--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/java.desktop/share/classes/sun/java2d/pisces/Stroker.java Tue Sep 12 19:03:39 2017 +0200
@@ -0,0 +1,1231 @@
+/*
+ * Copyright (c) 2007, 2015, 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.pisces;
+
+import java.util.Arrays;
+import java.util.Iterator;
+import static java.lang.Math.ulp;
+import static java.lang.Math.sqrt;
+
+import sun.awt.geom.PathConsumer2D;
+
+// 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 Stroker implements PathConsumer2D {
+
+ 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;
+
+ private final PathConsumer2D out;
+
+ private final int capStyle;
+ private final int joinStyle;
+
+ private final float lineWidth2;
+
+ private final float[][] offset = new float[3][2];
+ private final float[] miter = new float[2];
+ private final float miterLimitSq;
+
+ private int prev;
+
+ // The starting point of the path, and the slope there.
+ private float sx0, sy0, sdx, sdy;
+ // the current point and the slope there.
+ private float 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 float smx, smy, cmx, cmy;
+
+ private final PolyStack reverse = new PolyStack();
+
+ /**
+ * Constructs a {@code Stroker}.
+ *
+ * @param pc2d an output {@code PathConsumer2D}.
+ * @param lineWidth the desired line width in pixels
+ * @param capStyle the desired end cap style, one of
+ * {@code CAP_BUTT}, {@code CAP_ROUND} or
+ * {@code CAP_SQUARE}.
+ * @param joinStyle the desired line join style, one of
+ * {@code JOIN_MITER}, {@code JOIN_ROUND} or
+ * {@code JOIN_BEVEL}.
+ * @param miterLimit the desired miter limit
+ */
+ public Stroker(PathConsumer2D pc2d,
+ float lineWidth,
+ int capStyle,
+ int joinStyle,
+ float miterLimit)
+ {
+ this.out = pc2d;
+
+ this.lineWidth2 = lineWidth / 2;
+ this.capStyle = capStyle;
+ this.joinStyle = joinStyle;
+
+ float limit = miterLimit * lineWidth2;
+ this.miterLimitSq = limit*limit;
+
+ this.prev = CLOSE;
+ }
+
+ private static void computeOffset(final float lx, final float ly,
+ final float w, final float[] m)
+ {
+ final float len = (float) sqrt(lx*lx + ly*ly);
+ if (len == 0) {
+ m[0] = m[1] = 0;
+ } else {
+ 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 float dx1, final float dy1,
+ final float dx2, final float dy2)
+ {
+ return dx1 * dy2 <= dy1 * dx2;
+ }
+
+ // 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 float ROUND_JOIN_THRESHOLD = 1000/65536f;
+
+ private void drawRoundJoin(float x, float y,
+ float omx, float omy, float mx, float my,
+ boolean rev,
+ float threshold)
+ {
+ if ((omx == 0 && omy == 0) || (mx == 0 && my == 0)) {
+ return;
+ }
+
+ float domx = omx - mx;
+ float domy = omy - my;
+ float 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(float cx, float cy,
+ float omx, float omy,
+ float mx, float 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 float 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 >= 0f) ? 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).
+ float nx = my - omy, ny = omx - mx;
+ float nlen = (float) sqrt(nx*nx + ny*ny);
+ float scale = lineWidth2/nlen;
+ float 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;
+ }
+ }
+
+ // the input arc defined by omx,omy and mx,my must span <= 90 degrees.
+ private void drawBezApproxForArc(final float cx, final float cy,
+ final float omx, final float omy,
+ final float mx, final float my,
+ boolean rev)
+ {
+ final float cosext2 = (omx * mx + omy * my) / (2f * lineWidth2 * lineWidth2);
+
+ // 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 >= 0.5f) {
+ // 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|.
+ float cv = (float) ((4.0 / 3.0) * sqrt(0.5 - cosext2) /
+ (1.0 + sqrt(cosext2 + 0.5)));
+ // if clockwise, we need to negate cv.
