CUBICTO = (byte) 2;
+
+        // curves capacity = edges count (8192) = edges x 2 (coords)
+        private static final int INITIAL_CURVES_COUNT = INITIAL_EDGES_COUNT << 1;
+
+        // types capacity = edges count (4096)
+        private static final int INITIAL_TYPES_COUNT = INITIAL_EDGES_COUNT;
+
+        double[] curves;
+        int end;
+        byte[] curveTypes;
+        int numCurves;
+
+        // per-thread renderer context
+        final DRendererContext rdrCtx;
+
+        // curves ref (dirty)
+        final DoubleArrayCache.Reference curves_ref;
+        // curveTypes ref (dirty)
+        final ByteArrayCache.Reference curveTypes_ref;
+
+        // used marks (stats only)
+        int curveTypesUseMark;
+        int curvesUseMark;
+
+        /**
+         * Constructor
+         * @param rdrCtx per-thread renderer context
+         */
+        PolyStack(final DRendererContext rdrCtx) {
+            this.rdrCtx = rdrCtx;
+
+            curves_ref = rdrCtx.newDirtyDoubleArrayRef(INITIAL_CURVES_COUNT); // 32K
+            curves     = curves_ref.initial;
+
+            curveTypes_ref = rdrCtx.newDirtyByteArrayRef(INITIAL_TYPES_COUNT); // 4K
+            curveTypes     = curveTypes_ref.initial;
+            numCurves = 0;
+            end = 0;
+
+            if (DO_STATS) {
+                curveTypesUseMark = 0;
+                curvesUseMark = 0;
+            }
+        }
+
+        /**
+         * Disposes this PolyStack:
+         * clean up before reusing this instance
+         */
+        void dispose() {
+            end = 0;
+            numCurves = 0;
+
+            if (DO_STATS) {
+                rdrCtx.stats.stat_rdr_poly_stack_types.add(curveTypesUseMark);
+                rdrCtx.stats.stat_rdr_poly_stack_curves.add(curvesUseMark);
+                rdrCtx.stats.hist_rdr_poly_stack_curves.add(curvesUseMark);
+
+                // reset marks
+                curveTypesUseMark = 0;
+                curvesUseMark = 0;
+            }
+
+            // Return arrays:
+            // curves and curveTypes are kept dirty
+            curves     = curves_ref.putArray(curves);
+            curveTypes = curveTypes_ref.putArray(curveTypes);
+        }
+
+        private void ensureSpace(final int n) {
+            // use substraction to avoid integer overflow:
+            if (curves.length - end < n) {
+                if (DO_STATS) {
+                    rdrCtx.stats.stat_array_stroker_polystack_curves
+                        .add(end + n);
+                }
+                curves = curves_ref.widenArray(curves, end, end + n);
+            }
+            if (curveTypes.length <= numCurves) {
+                if (DO_STATS) {
+                    rdrCtx.stats.stat_array_stroker_polystack_curveTypes
+                        .add(numCurves + 1);
+                }
+                curveTypes = curveTypes_ref.widenArray(curveTypes,
+                                                       numCurves,
+                                                       numCurves + 1);
+            }
+        }
+
+        void pushCubic(double x0, double y0,
+                       double x1, double y1,
+                       double x2, double y2)
+        {
+            ensureSpace(6);
+            curveTypes[numCurves++] = TYPE_CUBICTO;
+            // we reverse the coordinate order to make popping easier
+            final double[] _curves = curves;
+            int e = end;
+            _curves[e++] = x2;    _curves[e++] = y2;
+            _curves[e++] = x1;    _curves[e++] = y1;
+            _curves[e++] = x0;    _curves[e++] = y0;
+            end = e;
+        }
+
+        void pushQuad(double x0, double y0,
+                      double x1, double y1)
+        {
+            ensureSpace(4);
+            curveTypes[numCurves++] = TYPE_QUADTO;
+            final double[] _curves = curves;
+            int e = end;
+            _curves[e++] = x1;    _curves[e++] = y1;
+            _curves[e++] = x0;    _curves[e++] = y0;
+            end = e;
+        }
+
+        void pushLine(double x, double y) {
+            ensureSpace(2);
+            curveTypes[numCurves++] = TYPE_LINETO;
+            curves[end++] = x;    curves[end++] = y;
+        }
+
+        void popAll(DPathConsumer2D io) {
+            if (DO_STATS) {
+                // update used marks:
+                if (numCurves > curveTypesUseMark) {
+                    curveTypesUseMark = numCurves;
+                }
+                if (end > curvesUseMark) {
+                    curvesUseMark = end;
+                }
+            }
+            final byte[]  _curveTypes = curveTypes;
+            final double[] _curves = curves;
+            int nc = numCurves;
+            int e  = end;
+
+            while (nc != 0) {
+                switch(_curveTypes[--nc]) {
+                case TYPE_LINETO:
+                    e -= 2;
+                    io.lineTo(_curves[e], _curves[e+1]);
+                    continue;
+                case TYPE_QUADTO:
+                    e -= 4;
+                    io.quadTo(_curves[e+0], _curves[e+1],
+                              _curves[e+2], _curves[e+3]);
+                    continue;
+                case TYPE_CUBICTO:
+                    e -= 6;
+                    io.curveTo(_curves[e+0], _curves[e+1],
+                               _curves[e+2], _curves[e+3],
+                               _curves[e+4], _curves[e+5]);
+                    continue;
+                default:
+                }
+            }
+            numCurves = 0;
+            end = 0;
+        }
+
+        @Override
+        public String toString() {
+            String ret = "";
+            int nc = numCurves;
+            int last = end;
+            int len;
+            while (nc != 0) {
+                switch(curveTypes[--nc]) {
+                case TYPE_LINETO:
+                    len = 2;
+                    ret += "line: ";
+                    break;
+                case TYPE_QUADTO:
+                    len = 4;
+                    ret += "quad: ";
+                    break;
+                case TYPE_CUBICTO:
+                    len = 6;
+                    ret += "cubic: ";
+                    break;
+                default:
+                    len = 0;
+                }
+                last -= len;
+                ret += Arrays.toString(Arrays.copyOfRange(curves, last, last+len))
+                                       + "\n";
+            }
+            return ret;
+        }
+    }
+}