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package com.sun.openpisces;

import com.sun.javafx.geom.PathConsumer2D;
import java.util.Arrays;
import java.util.Iterator;

// 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
// (RT-26922)
public 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.
/** * Constant value for join style. */
public static final int JOIN_MITER = 0;
Constant value for join style.
/** * Constant value for join style. */
public static final int JOIN_ROUND = 1;
Constant value for join style.
/** * Constant value for join style. */
public static final int JOIN_BEVEL = 2;
Constant value for end cap style.
/** * Constant value for end cap style. */
public static final int CAP_BUTT = 0;
Constant value for end cap style.
/** * Constant value for end cap style. */
public static final int CAP_ROUND = 1;
Constant value for end cap style.
/** * Constant value for end cap style. */
public static final int CAP_SQUARE = 2; private PathConsumer2D out; private int capStyle; private int joinStyle; private float lineWidth2; private final float[][] offset = new float[3][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 = new PolyStack();
Constructs a 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
/** * Constructs a <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 */
public Stroker(PathConsumer2D pc2d, float lineWidth, int capStyle, int joinStyle, float miterLimit) { this(pc2d); reset(lineWidth, capStyle, joinStyle, miterLimit); } public Stroker(PathConsumer2D pc2d) { setConsumer(pc2d); } public void setConsumer(PathConsumer2D pc2d) { this.out = pc2d; } public void reset(float lineWidth, int capStyle, int joinStyle, float miterLimit) { 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)Math.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). 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 ? 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)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); 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) { float cosext2 = (omx * mx + omy * my) / (2 * lineWidth2 * lineWidth2); // 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) * Math.sqrt(0.5-cosext2) / (1.0 + Math.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); } // Return the intersection point of the lines (x0, y0) -> (x1, y1) // and (x0p, y0p) -> (x1p, y1p) in m[0] and m[1] private 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, int off) { 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[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 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, int off) { 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) { m[off++] = (x0 + x0p) / 2.0f; m[off] = (y0 + y0p) / 2.0f; return; } 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; } computeMiter((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 (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 * Math.ulp(y2)); final boolean p3eqp4 = within(x3,y3,x4,y4, 6 * 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 * dotsq; float l1sq = dx1 * dx1 + dy1 * dy1, l4sq = dx4 * dx4 + dy4 * dy4; if (Helpers.within(dotsq, l1sq * l4sq, 4 * 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 = 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; } // 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(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]; float dx3 = x3 - x2; float dy3 = y3 - y2; float dx1 = x2 - x1; 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 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 * Math.ulp(y2)); final boolean p2eqp3 = within(x2,y2,x3,y3, 6 * 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 * dotsq; float l1sq = dx1 * dx1 + dy1 * dy1, l3sq = dx3 * dx3 + dy3 * dy3; if (Helpers.within(dotsq, l1sq * l3sq, 4 * 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, offset[0]); computeOffset(dx3, dy3, lineWidth2, offset[1]); float x1p = x1 + offset[0][0]; // start float y1p = y1 + offset[0][1]; // point float x3p = x3 + offset[1][0]; // end float y3p = y3 + offset[1][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 - offset[0][0]; y1p = y1 - offset[0][1]; x3p = x3 - offset[1][0]; y3p = y3 - offset[1][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; } // 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[MAX_N_CURVES*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)Math.sqrt(dxs*dxs + dys*dys); dxs /= len; dys /= len; } if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { float len = (float)Math.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 it = Curve.breakPtsAtTs(middle, type, subdivTs, nSplits); while(it.hasNext()) { int curCurveOff = it.next(); kind = 0; switch (type) { case 8: kind = computeOffsetCubic(middle, curCurveOff, lp, rp); break; case 6: kind = computeOffsetQuad(middle, curCurveOff, lp, rp); break; } if (kind != 0) { 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
/******************************* 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)Math.sqrt(dxs*dxs + dys*dys); dxs /= len; dys /= len; } if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { float len = (float)Math.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(); kind = 0; switch (type) { case 8: kind = computeOffsetCubic(middle, curCurveOff, lp, rp); break; case 6: kind = computeOffsetQuad(middle, curCurveOff, lp, rp); break; } if (kind != 0) { 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)Math.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 // (JDK-6675699) // 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)Math.sqrt(dxs*dxs + dys*dys); dxs /= len; dys /= len; } if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { float len = (float)Math.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); float prevT = 0f; for (int i = 0; i < nSplits; i++) { float t = subdivTs[i]; Helpers.subdivideCubicAt((t - prevT) / (1 - prevT), middle, i*6, middle, i*6, middle, i*6+6); prevT = t; } int kind = 0; for (int i = 0; i <= nSplits; i++) { kind = computeOffsetCubic(middle, i*6, lp, rp); if (kind != 0) { 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 // (JDK-6675699) // 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)Math.sqrt(dxs*dxs + dys*dys); dxs /= len; dys /= len; } if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { float len = (float)Math.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); float prevt = 0f; for (int i = 0; i < nSplits; i++) { float t = subdivTs[i]; Helpers.subdivideQuadAt((t - prevt) / (1 - prevt), middle, i*4, middle, i*4, middle, i*4+4); prevt = t; } int kind = 0; for (int i = 0; i <= nSplits; i++) { kind = computeOffsetQuad(middle, i*4, lp, rp); if (kind != 0) { 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 last = this.end; while (nc > 0) { nc--; int type = curveTypes[numCurves]; last -= (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, last, last+type-2)) + "\n"; } return ret; } } }