+ if (rev) { // rev is equivalent to isCW(omx, omy, mx, my)
+ cv = -cv;
+ }
+ final float x1 = cx + omx;
+ final float y1 = cy + omy;
+ final float x2 = x1 - cv * omy;
+ final float y2 = y1 + cv * omx;
+
+ final float x4 = cx + mx;
+ final float y4 = cy + my;
+ final float x3 = x4 + cv * my;
+ final float y3 = y4 - cv * mx;
+
+ emitCurveTo(x1, y1, x2, y2, x3, y3, x4, y4, rev);
+ }
+
+ private void drawRoundCap(float cx, float cy, float mx, float my) {
+ final float C = 0.5522847498307933f;
+ // the first and second arguments of the following two calls
+ // are really will be ignored by emitCurveTo (because of the false),
+ // but we put them in anyway, as opposed to just giving it 4 zeroes,
+ // because it's just 4 additions and it's not good to rely on this
+ // sort of assumption (right now it's true, but that may change).
+ emitCurveTo(cx+mx, cy+my,
+ cx+mx-C*my, cy+my+C*mx,
+ cx-my+C*mx, cy+mx+C*my,
+ cx-my, cy+mx,
+ false);
+ emitCurveTo(cx-my, cy+mx,
+ cx-my-C*mx, cy+mx-C*my,
+ cx-mx-C*my, cy-my+C*mx,
+ cx-mx, cy-my,
+ false);
+ }
+
+ // Put the intersection point of the lines (x0, y0) -> (x1, y1)
+ // and (x0p, y0p) -> (x1p, y1p) in m[off] and m[off+1].
+ // If the lines are parallel, it will put a non finite number in m.
+ private void computeIntersection(final float x0, final float y0,
+ final float x1, final float y1,
+ final float x0p, final float y0p,
+ final float x1p, final float y1p,
+ final float[] m, int off)
+ {
+ float x10 = x1 - x0;
+ float y10 = y1 - y0;
+ float x10p = x1p - x0p;
+ float y10p = y1p - y0p;
+
+ float den = x10*y10p - x10p*y10;
+ float t = x10p*(y0-y0p) - y10p*(x0-x0p);
+ t /= den;
+ m[off++] = x0 + t*x10;
+ m[off] = y0 + t*y10;
+ }
+
+ private void drawMiter(final float pdx, final float pdy,
+ final float x0, final float y0,
+ final float dx, final float dy,
+ float omx, float omy, float mx, float my,
+ boolean rev)
+ {
+ if ((mx == omx && my == omy) ||
+ (pdx == 0 && pdy == 0) ||
+ (dx == 0 && dy == 0))
+ {
+ return;
+ }
+
+ if (rev) {
+ omx = -omx;
+ omy = -omy;
+ mx = -mx;
+ my = -my;
+ }
+
+ computeIntersection((x0 - pdx) + omx, (y0 - pdy) + omy, x0 + omx, y0 + omy,
+ (dx + x0) + mx, (dy + y0) + my, x0 + mx, y0 + my,
+ miter, 0);
+
+ float lenSq = (miter[0]-x0)*(miter[0]-x0) + (miter[1]-y0)*(miter[1]-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(miter[0], miter[1], rev);
+ }
+ }
+
+ public void moveTo(float x0, float y0) {
+ if (prev == DRAWING_OP_TO) {
+ finish();
+ }
+ this.sx0 = this.cx0 = x0;
+ this.sy0 = this.cy0 = y0;
+ this.cdx = this.sdx = 1;
+ this.cdy = this.sdy = 0;
+ this.prev = MOVE_TO;
+ }
+
+ public void lineTo(float x1, float y1) {
+ float dx = x1 - cx0;
+ float dy = y1 - cy0;
+ if (dx == 0f && dy == 0f) {
+ dx = 1;
+ }
+ computeOffset(dx, dy, lineWidth2, offset[0]);
+ float mx = offset[0][0];
+ float my = offset[0][1];
+
+ drawJoin(cdx, cdy, cx0, cy0, dx, dy, cmx, cmy, mx, my);
+
+ emitLineTo(cx0 + mx, cy0 + my);
+ emitLineTo(x1 + mx, y1 + my);
+
+ emitLineTo(cx0 - mx, cy0 - my, true);
+ emitLineTo(x1 - mx, y1 - my, true);
+
+ this.cmx = mx;
+ this.cmy = my;
+ this.cdx = dx;
+ this.cdy = dy;
+ this.cx0 = x1;
+ this.cy0 = y1;
+ this.prev = DRAWING_OP_TO;
+ }
+
+ public void closePath() {
