| /* |
| * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| package sun.java2d.pisces; |
| |
| import java.util.Arrays; |
| import java.util.Iterator; |
| import static java.lang.Math.ulp; |
| import static java.lang.Math.sqrt; |
| |
| import sun.awt.geom.PathConsumer2D; |
| |
| // TODO: some of the arithmetic here is too verbose and prone to hard to |
| // debug typos. We should consider making a small Point/Vector class that |
| // has methods like plus(Point), minus(Point), dot(Point), cross(Point)and such |
| final class Stroker implements PathConsumer2D { |
| |
| private static final int MOVE_TO = 0; |
| private static final int DRAWING_OP_TO = 1; // ie. curve, line, or quad |
| private static final int CLOSE = 2; |
| |
| /** |
| * Constant value for join style. |
| */ |
| public static final int JOIN_MITER = 0; |
| |
| /** |
| * Constant value for join style. |
| */ |
| public static final int JOIN_ROUND = 1; |
| |
| /** |
| * Constant value for join style. |
| */ |
| public static final int JOIN_BEVEL = 2; |
| |
| /** |
| * Constant value for end cap style. |
| */ |
| public static final int CAP_BUTT = 0; |
| |
| /** |
| * Constant value for end cap style. |
| */ |
| public static final int CAP_ROUND = 1; |
| |
| /** |
| * Constant value for end cap style. |
| */ |
| public static final int CAP_SQUARE = 2; |
| |
| private final PathConsumer2D out; |
| |
| private final int capStyle; |
| private final int joinStyle; |
| |
| private final float lineWidth2; |
| |
| private final float[][] offset = new float[3][2]; |
| private final float[] miter = new float[2]; |
| private final float miterLimitSq; |
| |
| private int prev; |
| |
| // The starting point of the path, and the slope there. |
| private float sx0, sy0, sdx, sdy; |
| // the current point and the slope there. |
| private float cx0, cy0, cdx, cdy; // c stands for current |
| // vectors that when added to (sx0,sy0) and (cx0,cy0) respectively yield the |
| // first and last points on the left parallel path. Since this path is |
| // parallel, it's slope at any point is parallel to the slope of the |
| // original path (thought they may have different directions), so these |
| // could be computed from sdx,sdy and cdx,cdy (and vice versa), but that |
| // would be error prone and hard to read, so we keep these anyway. |
| private float smx, smy, cmx, cmy; |
| |
| private final PolyStack reverse = new PolyStack(); |
| |
| /** |
| * Constructs a <code>Stroker</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.out = pc2d; |
| |
| this.lineWidth2 = lineWidth / 2; |
| this.capStyle = capStyle; |
| this.joinStyle = joinStyle; |
| |
| float limit = miterLimit * lineWidth2; |
| this.miterLimitSq = limit*limit; |
| |
| this.prev = CLOSE; |
| } |
| |
| private static void computeOffset(final float lx, final float ly, |
| final float w, final float[] m) |
| { |
| final float len = (float) sqrt(lx*lx + ly*ly); |
| if (len == 0) { |
| m[0] = m[1] = 0; |
| } else { |
| m[0] = (ly * w)/len; |
| m[1] = -(lx * w)/len; |
| } |
| } |
| |
| // Returns true if the vectors (dx1, dy1) and (dx2, dy2) are |
| // clockwise (if dx1,dy1 needs to be rotated clockwise to close |
| // the smallest angle between it and dx2,dy2). |
| // This is equivalent to detecting whether a point q is on the right side |
