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 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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package sun.java2d.marlin;

import java.util.Arrays;

import sun.awt.geom.PathConsumer2D;
import sun.java2d.marlin.Helpers.PolyStack;
import sun.java2d.marlin.TransformingPathConsumer2D.CurveBasicMonotonizer;
import sun.java2d.marlin.TransformingPathConsumer2D.CurveClipSplitter;

// 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, 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;

    // round join threshold = 1 subpixel
    private static final float ERR_JOIN = (1.0f / MIN_SUBPIXELS);
    private static final float ROUND_JOIN_THRESHOLD = ERR_JOIN * ERR_JOIN;

    // kappa = (4/3) * (SQRT(2) - 1)
    private static final float C = (float)(4.0d * (Math.sqrt(2.0d) - 1.0d) / 3.0d);

    // SQRT(2)
    private static final float SQRT_2 = (float)Math.sqrt(2.0d);

    private PathConsumer2D out;

    private int capStyle;
    private int joinStyle;

    private float lineWidth2;
    private float invHalfLineWidth2Sq;

    private final float[] offset0 = new float[2];
    private final float[] offset1 = new float[2];
    private final float[] offset2 = new float[2];
    private final float[] miter = new float[2];
    private 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;

    private final float[] lp = new float[8];
    private final float[] rp = new float[8];

    // per-thread renderer context
    final RendererContext rdrCtx;

    // dirty curve
    final Curve curve;

    // Bounds of the drawing region, at pixel precision.
    private float[] clipRect;

    // the outcode of the current point
    private int cOutCode = 0;

    // the outcode of the starting point
    private int sOutCode = 0;

    // flag indicating if the path is opened (clipped)
    private boolean opened = false;
    // flag indicating if the starting point's cap is done
    private boolean capStart = false;
    // flag indicating to monotonize curves
    private boolean monotonize;

    private boolean subdivide = DO_CLIP_SUBDIVIDER;
    private final CurveClipSplitter curveSplitter;