+ if (prev != DRAWING_OP_TO) {
+ if (prev == CLOSE) {
+ return;
+ }
+ emitMoveTo(cx0, cy0 - lineWidth2);
+ this.cmx = this.smx = 0;
+ this.cmy = this.smy = -lineWidth2;
+ this.cdx = this.sdx = 1;
+ this.cdy = this.sdy = 0;
+ 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() {
+ while(!reverse.isEmpty()) {
+ reverse.pop(out);
+ }
+ }
+
+ 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;
+ }
+
+ 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 float x0, final float y0) {
+ out.moveTo(x0, y0);
+ }
+
+ private void emitLineTo(final float x1, final float y1) {
+ out.lineTo(x1, y1);
+ }
+
+ private void emitLineTo(final float x1, final float y1,
+ final boolean rev)
+ {
+ if (rev) {
+ reverse.pushLine(x1, y1);
+ } else {
+ emitLineTo(x1, y1);
+ }
+ }
+
+ private void emitQuadTo(final float x0, final float y0,
+ final float x1, final float y1,
+ final float x2, final float y2, final boolean rev)
+ {
+ if (rev) {
+ reverse.pushQuad(x0, y0, x1, y1);
+ } else {
+ out.quadTo(x1, y1, x2, y2);
+ }
+ }
+
+ private void emitCurveTo(final float x0, final float y0,
+ final float x1, final float y1,
+ final float x2, final float y2,
+ final float x3, final float 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(float pdx, float pdy,
+ float x0, float y0,
+ float dx, float dy,
+ float omx, float omy,
+ float mx, float 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 float x1, final float y1,
+ final float x2, final float y2,
+ final float ERR)
+ {
+ assert ERR > 0 : "";
+ // compare taxicab distance. ERR will always be small, so using
+ // true distance won't give much benefit
+ return (Helpers.within(x1, x2, ERR) && // we want to avoid calling Math.abs
+ Helpers.within(y1, y2, ERR)); // this is just as good.
+ }
+
+ private void getLineOffsets(float x1, float y1,
+ float x2, float y2,
+ float[] left, float[] right) {
+ computeOffset(x2 - x1, y2 - y1, lineWidth2, offset[0]);
+ left[0] = x1 + offset[0][0];
+ left[1] = y1 + offset[0][1];
+ left[2] = x2 + offset[0][0];
+ left[3] = y2 + offset[0][1];
+ right[0] = x1 - offset[0][0];
+ right[1] = y1 - offset[0][1];
+ right[2] = x2 - offset[0][0];
+ right[3] = y2 - offset[0][1];
+ }
+
+ private int computeOffsetCubic(float[] pts, final int off,
+ float[] leftOff, float[] 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 winden
+ // 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 float x1 = pts[off + 0], y1 = pts[off + 1];
+ final float x2 = pts[off + 2], y2 = pts[off + 3];
+ final float x3 = pts[off + 4], y3 = pts[off + 5];
+ final float x4 = pts[off + 6], y4 = pts[off + 7];
+
+ float dx4 = x4 - x3;
+ float dy4 = y4 - y3;
+ float dx1 = x2 - x1;
+ float 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 * ulp(y2));
+ final boolean p3eqp4 = within(x3,y3,x4,y4, 6 * 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
+ float dotsq = (dx1 * dx4 + dy1 * dy4);
+ dotsq = dotsq * dotsq;
+ float l1sq = dx1 * dx1 + dy1 * dy1, l4sq = dx4 * dx4 + dy4 * dy4;
+ if (Helpers.within(dotsq, l1sq * l4sq, 4 * 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.
+
+ float x = 0.125f * (x1 + 3 * (x2 + x3) + x4);
+ float y = 0.125f * (y1 + 3 * (y2 + y3) + y4);
+ // (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.
