--- /dev/null 2017-04-22 10:40:35.471249043 +0200 +++ new/src/java.desktop/share/classes/sun/java2d/marlin/DStroker.java 2017-04-22 13:16:13.492612520 +0200 @@ -0,0 +1,1325 @@ +/* + * Copyright (c) 2007, 2016, 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 * 8]; + 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 DStroker. + * @param rdrCtx per-thread renderer context + */ + DStroker(final DRendererContext rdrCtx) { + this.rdrCtx = rdrCtx; + + this.reverse = new PolyStack(rdrCtx); + this.curve = rdrCtx.curve; + } + + /** + * Inits the DStroker. + * + * @param pc2d an output DPathConsumer2D. + * @param lineWidth the desired line width in pixels + * @param capStyle the desired end cap style, one of + * CAP_BUTT, CAP_ROUND or + * CAP_SQUARE. + * @param joinStyle the desired line join style, one of + * JOIN_MITER, JOIN_ROUND or + * JOIN_BEVEL. + * @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[0] and m[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[0] and m[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 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 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 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. + + // 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; + } + } +}