| // of a line passing through points p1, p2 where p2 = p1+(dx1,dy1) and |
| // q = p2+(dx2,dy2), which is the same as saying p1, p2, q are in a |
| // clockwise order. |
| // NOTE: "clockwise" here assumes coordinates with 0,0 at the bottom left. |
| private static boolean isCW(final float dx1, final float dy1, |
| final float dx2, final float dy2) |
| { |
| return dx1 * dy2 <= dy1 * dx2; |
| } |
| |
| // pisces used to use fixed point arithmetic with 16 decimal digits. I |
| // didn't want to change the values of the constant below when I converted |
| // it to floating point, so that's why the divisions by 2^16 are there. |
| private static final float ROUND_JOIN_THRESHOLD = 1000/65536f; |
| |
| private void drawRoundJoin(float x, float y, |
| float omx, float omy, float mx, float my, |
| boolean rev, |
| float threshold) |
| { |
| if ((omx == 0 && omy == 0) || (mx == 0 && my == 0)) { |
| return; |
| } |
| |
| float domx = omx - mx; |
| float domy = omy - my; |
| float len = domx*domx + domy*domy; |
| if (len < threshold) { |
| return; |
| } |
| |
| if (rev) { |
| omx = -omx; |
| omy = -omy; |
| mx = -mx; |
| my = -my; |
| } |
| drawRoundJoin(x, y, omx, omy, mx, my, rev); |
| } |
| |
| private void drawRoundJoin(float cx, float cy, |
| float omx, float omy, |
| float mx, float my, |
| boolean rev) |
| { |
| // The sign of the dot product of mx,my and omx,omy is equal to the |
| // the sign of the cosine of ext |
| // (ext is the angle between omx,omy and mx,my). |
| 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) 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) * sqrt(0.5-cosext2) / |
| (1.0 + sqrt(cosext2+0.5))); |
| // if clockwise, we need to negate cv. |
| if (rev) { // rev is equivalent to isCW(omx, omy, mx, my) |
| cv = -cv; |
| } |
| final float x1 = cx + omx; |
| final float y1 = cy + omy; |
| final float x2 = x1 - cv * omy; |
| final float y2 = y1 + cv * omx; |
| |
| final float x4 = cx + mx; |
| final float y4 = cy + my; |
| final float x3 = x4 + cv * my; |
| final float y3 = y4 - cv * mx; |
| |
| emitCurveTo(x1, y1, x2, y2, x3, y3, x4, y4, rev); |
| } |
| |
| private void drawRoundCap(float cx, float cy, float mx, float my) { |
| final float C = 0.5522847498307933f; |
| // the first and second arguments of the following two calls |
| // are really will be ignored by emitCurveTo (because of the false), |
| // but we put them in anyway, as opposed to just giving it 4 zeroes, |
| // because it's just 4 additions and it's not good to rely on this |
| // sort of assumption (right now it's true, but that may change). |
| emitCurveTo(cx+mx, cy+my, |
| cx+mx-C*my, cy+my+C*mx, |
| cx-my+C*mx, cy+mx+C*my, |
| cx-my, cy+mx, |
| false); |
| emitCurveTo(cx-my, cy+mx, |
| cx-my-C*mx, cy+mx-C*my, |
| cx-mx-C*my, cy-my+C*mx, |
| cx-mx, cy-my, |
| false); |
| } |
| |
| // Put the intersection point of the lines (x0, y0) -> (x1, y1) |
| // and (x0p, y0p) -> (x1p, y1p) in m[off] and m[off+1]. |
| // If the lines are parallel, it will put a non finite number in m. |
| private void computeIntersection(final float x0, final float y0, |
| final float x1, final float y1, |
| final float x0p, final float y0p, |
| final float x1p, final float y1p, |
| final float[] m, int off) |