+ float 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, offset[0]);
+ computeOffset(dxm, dym, lineWidth2, offset[1]);
+ computeOffset(dx4, dy4, lineWidth2, offset[2]);
+ float x1p = x1 + offset[0][0]; // start
+ float y1p = y1 + offset[0][1]; // point
+ float xi = x + offset[1][0]; // interpolation
+ float yi = y + offset[1][1]; // point
+ float x4p = x4 + offset[2][0]; // end
+ float y4p = y4 + offset[2][1]; // point
+
+ float invdet43 = 4f / (3f * (dx1 * dy4 - dy1 * dx4));
+
+ float two_pi_m_p1_m_p4x = 2*xi - x1p - x4p;
+ float two_pi_m_p1_m_p4y = 2*yi - y1p - y4p;
+ float c1 = invdet43 * (dy4 * two_pi_m_p1_m_p4x - dx4 * two_pi_m_p1_m_p4y);
+ float c2 = invdet43 * (dx1 * two_pi_m_p1_m_p4y - dy1 * two_pi_m_p1_m_p4x);
+
+ float 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 - offset[0][0]; y1p = y1 - offset[0][1];
+ xi = xi - 2 * offset[1][0]; yi = yi - 2 * offset[1][1];
+ x4p = x4 - offset[2][0]; y4p = y4 - offset[2][1];
+
+ two_pi_m_p1_m_p4x = 2*xi - x1p - x4p;
+ two_pi_m_p1_m_p4y = 2*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;
+ }
+
+ // return the kind of curve in the right and left arrays.
+ private int computeOffsetQuad(float[] pts, final int off,
+ float[] leftOff, float[] rightOff)
+ {
+ final float x1 = pts[off + 0], y1 = pts[off + 1];
+ final float x2 = pts[off + 2], y2 = pts[off + 3];
+ final float x3 = pts[off + 4], y3 = pts[off + 5];
+
+ final float dx3 = x3 - x2;
+ final float dy3 = y3 - y2;
+ final float dx1 = x2 - x1;
+ final float dy1 = y2 - y1;
+
+ // this computes the offsets at t = 0, 1
+ computeOffset(dx1, dy1, lineWidth2, offset[0]);
+ computeOffset(dx3, dy3, lineWidth2, offset[1]);
+
+ leftOff[0] = x1 + offset[0][0]; leftOff[1] = y1 + offset[0][1];
+ leftOff[4] = x3 + offset[1][0]; leftOff[5] = y3 + offset[1][1];
+ rightOff[0] = x1 - offset[0][0]; rightOff[1] = y1 - offset[0][1];
+ rightOff[4] = x3 - offset[1][0]; rightOff[5] = y3 - offset[1][1];
+
+ float x1p = leftOff[0]; // start
+ float y1p = leftOff[1]; // point
+ float x3p = leftOff[4]; // end
+ float y3p = leftOff[5]; // point
+
+ // Corner cases:
+ // 1. If the two control vectors are parallel, we'll end up with NaN's
+ // in leftOff (and rightOff in the body of the if below), so we'll
+ // do getLineOffsets, which is right.
+ // 2. If the first or second two points are equal, then (dx1,dy1)==(0,0)
+ // or (dx3,dy3)==(0,0), so (x1p, y1p)==(x1p+dx1, y1p+dy1)
+ // or (x3p, y3p)==(x3p-dx3, y3p-dy3), which means that
+ // computeIntersection will put NaN's in leftOff and right off, and
+ // we will do getLineOffsets, which is right.
+ computeIntersection(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, leftOff, 2);
+ float cx = leftOff[2];
+ float cy = leftOff[3];
+
+ if (!(isFinite(cx) && isFinite(cy))) {
+ // maybe the right path is not degenerate.
+ x1p = rightOff[0];
+ y1p = rightOff[1];
+ x3p = rightOff[4];
+ y3p = rightOff[5];
+ computeIntersection(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, rightOff, 2);
+ cx = rightOff[2];
+ cy = rightOff[3];
+ if (!(isFinite(cx) && isFinite(cy))) {
+ // both are degenerate. This curve is a line.
+ getLineOffsets(x1, y1, x3, y3, leftOff, rightOff);
+ return 4;
+ }
+ // {left,right}Off[0,1,4,5] are already set to the correct values.