    
Constructs a Stroker.
Params:
  • rdrCtx – per-thread renderer context
/** * Constructs a <code>Stroker</code>. * @param rdrCtx per-thread renderer context */
Stroker(final RendererContext rdrCtx) { this.rdrCtx = rdrCtx; this.reverse = (rdrCtx.stats != null) ? new PolyStack(rdrCtx, rdrCtx.stats.stat_str_polystack_types, rdrCtx.stats.stat_str_polystack_curves, rdrCtx.stats.hist_str_polystack_curves, rdrCtx.stats.stat_array_str_polystack_curves, rdrCtx.stats.stat_array_str_polystack_types) : new PolyStack(rdrCtx); this.curve = rdrCtx.curve; this.curveSplitter = rdrCtx.curveClipSplitter; }
Inits the Stroker.
Params:
  • pc2d – an output PathConsumer2D.
  • lineWidth – the desired line width in pixels
  • capStyle – the desired end cap style, one of CAP_BUTT, CAP_ROUND or CAP_SQUARE.
  • joinStyle – the desired line join style, one of JOIN_MITER, JOIN_ROUND or JOIN_BEVEL.
  • miterLimit – the desired miter limit
  • subdivideCurves – true to indicate to subdivide curves, false if dasher does
Returns:this instance
/** * Inits the <code>Stroker</code>. * * @param pc2d an output <code>PathConsumer2D</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 * @param subdivideCurves true to indicate to subdivide curves, false if dasher does * @return this instance */
Stroker init(final PathConsumer2D pc2d, final float lineWidth, final int capStyle, final int joinStyle, final float miterLimit, final boolean subdivideCurves) { this.out = pc2d; this.lineWidth2 = lineWidth / 2.0f; this.invHalfLineWidth2Sq = 1.0f / (2.0f * lineWidth2 * lineWidth2); this.monotonize = subdivideCurves; this.capStyle = capStyle; this.joinStyle = joinStyle; final float limit = miterLimit * lineWidth2; this.miterLimitSq = limit * limit; this.prev = CLOSE; rdrCtx.stroking = 1; if (rdrCtx.doClip) { // Adjust the clipping rectangle with the stroker margin (miter limit, width) float margin = lineWidth2; if (capStyle == CAP_SQUARE) { margin *= SQRT_2; } if ((joinStyle == JOIN_MITER) && (margin < limit)) { margin = limit; } // bounds as half-open intervals: minX <= x < maxX and minY <= y < maxY // adjust clip rectangle (ymin, ymax, xmin, xmax): final float[] _clipRect = rdrCtx.clipRect; _clipRect[0] -= margin; _clipRect[1] += margin; _clipRect[2] -= margin; _clipRect[3] += margin; this.clipRect = _clipRect; if (MarlinConst.DO_LOG_CLIP) { MarlinUtils.logInfo("clipRect (stroker): " + Arrays.toString(rdrCtx.clipRect)); } // initialize curve splitter here for stroker & dasher: if (DO_CLIP_SUBDIVIDER) { subdivide = subdivideCurves; // adjust padded clip rectangle: curveSplitter.init(); } else { subdivide = false; } } else { this.clipRect = null; this.cOutCode = 0; this.sOutCode = 0; } return this; // fluent API } void disableClipping() { this.clipRect = null; this.cOutCode = 0; this.sOutCode = 0; }
Disposes this stroker: clean up before reusing this instance
/** * Disposes this stroker: * clean up before reusing this instance */
void dispose() { reverse.dispose(); opened = false; capStart = false; if (DO_CLEAN_DIRTY) { // Force zero-fill dirty arrays: Arrays.fill(offset0, 0.0f); Arrays.fill(offset1, 0.0f); Arrays.fill(offset2, 0.0f); Arrays.fill(miter, 0.0f); Arrays.fill(lp, 0.0f); Arrays.fill(rp, 0.0f); } } private static void computeOffset(final float lx, final float ly, final float w, final float[] m) { float len = lx*lx + ly*ly; if (len == 0.0f) { m[0] = 0.0f; m[1] = 0.0f; } else { len = (float) 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 float dx1, final float dy1, final float dx2, final float dy2) { return dx1 * dy2 <= dy1 * dx2; } private void mayDrawRoundJoin(float cx, float cy, float omx, float omy, float mx, float my, boolean rev) { if ((omx == 0.0f && omy == 0.0f) || (mx == 0.0f && my == 0.0f)) { return; } final float domx = omx - mx; final float domy = omy - my; final float lenSq = domx*domx + domy*domy; if (lenSq < ROUND_JOIN_THRESHOLD) { return; } if (rev) { omx = -omx; omy = -omy; mx = -mx; my = -my; } drawRoundJoin(cx, cy, 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. if (cosext >= 0.0f) { drawBezApproxForArc(cx, cy, omx, omy, mx, my, rev); } else { // 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) Math.