| { |
| float x10 = x1 - x0; |
| float y10 = y1 - y0; |
| float x10p = x1p - x0p; |
| float y10p = y1p - y0p; |
| |
| float den = x10*y10p - x10p*y10; |
| float t = x10p*(y0-y0p) - y10p*(x0-x0p); |
| t /= den; |
| m[off++] = x0 + t*x10; |
| m[off] = y0 + t*y10; |
| } |
| |
| private void drawMiter(final float pdx, final float pdy, |
| final float x0, final float y0, |
| final float dx, final float dy, |
| float omx, float omy, float mx, float my, |
| boolean rev) |
| { |
| if ((mx == omx && my == omy) || |
| (pdx == 0 && pdy == 0) || |
| (dx == 0 && dy == 0)) |
| { |
| return; |
| } |
| |
| if (rev) { |
| omx = -omx; |
| omy = -omy; |
| mx = -mx; |
| my = -my; |
| } |
| |
| computeIntersection((x0 - pdx) + omx, (y0 - pdy) + omy, x0 + omx, y0 + omy, |
| (dx + x0) + mx, (dy + y0) + my, x0 + mx, y0 + my, |
| miter, 0); |
| |
| float lenSq = (miter[0]-x0)*(miter[0]-x0) + (miter[1]-y0)*(miter[1]-y0); |
| |
| // If the lines are parallel, lenSq will be either NaN or +inf |
| // (actually, I'm not sure if the latter is possible. The important |
| // thing is that -inf is not possible, because lenSq is a square). |
| // For both of those values, the comparison below will fail and |
| // no miter will be drawn, which is correct. |
| if (lenSq < miterLimitSq) { |
| emitLineTo(miter[0], miter[1], rev); |
| } |
| } |
| |
| public void moveTo(float x0, float y0) { |
| if (prev == DRAWING_OP_TO) { |
| finish(); |
| } |
| this.sx0 = this.cx0 = x0; |
| this.sy0 = this.cy0 = y0; |
| this.cdx = this.sdx = 1; |
| this.cdy = this.sdy = 0; |
| this.prev = MOVE_TO; |
| } |
| |
| public void lineTo(float x1, float y1) { |
| float dx = x1 - cx0; |
| float dy = y1 - cy0; |
| if (dx == 0f && dy == 0f) { |
| dx = 1; |
| } |
| computeOffset(dx, dy, lineWidth2, offset[0]); |
| float mx = offset[0][0]; |
| float my = offset[0][1]; |
| |
| drawJoin(cdx, cdy, cx0, cy0, dx, dy, cmx, cmy, mx, my); |
| |
| emitLineTo(cx0 + mx, cy0 + my); |
| emitLineTo(x1 + mx, y1 + my); |
| |
| emitLineTo(cx0 - mx, cy0 - my, true); |
| emitLineTo(x1 - mx, y1 - my, true); |
| |
| this.cmx = mx; |
| this.cmy = my; |
| this.cdx = dx; |
| this.cdy = dy; |
| this.cx0 = x1; |
| this.cy0 = y1; |
| this.prev = DRAWING_OP_TO; |
| } |
| |
| public void closePath() { |
| if (prev != DRAWING_OP_TO) { |
| if (prev == CLOSE) { |
| return; |
| } |
| emitMoveTo(cx0, cy0 - lineWidth2); |
| this.cmx = this.smx = 0; |
| this.cmy = this.smy = -lineWidth2; |
| this.cdx = this.sdx = 1; |
| this.cdy = this.sdy = 0; |
| finish(); |
| return; |
| } |
| |
| if (cx0 != sx0 || cy0 != sy0) { |
| lineTo(sx0, sy0); |
| } |
| |
| drawJoin(cdx, cdy, cx0, cy0, sdx, sdy, cmx, cmy, smx, smy); |
| |
| emitLineTo(sx0 + smx, sy0 + smy); |
| |
| emitMoveTo(sx0 - smx, sy0 - smy); |
| emitReverse(); |
| |
| this.prev = CLOSE; |
| emitClose(); |
| } |
| |
| private void emitReverse() { |
| while(!reverse.isEmpty()) { |
| reverse.pop(out); |
| } |
| } |
| |
| public void pathDone() { |
| if (prev == DRAWING_OP_TO) { |
| finish(); |
| } |
| |
| out.pathDone(); |
| // this shouldn't matter since this object won't be used |
| // after the call to this method. |
| this.prev = CLOSE; |
| } |
| |
| private void finish() { |
| if (capStyle == CAP_ROUND) { |
| drawRoundCap(cx0, cy0, cmx, cmy); |