+ leftOff[2] = 2*x2 - cx;
+ leftOff[3] = 2*y2 - cy;
+ return 6;
+ }
+
+ // rightOff[2,3] = (x2,y2) - ((left_x2, left_y2) - (x2, y2))
+ // == 2*(x2, y2) - (left_x2, left_y2)
+ rightOff[2] = 2*x2 - cx;
+ rightOff[3] = 2*y2 - cy;
+ return 6;
+ }
+
+ private static boolean isFinite(float x) {
+ return (Float.NEGATIVE_INFINITY < x && x < Float.POSITIVE_INFINITY);
+ }
+
+ // This is where the curve to be processed is put. We give it
+ // enough room to store 2 curves: one for the current subdivision, the
+ // other for the rest of the curve.
+ private float[] middle = new float[2*8];
+ private float[] lp = new float[8];
+ private float[] rp = new float[8];
+ private static final int MAX_N_CURVES = 11;
+ private float[] subdivTs = new float[MAX_N_CURVES - 1];
+
+ // If this class is compiled with ecj, then Hotspot crashes when OSR
+ // compiling this function. See bugs 7004570 and 6675699
+ // TODO: until those are fixed, we should work around that by
+ // manually inlining this into curveTo and quadTo.
+/******************************* WORKAROUND **********************************
+ private void somethingTo(final int type) {
+ // need these so we can update the state at the end of this method
+ final float xf = middle[type-2], yf = middle[type-1];
+ float dxs = middle[2] - middle[0];
+ float dys = middle[3] - middle[1];
+ float dxf = middle[type - 2] - middle[type - 4];
+ float dyf = middle[type - 1] - middle[type - 3];
+ switch(type) {
+ case 6:
+ if ((dxs == 0f && dys == 0f) ||
+ (dxf == 0f && dyf == 0f)) {
+ dxs = dxf = middle[4] - middle[0];
+ dys = dyf = middle[5] - middle[1];
+ }
+ break;
+ case 8:
+ boolean p1eqp2 = (dxs == 0f && dys == 0f);
+ boolean p3eqp4 = (dxf == 0f && dyf == 0f);
+ if (p1eqp2) {
+ dxs = middle[4] - middle[0];
+ dys = middle[5] - middle[1];
+ if (dxs == 0f && dys == 0f) {
+ dxs = middle[6] - middle[0];
+ dys = middle[7] - middle[1];
+ }
+ }
+ if (p3eqp4) {
+ dxf = middle[6] - middle[2];
+ dyf = middle[7] - middle[3];
+ if (dxf == 0f && dyf == 0f) {
+ dxf = middle[6] - middle[0];
+ dyf = middle[7] - middle[1];
+ }
+ }
+ }
+ if (dxs == 0f && dys == 0f) {
+ // this happens iff the "curve" is just a point
+ lineTo(middle[0], middle[1]);
+ return;
+ }
+ // if these vectors are too small, normalize them, to avoid future
+ // precision problems.