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); } } // 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) * 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 >= 0.5f) { // 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) ((4.0d / 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 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 Cmx = C * mx; final float 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 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) { float x10 = x1 - x0; float y10 = y1 - y0; float x10p = x1p - x0p; float 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). float den = x10*y10p - x10p*y10; float t = x10p*(y0-y0p) - y10p*(x0-x0p); t /= den; m[0] = x0 + t*x10; m[1] = 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 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) { float x10 = x1 - x0; float y10 = y1 - y0; float x10p = x1p - x0p; float 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). float den = x10*y10p - x10p*y10; if (den == 0.0f) { m[2] = (x0 + x0p) / 2.0f; m[3] = (y0 + y0p) / 2.0f; } else { float t = x10p*(y0-y0p) - y10p*(x0-x0p); t /= den; m[2] = x0 + t*x10; m[3] = 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 == 0.0f && pdy == 0.0f) || (dx == 0.0f && dy == 0.0f)) { 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); final float miterX = miter[0]; final float miterY = miter[1]; float 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(final float x0, final float y0) { _moveTo(x0, y0, cOutCode); // update starting point: this.sx0 = x0; this.sy0 = y0; this.sdx = 1.0f; this.sdy = 0.0f; this.opened = false; this.capStart = false; if (clipRect != null) { final int outcode = Helpers.outcode(x0, y0, clipRect); this.cOutCode = outcode; this.sOutCode = outcode; } } private void _moveTo(final float x0, final float y0, final int outcode) { if (prev == MOVE_TO) { this.cx0 = x0; this.cy0 = y0; } else { if (prev == DRAWING_OP_TO) { finish(outcode); } this.prev = MOVE_TO; this.cx0 = x0; this.cy0 = y0; this.cdx = 1.0f; this.cdy = 0.0f; } } @Override public void lineTo(final float x1, final float y1) { lineTo(x1, y1, false); } private void lineTo(final float x1, final float y1, final boolean force) { final int outcode0 = this.cOutCode; if (!force && clipRect != null) { final int outcode1 = Helpers.outcode(x1, y1, clipRect); // Should clip final int orCode = (outcode0 | outcode1); if (orCode != 0) { final int sideCode = outcode0 & outcode1; // basic rejection criteria: if (sideCode == 0) { // ovelap clip: if (subdivide) { // avoid reentrance subdivide = false; // subdivide curve => callback with subdivided parts: boolean ret = curveSplitter.splitLine(cx0, cy0, x1, y1, orCode, this); // reentrance is done: subdivide = true; if (ret) { return; } } // already subdivided so render it } else { this.cOutCode = outcode1; _moveTo(x1, y1, outcode0); opened = true; return; } } this.cOutCode = outcode1; } float dx = x1 - cx0; float dy = y1 - cy0; if (dx == 0.0f && dy == 0.0f) { dx = 1.0f; } computeOffset(dx, dy, lineWidth2, offset0); final float mx = offset0[0]; final float my = offset0[1]; drawJoin(cdx, cdy, cx0, cy0, dx, dy, cmx, cmy, mx, my, outcode0); emitLineTo(cx0 + mx, cy0 + my); emitLineTo( x1 + mx, y1 + my); emitLineToRev(cx0 - mx, cy0 - my); emitLineToRev( x1 - mx, y1 - my); this.prev = DRAWING_OP_TO; this.cx0 = x1; this.cy0 = y1; this.cdx = dx; this.cdy = dy; this.cmx = mx; this.cmy = my; } @Override public void closePath() { // distinguish empty path at all vs opened path ? if (prev != DRAWING_OP_TO && !opened) { if (prev == CLOSE) { return; } emitMoveTo(cx0, cy0 - lineWidth2); this.sdx = 1.0f; this.sdy = 0.0f; this.cdx = 1.0f; this.cdy = 0.0f; this.smx = 0.0f; this.smy = -lineWidth2; this.cmx = 0.0f; this.cmy = -lineWidth2; finish(cOutCode); return; } // basic acceptance criteria if ((sOutCode & cOutCode) == 0) { if (cx0 != sx0 || cy0 != sy0) { lineTo(sx0, sy0, true); } drawJoin(cdx, cdy, cx0, cy0, sdx, sdy, cmx, cmy, smx, smy, sOutCode); emitLineTo(sx0 + smx, sy0 + smy); if (opened) { emitLineTo(sx0 - smx, sy0 - smy); } else { emitMoveTo(sx0 - smx, sy0 - smy); } } // Ignore caps like finish(false) emitReverse(); this.prev = CLOSE; if (opened) { // do not emit close opened = false; } else { emitClose(); } } private void emitReverse() { reverse.popAll(out); } @Override public void pathDone() { if (prev == DRAWING_OP_TO) { finish(cOutCode); } 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(final int outcode) { // Problem: impossible to guess if the path will be closed in advance // i.e. if caps must be drawn or not ? // Solution: use the ClosedPathDetector before Stroker to determine // if the path is a closed path or not if (!rdrCtx.closedPath) { if (outcode == 0) { // current point = end's cap: 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 (!capStart) { capStart = true; if (sOutCode == 0) { // starting point = initial cap: 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); } } } } else { emitReverse(); } 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 emitLineToRev(final float x1, final float