| } else if (capStyle == CAP_SQUARE) { |
| emitLineTo(cx0 - cmy + cmx, cy0 + cmx + cmy); |
| emitLineTo(cx0 - cmy - cmx, cy0 + cmx - cmy); |
| } |
| |
| emitReverse(); |
| |
| if (capStyle == CAP_ROUND) { |
| drawRoundCap(sx0, sy0, -smx, -smy); |
| } else if (capStyle == CAP_SQUARE) { |
| emitLineTo(sx0 + smy - smx, sy0 - smx - smy); |
| emitLineTo(sx0 + smy + smx, sy0 - smx + smy); |
| } |
| |
| emitClose(); |
| } |
| |
| private void emitMoveTo(final float x0, final float y0) { |
| out.moveTo(x0, y0); |
| } |
| |
| private void emitLineTo(final float x1, final float y1) { |
| out.lineTo(x1, y1); |
| } |
| |
| private void emitLineTo(final float x1, final float y1, |
| final boolean rev) |
| { |
| if (rev) { |
| reverse.pushLine(x1, y1); |
| } else { |
| emitLineTo(x1, y1); |
| } |
| } |
| |
| private void emitQuadTo(final float x0, final float y0, |
| final float x1, final float y1, |
| final float x2, final float y2, final boolean rev) |
| { |
| if (rev) { |
| reverse.pushQuad(x0, y0, x1, y1); |
| } else { |
| out.quadTo(x1, y1, x2, y2); |
| } |
| } |
| |
| private void emitCurveTo(final float x0, final float y0, |
| final float x1, final float y1, |
| final float x2, final float y2, |
| final float x3, final float y3, final boolean rev) |
| { |
| if (rev) { |
| reverse.pushCubic(x0, y0, x1, y1, x2, y2); |
| } else { |
| out.curveTo(x1, y1, x2, y2, x3, y3); |
| } |
| } |
| |
| private void emitClose() { |
| out.closePath(); |
| } |
| |
| private void drawJoin(float pdx, float pdy, |
| float x0, float y0, |
| float dx, float dy, |
| float omx, float omy, |
| float mx, float my) |
| { |
| if (prev != DRAWING_OP_TO) { |
| emitMoveTo(x0 + mx, y0 + my); |
| this.sdx = dx; |
| this.sdy = dy; |
| this.smx = mx; |
| this.smy = my; |
| } else { |
| boolean cw = isCW(pdx, pdy, dx, dy); |
| if (joinStyle == JOIN_MITER) { |
| drawMiter(pdx, pdy, x0, y0, dx, dy, omx, omy, mx, my, cw); |
| } else if (joinStyle == JOIN_ROUND) { |
| drawRoundJoin(x0, y0, |
| omx, omy, |
| mx, my, cw, |
| ROUND_JOIN_THRESHOLD); |
| } |
| emitLineTo(x0, y0, !cw); |
| } |
| prev = DRAWING_OP_TO; |
| } |
| |
| private static boolean within(final float x1, final float y1, |
| final float x2, final float y2, |
| final float ERR) |
| { |
| assert ERR > 0 : ""; |
| // compare taxicab distance. ERR will always be small, so using |
| // true distance won't give much benefit |
| return (Helpers.within(x1, x2, ERR) && // we want to avoid calling Math.abs |
| Helpers.within(y1, y2, ERR)); // this is just as good. |
| } |
| |
| private void getLineOffsets(float x1, float y1, |
| float x2, float y2, |
| float[] left, float[] right) { |
| computeOffset(x2 - x1, y2 - y1, lineWidth2, offset[0]); |
| left[0] = x1 + offset[0][0]; |
| left[1] = y1 + offset[0][1]; |
| left[2] = x2 + offset[0][0]; |
| left[3] = y2 + offset[0][1]; |
| right[0] = x1 - offset[0][0]; |
| right[1] = y1 - offset[0][1]; |
| right[2] = x2 - offset[0][0]; |
| right[3] = y2 - offset[0][1]; |
| } |
| |
| private int computeOffsetCubic(float[] pts, final int off, |
| float[] leftOff, float[] rightOff) |
| { |
| // if p1=p2 or p3=p4 it means that the derivative at the endpoint |
| // vanishes, which creates problems with computeOffset. Usually |
| // this happens when this stroker object is trying to winden |