+ if (Math.abs(dxs) < 0.1f && Math.abs(dys) < 0.1f) {
+ float len = (float) sqrt(dxs*dxs + dys*dys);
+ dxs /= len;
+ dys /= len;
+ }
+ if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) {
+ float len = (float) sqrt(dxf*dxf + dyf*dyf);
+ dxf /= len;
+ dyf /= len;
+ }
+
+ computeOffset(dxs, dys, lineWidth2, offset[0]);
+ final float mx = offset[0][0];
+ final float my = offset[0][1];
+ drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, mx, my);
+
+ int nSplits = findSubdivPoints(middle, subdivTs, type, lineWidth2);
+
+ int kind = 0;
+ Iterator<Integer> it = Curve.breakPtsAtTs(middle, type, subdivTs, nSplits);
+ while(it.hasNext()) {
+ int curCurveOff = it.next();
+
+ switch (type) {
+ case 8:
+ kind = computeOffsetCubic(middle, curCurveOff, lp, rp);
+ break;
+ case 6:
+ kind = computeOffsetQuad(middle, curCurveOff, lp, rp);
+ break;
+ }
+ emitLineTo(lp[0], lp[1]);
+ switch(kind) {
+ case 8:
+ emitCurveTo(lp[0], lp[1], lp[2], lp[3], lp[4], lp[5], lp[6], lp[7], false);
+ emitCurveTo(rp[0], rp[1], rp[2], rp[3], rp[4], rp[5], rp[6], rp[7], true);
+ break;
+ case 6:
+ emitQuadTo(lp[0], lp[1], lp[2], lp[3], lp[4], lp[5], false);
+ emitQuadTo(rp[0], rp[1], rp[2], rp[3], rp[4], rp[5], true);
+ break;
+ case 4:
+ emitLineTo(lp[2], lp[3]);
+ emitLineTo(rp[0], rp[1], true);
+ break;
+ }
+ emitLineTo(rp[kind - 2], rp[kind - 1], true);
+ }
+
+ this.cmx = (lp[kind - 2] - rp[kind - 2]) / 2;
+ this.cmy = (lp[kind - 1] - rp[kind - 1]) / 2;
+ this.cdx = dxf;
+ this.cdy = dyf;
+ this.cx0 = xf;
+ this.cy0 = yf;
+ this.prev = DRAWING_OP_TO;
+ }
+****************************** END WORKAROUND *******************************/
+
+ // 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 Curve c = new Curve();
+ private static int findSubdivPoints(float[] pts, float[] ts, final int type, final float w)
+ {
+ final float x12 = pts[2] - pts[0];
+ final float y12 = pts[3] - pts[1];
+ // if the curve is already parallel to either axis we gain nothing
+ // from rotating it.
+ if (y12 != 0f && x12 != 0f) {
+ // 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 float hypot = (float) sqrt(x12 * x12 + y12 * y12);
+ final float cos = x12 / hypot;
+ final float sin = y12 / hypot;
+ final float x1 = cos * pts[0] + sin * pts[1];
+ final float y1 = cos * pts[1] - sin * pts[0];
+ final float x2 = cos * pts[2] + sin * pts[3];
+ final float y2 = cos * pts[3] - sin * pts[2];
+ final float x3 = cos * pts[4] + sin * pts[5];
+ final float y3 = cos * pts[5] - sin * pts[4];
+ switch(type) {
+ case 8:
+ final float x4 = cos * pts[6] + sin * pts[7];
+ final float 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;
+ }
+ } 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, 0.0001f);
+
+ ret = Helpers.filterOutNotInAB(ts, 0, ret, 0.0001f, 0.9999f);
+ Helpers.isort(ts, 0, ret);
+ return ret;
+ }
+
+ @Override public void curveTo(float x1, float y1,
+ float x2, float y2,
+ float x3, float y3)
+ {
+ middle[0] = cx0; middle[1] = cy0;
+ middle[2] = x1; middle[3] = y1;
+ middle[4] = x2; middle[5] = y2;
+ middle[6] = x3; middle[7] = y3;
+
+ // inlined version of somethingTo(8);
+ // See the TODO on somethingTo
+
+ // need these so we can update the state at the end of this method
+ final float xf = middle[6], yf = middle[7];
+ float dxs = middle[2] - middle[0];
+ float dys = middle[3] - middle[1];
+ float dxf = middle[6] - middle[4];
+ float dyf = middle[7] - middle[5];
+
+ boolean p1eqp2 = (dxs == 0f && dys == 0f);
+ boolean p3eqp4 = (dxf == 0f && dyf == 0f);
+ if (p1eqp2) {
+ dxs = middle[4] - middle[0];
+ dys = middle[5] - middle[1];
+ if (dxs == 0f && dys == 0f) {
+ dxs = middle[6] - middle[0];
+ dys = middle[7] - middle[1];
+ }
+ }
+ if (p3eqp4) {
+ dxf = middle[6] - middle[2];
+ dyf = middle[7] - middle[3];
+ if (dxf == 0f && dyf == 0f) {
+ dxf = middle[6] - middle[0];
+ dyf = middle[7] - middle[1];
+ }
+ }
+ if (dxs == 0f && dys == 0f) {
+ // this happens iff the "curve" is just a point
+ lineTo(middle[0], middle[1]);
+ return;
+ }
+
+ // if these vectors are too small, normalize them, to avoid future
+ // precision problems.