y1) { reverse.pushLine(x1, y1); } private void emitLineTo(final float x1, final float y1, final boolean rev) { if (rev) { emitLineToRev(x1, y1); } else { emitLineTo(x1, y1); } } private void emitQuadTo(final float x1, final float y1, final float x2, final float y2) { out.quadTo(x1, y1, x2, y2); } private void emitQuadToRev(final float x0, final float y0, final float x1, final float y1) { reverse.pushQuad(x0, y0, x1, y1); } private void emitCurveTo(final float x1, final float y1, final float x2, final float y2, final float x3, final float y3) { out.curveTo(x1, y1, x2, y2, x3, y3); } private void emitCurveToRev(final float x0, final float y0, final float x1, final float y1, final float x2, final float y2) { reverse.pushCubic(x0, y0, 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, final int outcode) { if (prev != DRAWING_OP_TO) { emitMoveTo(x0 + mx, y0 + my); if (!opened) { this.sdx = dx; this.sdy = dy; this.smx = mx; this.smy = my; } } else { final boolean cw = isCW(pdx, pdy, dx, dy); if (outcode == 0) { if (joinStyle == JOIN_MITER) { drawMiter(pdx, pdy, x0, y0, dx, dy, omx, omy, mx, my, cw); } else if (joinStyle == JOIN_ROUND) { mayDrawRoundJoin(x0, y0, omx, omy, mx, my, cw); } } 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(final float x1, final float y1, final float x2, final float y2, final float[] left, final float[] right) { computeOffset(x2 - x1, y2 - y1, lineWidth2, offset0); final float mx = offset0[0]; final float 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(final float[] pts, final int off, final float[] leftOff, final 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 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 float x1 = pts[off ], 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, 6.0f * Math.ulp(y2)); final boolean p3eqp4 = within(x3, y3, x4, y4, 6.0f * 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 float dotsq = (dx1 * dx4 + dy1 * dy4); dotsq *= dotsq; float l1sq = dx1 * dx1 + dy1 * dy1, l4sq = dx4 * dx4 + dy4 * dy4; if (Helpers.within(dotsq, l1sq * l4sq, 4.0f * 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. float x = (x1 + 3.0f * (x2 + x3) + x4) / 8.0f; float y = (y1 + 3.0f * (y2 + y3) + y4) / 8.0f; // (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, offset0); computeOffset(dxm, dym, lineWidth2, offset1); computeOffset(dx4, dy4, lineWidth2, offset2); float x1p = x1 + offset0[0]; // start float y1p = y1 + offset0[1]; // point float xi = x + offset1[0]; // interpolation float yi = y + offset1[1]; // point float x4p = x4 + offset2[0]; // end float y4p = y4 + offset2[1]; // point float invdet43 = 4.0f / (3.0f * (dx1 * dy4 - dy1 * dx4)); float two_pi_m_p1_m_p4x = 2.0f * xi - x1p - x4p; float two_pi_m_p1_m_p4y = 2.0f * 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 - offset0[0]; y1p = y1 - offset0[1]; xi = xi - 2.0f * offset1[0]; yi = yi - 2.0f * offset1[1]; x4p = x4 - offset2[0]; y4p = y4 - offset2[1]; two_pi_m_p1_m_p4x = 2.0f * xi - x1p - x4p; two_pi_m_p1_m_p4y = 2.0f * 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(final float[] pts, final int off, final float[] leftOff, final float[] rightOff) { final float x1 = pts[off ], 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; // 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, 6.0f * Math.ulp(y2)); final boolean p2eqp3 = within(x2, y2, x3, y3, 6.0f * 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 float dotsq = (dx1 * dx3 + dy1 * dy3); dotsq *= dotsq; float l1sq = dx1 * dx1 + dy1 * dy1, l3sq = dx3 * dx3 + dy3 * dy3; if (Helpers.within(dotsq, l1sq * l3sq, 4.0f * 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); float x1p = x1 + offset0[0]; // start float y1p = y1 + offset0[1]; // point float x3p = x3 + offset1[0]; // end float y3p = y3 + offset1[1]; // point safeComputeMiter(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, leftOff); 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); rightOff[0] = x1p; rightOff[1] = y1p; rightOff[4] = x3p; rightOff[5] = y3p; return 6; } @Override public void curveTo(final float x1, final float y1, final float x2, final float y2, final float x3, final float y3) { final int outcode0 = this.cOutCode; if (clipRect != null) { final int outcode1 = Helpers.outcode(x1, y1, clipRect); final int outcode2 = Helpers.outcode(x2, y2, clipRect); final int outcode3 = Helpers.outcode(x3, y3, clipRect); // Should clip final int orCode = (outcode0 | outcode1 | outcode2 | outcode3); if (orCode != 0) { final int sideCode = outcode0 & outcode1 & outcode2 & outcode3; // basic rejection criteria: if (sideCode == 0) { // ovelap clip: if (subdivide) { // avoid reentrance subdivide = false; // subdivide curve => callback with subdivided parts: boolean ret = curveSplitter.splitCurve(cx0, cy0, x1, y1, x2, y2, x3, y3, orCode, this); // reentrance is done: subdivide = true; if (ret) { return; } } // already subdivided so render it } else { this.cOutCode = outcode3; _moveTo(x3, y3, outcode0); opened = true; return; } } this.cOutCode = outcode3; } _curveTo(x1, y1, x2, y2, x3, y3, outcode0); } private void _curveTo(final float x1, final float y1, final float x2, final float y2, final float x3, final float y3, final int outcode0) { // need these so we can update the state at the end of this method float dxs = x1 - cx0; float dys = y1 - cy0; float dxf = x3 - x2; float dyf = y3 - y2; if ((dxs == 0.0f) && (dys == 0.0f)) { dxs = x2 - cx0; dys = y2 - cy0; if ((dxs == 0.0f) && (dys == 0.0f)) { dxs = x3 - cx0; dys = y3 - cy0; } } if ((dxf == 0.0f) && (dyf == 0.0f)) { dxf = x3 - x1; dyf = y3 - y1; if ((dxf == 0.0f) && (dyf == 0.0f)) { dxf = x3 - cx0; dyf = y3 - cy0; } } if ((dxs == 0.0f) && (dys == 0.0f)) { // this happens if the "curve" is just a point // fix outcode0 for lineTo() call: if (clipRect != null) { this.cOutCode = outcode0; } lineTo(cx0, cy0); 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) { final float len = (float)Math.sqrt(dxs * dxs + dys * dys); dxs /= len; dys /= len; } if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { final float len = (float)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], outcode0); int nSplits = 0; final float[] mid; final float[] l = lp; if (monotonize) { // monotonize curve: final CurveBasicMonotonizer monotonizer = rdrCtx.monotonizer.curve(cx0, cy0, x1, y1, x2, y2, x3, y3); nSplits = monotonizer.nbSplits; mid = monotonizer.middle; } else { // use left instead: mid = l; mid[0] = cx0; mid[1] = cy0; mid[2] = x1; mid[3] = y1; mid[4] = x2; mid[5] = y2; mid[6] = x3; mid[7] = y3; } final float[] 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.prev = DRAWING_OP_TO; this.cx0 = x3; this.cy0 = y3; this.cdx = dxf; this.cdy = dyf; this.cmx = (l[kind - 2] - r[kind - 2]) / 2.0f; this.cmy = (l[kind - 1] - r[kind - 1]) / 2.0f; } @Override public void quadTo(final float x1, final float y1, final float x2, final float y2) { final int outcode0 = this.cOutCode; if (clipRect != null) { final int outcode1 = Helpers.outcode(x1, y1, clipRect); final int outcode2 = Helpers.outcode(x2, y2, clipRect); // Should clip final int orCode = (outcode0 | outcode1 | outcode2); if (orCode != 0) { final int sideCode = outcode0 & outcode1 & outcode2; // basic rejection criteria: if (sideCode == 0) { // ovelap clip: if (subdivide) { // avoid reentrance subdivide = false; // subdivide curve => call lineTo() with subdivided curves: boolean ret = curveSplitter.splitQuad(cx0, cy0, x1, y1, x2, y2, orCode, this); // reentrance is done: subdivide = true; if (ret) { return; } } // already subdivided so render it } else { this.cOutCode = outcode2; _moveTo(x2, y2, outcode0); opened = true; return; } } this.cOutCode = outcode2; } _quadTo(x1, y1, x2, y2, outcode0); } private void _quadTo(final float x1, final float y1, final float x2, final float y2, final int outcode0) { // need these so we can update the state at the end of this method float dxs = x1 - cx0; float dys = y1 - cy0; float dxf = x2 - x1; float dyf = y2 - y1; if (((dxs == 0.0f) && (dys == 0.0f)) || ((dxf == 0.0f) && (dyf == 0.0f))) { dxs = dxf = x2 - cx0; dys = dyf = y2 - cy0; } if ((dxs == 0.0f) && (dys == 0.0f)) { // this happens if the "curve" is just a point // fix outcode0 for lineTo() call: if (clipRect != null) { this.cOutCode = outcode0; } lineTo(cx0, cy0); 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) { final float len = (float)Math.sqrt(dxs * dxs + dys * dys); dxs /= len; dys /= len; } if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { final float len = (float)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], outcode0); int nSplits = 0; final float[] mid; final float[] l = lp; if (monotonize) { // monotonize quad: final CurveBasicMonotonizer monotonizer = rdrCtx.monotonizer.quad(cx0, cy0, x1, y1, x2, y2); nSplits = monotonizer.nbSplits; mid = monotonizer.middle; } else { // use left instead: mid = l; mid[0] = cx0; mid[1] = cy0; mid[2] = x1; mid[3] = y1; mid[4] = x2; mid[5] = y2; } final float[] 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.prev = DRAWING_OP_TO; this.cx0 = x2; this.cy0 = y2; this.cdx = dxf; this.cdy = dyf; this.cmx = (l[kind - 2] - r[kind - 2]) / 2.0f; this.cmy = (l[kind - 1] - r[kind - 1]) / 2.0f; } @Override public long getNativeConsumer() { throw new InternalError("Stroker doesn't use a native consumer"); } }