| // a curve with a cusp. What happens is that curveTo splits |
| // the input curve at the cusp, and passes it to this function. |
| // because of inaccuracies in the splitting, we consider points |
| // equal if they're very close to each other. |
| final float x1 = pts[off + 0], y1 = pts[off + 1]; |
| final float x2 = pts[off + 2], y2 = pts[off + 3]; |
| final float x3 = pts[off + 4], y3 = pts[off + 5]; |
| final float x4 = pts[off + 6], y4 = pts[off + 7]; |
| |
| float dx4 = x4 - x3; |
| float dy4 = y4 - y3; |
| float dx1 = x2 - x1; |
| float dy1 = y2 - y1; |
| |
| // if p1 == p2 && p3 == p4: draw line from p1->p4, unless p1 == p4, |
| // in which case ignore if p1 == p2 |
| final boolean p1eqp2 = within(x1,y1,x2,y2, 6 * ulp(y2)); |
| final boolean p3eqp4 = within(x3,y3,x4,y4, 6 * ulp(y4)); |
| if (p1eqp2 && p3eqp4) { |
| getLineOffsets(x1, y1, x4, y4, leftOff, rightOff); |
| return 4; |
| } else if (p1eqp2) { |
| dx1 = x3 - x1; |
| dy1 = y3 - y1; |
| } else if (p3eqp4) { |
| dx4 = x4 - x2; |
| dy4 = y4 - y2; |
| } |
| |
| // if p2-p1 and p4-p3 are parallel, that must mean this curve is a line |
| float dotsq = (dx1 * dx4 + dy1 * dy4); |
| dotsq = dotsq * dotsq; |
| float l1sq = dx1 * dx1 + dy1 * dy1, l4sq = dx4 * dx4 + dy4 * dy4; |
| if (Helpers.within(dotsq, l1sq * l4sq, 4 * ulp(dotsq))) { |
| getLineOffsets(x1, y1, x4, y4, leftOff, rightOff); |
| return 4; |
| } |
| |
| // What we're trying to do in this function is to approximate an ideal |
| // offset curve (call it I) of the input curve B using a bezier curve Bp. |
| // The constraints I use to get the equations are: |
| // |
| // 1. The computed curve Bp should go through I(0) and I(1). These are |
| // x1p, y1p, x4p, y4p, which are p1p and p4p. We still need to find |
| // 4 variables: the x and y components of p2p and p3p (i.e. x2p, y2p, x3p, y3p). |
| // |
| // 2. Bp should have slope equal in absolute value to I at the endpoints. So, |
| // (by the way, the operator || in the comments below means "aligned with". |
| // It is defined on vectors, so when we say I'(0) || Bp'(0) we mean that |
| // vectors I'(0) and Bp'(0) are aligned, which is the same as saying |
| // that the tangent lines of I and Bp at 0 are parallel. Mathematically |
| // this means (I'(t) || Bp'(t)) <==> (I'(t) = c * Bp'(t)) where c is some |
| // nonzero constant.) |
| // I'(0) || Bp'(0) and I'(1) || Bp'(1). Obviously, I'(0) || B'(0) and |
| // I'(1) || B'(1); therefore, Bp'(0) || B'(0) and Bp'(1) || B'(1). |
| // We know that Bp'(0) || (p2p-p1p) and Bp'(1) || (p4p-p3p) and the same |
| // is true for any bezier curve; therefore, we get the equations |
| // (1) p2p = c1 * (p2-p1) + p1p |
| // (2) p3p = c2 * (p4-p3) + p4p |
| // We know p1p, p4p, p2, p1, p3, and p4; therefore, this reduces the number |
| // of unknowns from 4 to 2 (i.e. just c1 and c2). |
| // To eliminate these 2 unknowns we use the following constraint: |
| // |
| // 3. Bp(0.5) == I(0.5). Bp(0.5)=(x,y) and I(0.5)=(xi,yi), and I should note |
| // that I(0.5) is *the only* reason for computing dxm,dym. This gives us |
| // (3) Bp(0.5) = (p1p + 3 * (p2p + p3p) + p4p)/8, which is equivalent to |
| // (4) p2p + p3p = (Bp(0.5)*8 - p1p - p4p) / 3 |
| // We can substitute (1) and (2) from above into (4) and we get: |