+ if (Math.abs(dxs) < 0.1f && Math.abs(dys) < 0.1f) {
+ float len = (float) sqrt(dxs*dxs + dys*dys);
+ dxs /= len;
+ dys /= len;
+ }
+ if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) {
+ float len = (float) sqrt(dxf*dxf + dyf*dyf);
+ dxf /= len;
+ dyf /= len;
+ }
+
+ computeOffset(dxs, dys, lineWidth2, offset[0]);
+ final float mx = offset[0][0];
+ final float my = offset[0][1];
+ drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, mx, my);
+
+ int nSplits = findSubdivPoints(middle, subdivTs, 8, lineWidth2);
+
+ int kind = 0;
+ Iterator<Integer> it = Curve.breakPtsAtTs(middle, 8, subdivTs, nSplits);
+ while(it.hasNext()) {
+ int curCurveOff = it.next();
+
+ kind = computeOffsetCubic(middle, curCurveOff, lp, rp);
+ emitLineTo(lp[0], lp[1]);
+ switch(kind) {
+ case 8:
+ emitCurveTo(lp[0], lp[1], lp[2], lp[3], lp[4], lp[5], lp[6], lp[7], false);
+ emitCurveTo(rp[0], rp[1], rp[2], rp[3], rp[4], rp[5], rp[6], rp[7], true);
+ break;
+ case 4:
+ emitLineTo(lp[2], lp[3]);
+ emitLineTo(rp[0], rp[1], true);
+ break;
+ }
+ emitLineTo(rp[kind - 2], rp[kind - 1], true);
+ }
+
+ this.cmx = (lp[kind - 2] - rp[kind - 2]) / 2;
+ this.cmy = (lp[kind - 1] - rp[kind - 1]) / 2;
+ this.cdx = dxf;
+ this.cdy = dyf;
+ this.cx0 = xf;
+ this.cy0 = yf;
+ this.prev = DRAWING_OP_TO;
+ }
+
+ @Override public void quadTo(float x1, float y1, float x2, float y2) {
+ middle[0] = cx0; middle[1] = cy0;
+ middle[2] = x1; middle[3] = y1;
+ middle[4] = x2; middle[5] = y2;
+
+ // inlined version of somethingTo(8);
+ // See the TODO on somethingTo
+
+ // need these so we can update the state at the end of this method
+ final float xf = middle[4], yf = middle[5];
+ float dxs = middle[2] - middle[0];
+ float dys = middle[3] - middle[1];
+ float dxf = middle[4] - middle[2];
+ float dyf = middle[5] - middle[3];
+ if ((dxs == 0f && dys == 0f) || (dxf == 0f && dyf == 0f)) {
+ dxs = dxf = middle[4] - middle[0];
+ dys = dyf = middle[5] - middle[1];
+ }
+ if (dxs == 0f && dys == 0f) {
+ // this happens iff the "curve" is just a point
+ lineTo(middle[0], middle[1]);
+ return;
+ }
+ // if these vectors are too small, normalize them, to avoid future
+ // precision problems.
+ if (Math.abs(dxs) < 0.1f && Math.abs(dys) < 0.1f) {
+ float len = (float) sqrt(dxs*dxs + dys*dys);
+ dxs /= len;
+ dys /= len;
+ }
+ if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) {
+ float len = (float) sqrt(dxf*dxf + dyf*dyf);
+ dxf /= len;
+ dyf /= len;
+ }
+
+ computeOffset(dxs, dys, lineWidth2, offset[0]);
+ final float mx = offset[0][0];
+ final float my = offset[0][1];
+ drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, mx, my);
+
+ int nSplits = findSubdivPoints(middle, subdivTs, 6, lineWidth2);
+
+ int kind = 0;
+ Iterator<Integer> it = Curve.breakPtsAtTs(middle, 6, subdivTs, nSplits);
+ while(it.hasNext()) {
+ int curCurveOff = it.next();
+
+ kind = computeOffsetQuad(middle, curCurveOff, lp, rp);
+ emitLineTo(lp[0], lp[1]);
+ switch(kind) {
+ case 6:
+ emitQuadTo(lp[0], lp[1], lp[2], lp[3], lp[4], lp[5], false);
+ emitQuadTo(rp[0], rp[1], rp[2], rp[3], rp[4], rp[5], true);
+ break;
+ case 4:
+ emitLineTo(lp[2], lp[3]);
+ emitLineTo(rp[0], rp[1], true);
+ break;
+ }
+ emitLineTo(rp[kind - 2], rp[kind - 1], true);
+ }
+
+ this.cmx = (lp[kind - 2] - rp[kind - 2]) / 2;
+ this.cmy = (lp[kind - 1] - rp[kind - 1]) / 2;
+ 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.