| // (5) c1*(p2-p1) + c2*(p4-p3) = (Bp(0.5)*8 - p1p - p4p)/3 - p1p - p4p |
| // which is equivalent to |
| // (6) c1*(p2-p1) + c2*(p4-p3) = (4/3) * (Bp(0.5) * 2 - p1p - p4p) |
| // |
| // The right side of this is a 2D vector, and we know I(0.5), which gives us |
| // Bp(0.5), which gives us the value of the right side. |
| // The left side is just a matrix vector multiplication in disguise. It is |
| // |
| // [x2-x1, x4-x3][c1] |
| // [y2-y1, y4-y3][c2] |
| // which, is equal to |
| // [dx1, dx4][c1] |
| // [dy1, dy4][c2] |
| // At this point we are left with a simple linear system and we solve it by |
| // getting the inverse of the matrix above. Then we use [c1,c2] to compute |
| // p2p and p3p. |
| |
| float x = 0.125f * (x1 + 3 * (x2 + x3) + x4); |
| float y = 0.125f * (y1 + 3 * (y2 + y3) + y4); |
| // (dxm,dym) is some tangent of B at t=0.5. This means it's equal to |
| // c*B'(0.5) for some constant c. |
| float dxm = x3 + x4 - x1 - x2, dym = y3 + y4 - y1 - y2; |
| |
| // this computes the offsets at t=0, 0.5, 1, using the property that |
| // for any bezier curve the vectors p2-p1 and p4-p3 are parallel to |
| // the (dx/dt, dy/dt) vectors at the endpoints. |
| computeOffset(dx1, dy1, lineWidth2, offset[0]); |
| computeOffset(dxm, dym, lineWidth2, offset[1]); |
| computeOffset(dx4, dy4, lineWidth2, offset[2]); |
| float x1p = x1 + offset[0][0]; // start |
| float y1p = y1 + offset[0][1]; // point |
| float xi = x + offset[1][0]; // interpolation |
| float yi = y + offset[1][1]; // point |
| float x4p = x4 + offset[2][0]; // end |
| float y4p = y4 + offset[2][1]; // point |
| |
| float invdet43 = 4f / (3f * (dx1 * dy4 - dy1 * dx4)); |
| |
| float two_pi_m_p1_m_p4x = 2*xi - x1p - x4p; |
| float two_pi_m_p1_m_p4y = 2*yi - y1p - y4p; |
| float c1 = invdet43 * (dy4 * two_pi_m_p1_m_p4x - dx4 * two_pi_m_p1_m_p4y); |
| float c2 = invdet43 * (dx1 * two_pi_m_p1_m_p4y - dy1 * two_pi_m_p1_m_p4x); |
| |
| float x2p, y2p, x3p, y3p; |
| x2p = x1p + c1*dx1; |
| y2p = y1p + c1*dy1; |
| x3p = x4p + c2*dx4; |
| y3p = y4p + c2*dy4; |
| |
| leftOff[0] = x1p; leftOff[1] = y1p; |
| leftOff[2] = x2p; leftOff[3] = y2p; |
| leftOff[4] = x3p; leftOff[5] = y3p; |
| leftOff[6] = x4p; leftOff[7] = y4p; |
| |
| x1p = x1 - offset[0][0]; y1p = y1 - offset[0][1]; |
| xi = xi - 2 * offset[1][0]; yi = yi - 2 * offset[1][1]; |
| x4p = x4 - offset[2][0]; y4p = y4 - offset[2][1]; |
| |
| two_pi_m_p1_m_p4x = 2*xi - x1p - x4p; |
| two_pi_m_p1_m_p4y = 2*yi - y1p - y4p; |
| c1 = invdet43 * (dy4 * two_pi_m_p1_m_p4x - dx4 * two_pi_m_p1_m_p4y); |
| c2 = invdet43 * (dx1 * two_pi_m_p1_m_p4y - dy1 * two_pi_m_p1_m_p4x); |
| |
| x2p = x1p + c1*dx1; |
| y2p = y1p + c1*dy1; |
| x3p = x4p + c2*dx4; |
| y3p = y4p + c2*dy4; |
| |
| rightOff[0] = x1p; rightOff[1] = y1p; |
| rightOff[2] = x2p; rightOff[3] = y2p; |
| rightOff[4] = x3p; rightOff[5] = y3p; |
| rightOff[6] = x4p; rightOff[7] = y4p; |
| return 8; |
| } |
| |
| // return the kind of curve in the right and left arrays. |
| private int computeOffsetQuad(float[] pts, final int off, |
| float[] leftOff, float[] rightOff) |
| { |
| final float x1 = pts[off + 0], y1 = pts[off + 1]; |
| final float x2 = pts[off + 2], y2 = pts[off + 3]; |
| final float x3 = pts[off + 4], y3 = pts[off + 5]; |