+ private static final class PolyStack {
+ float[] curves;
+ int end;
+ int[] curveTypes;
+ int numCurves;
+
+ private static final int INIT_SIZE = 50;
+
+ PolyStack() {
+ curves = new float[8 * INIT_SIZE];
+ curveTypes = new int[INIT_SIZE];
+ end = 0;
+ numCurves = 0;
+ }
+
+ public boolean isEmpty() {
+ return numCurves == 0;
+ }
+
+ private void ensureSpace(int n) {
+ if (end + n >= curves.length) {
+ int newSize = (end + n) * 2;
+ curves = Arrays.copyOf(curves, newSize);
+ }
+ if (numCurves >= curveTypes.length) {
+ int newSize = numCurves * 2;
+ curveTypes = Arrays.copyOf(curveTypes, newSize);
+ }
+ }
+
+ public void pushCubic(float x0, float y0,
+ float x1, float y1,
+ float x2, float y2)
+ {
+ ensureSpace(6);
+ curveTypes[numCurves++] = 8;
+ // assert(x0 == lastX && y0 == lastY)
+
+ // we reverse the coordinate order to make popping easier
+ curves[end++] = x2; curves[end++] = y2;
+ curves[end++] = x1; curves[end++] = y1;
+ curves[end++] = x0; curves[end++] = y0;
+ }
+
+ public void pushQuad(float x0, float y0,
+ float x1, float y1)
+ {
+ ensureSpace(4);
+ curveTypes[numCurves++] = 6;
+ // assert(x0 == lastX && y0 == lastY)
+ curves[end++] = x1; curves[end++] = y1;
+ curves[end++] = x0; curves[end++] = y0;
+ }
+
+ public void pushLine(float x, float y) {
+ ensureSpace(2);
+ curveTypes[numCurves++] = 4;
+ // assert(x0 == lastX && y0 == lastY)
+ curves[end++] = x; curves[end++] = y;
+ }
+
+ @SuppressWarnings("unused")
+ public int pop(float[] pts) {
+ int ret = curveTypes[numCurves - 1];
+ numCurves--;
+ end -= (ret - 2);
+ System.arraycopy(curves, end, pts, 0, ret - 2);
+ return ret;
+ }
+
+ public void pop(PathConsumer2D io) {
+ numCurves--;
+ int type = curveTypes[numCurves];
+ end -= (type - 2);
+ switch(type) {
+ case 8:
+ io.curveTo(curves[end+0], curves[end+1],
+ curves[end+2], curves[end+3],
+ curves[end+4], curves[end+5]);
+ break;
+ case 6:
+ io.quadTo(curves[end+0], curves[end+1],
+ curves[end+2], curves[end+3]);
+ break;
+ case 4:
+ io.lineTo(curves[end], curves[end+1]);
+ }
+ }
+
+ @Override
+ public String toString() {
+ String ret = "";
+ int nc = numCurves;
+ int end = this.end;
+ while (nc > 0) {
+ nc--;
+ int type = curveTypes[numCurves];
+ end -= (type - 2);
+ switch(type) {
+ case 8:
+ ret += "cubic: ";
+ break;
+ case 6:
+ ret += "quad: ";
+ break;
+ case 4:
+ ret += "line: ";
+ break;
+ }
+ ret += Arrays.toString(Arrays.copyOfRange(curves, end, end+type-2)) + "\n";
+ }
+ return ret;
+ }
+ }
+}