| |
| final float dx3 = x3 - x2; |
| final float dy3 = y3 - y2; |
| final float dx1 = x2 - x1; |
| final float dy1 = y2 - y1; |
| |
| // this computes the offsets at t = 0, 1 |
| computeOffset(dx1, dy1, lineWidth2, offset[0]); |
| computeOffset(dx3, dy3, lineWidth2, offset[1]); |
| |
| leftOff[0] = x1 + offset[0][0]; leftOff[1] = y1 + offset[0][1]; |
| leftOff[4] = x3 + offset[1][0]; leftOff[5] = y3 + offset[1][1]; |
| rightOff[0] = x1 - offset[0][0]; rightOff[1] = y1 - offset[0][1]; |
| rightOff[4] = x3 - offset[1][0]; rightOff[5] = y3 - offset[1][1]; |
| |
| float x1p = leftOff[0]; // start |
| float y1p = leftOff[1]; // point |
| float x3p = leftOff[4]; // end |
| float y3p = leftOff[5]; // point |
| |
| // Corner cases: |
| // 1. If the two control vectors are parallel, we'll end up with NaN's |
| // in leftOff (and rightOff in the body of the if below), so we'll |
| // do getLineOffsets, which is right. |
| // 2. If the first or second two points are equal, then (dx1,dy1)==(0,0) |
| // or (dx3,dy3)==(0,0), so (x1p, y1p)==(x1p+dx1, y1p+dy1) |
| // or (x3p, y3p)==(x3p-dx3, y3p-dy3), which means that |
| // computeIntersection will put NaN's in leftOff and right off, and |
| // we will do getLineOffsets, which is right. |
| computeIntersection(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, leftOff, 2); |
| float cx = leftOff[2]; |
| float cy = leftOff[3]; |
| |
| if (!(isFinite(cx) && isFinite(cy))) { |
| // maybe the right path is not degenerate. |
| x1p = rightOff[0]; |
| y1p = rightOff[1]; |
| x3p = rightOff[4]; |
| y3p = rightOff[5]; |
| computeIntersection(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, rightOff, 2); |
| cx = rightOff[2]; |
| cy = rightOff[3]; |
| if (!(isFinite(cx) && isFinite(cy))) { |
| // both are degenerate. This curve is a line. |
| getLineOffsets(x1, y1, x3, y3, leftOff, rightOff); |
| return 4; |
| } |
| // {left,right}Off[0,1,4,5] are already set to the correct values. |
| leftOff[2] = 2*x2 - cx; |
| leftOff[3] = 2*y2 - cy; |
| return 6; |
| } |
| |
| // rightOff[2,3] = (x2,y2) - ((left_x2, left_y2) - (x2, y2)) |
| // == 2*(x2, y2) - (left_x2, left_y2) |
| rightOff[2] = 2*x2 - cx; |
| rightOff[3] = 2*y2 - cy; |
| return 6; |
| } |
| |
| private static boolean isFinite(float x) { |
| return (Float.NEGATIVE_INFINITY < x && x < Float.POSITIVE_INFINITY); |
| } |
| |
| // This is where the curve to be processed is put. We give it |
| // enough room to store 2 curves: one for the current subdivision, the |
| // other for the rest of the curve. |
| private float[] middle = new float[2*8]; |
| private float[] lp = new float[8]; |
| private float[] rp = new float[8]; |
| private static final int MAX_N_CURVES = 11; |
| private float[] subdivTs = new float[MAX_N_CURVES - 1]; |
| |
| // If this class is compiled with ecj, then Hotspot crashes when OSR |
| // compiling this function. See bugs 7004570 and 6675699 |
| // TODO: until those are fixed, we should work around that by |
| // manually inlining this into curveTo and quadTo. |
| /******************************* WORKAROUND ********************************** |
| private void somethingTo(final int type) { |
| // need these so we can update the state at the end of this method |
| final float xf = middle[type-2], yf = middle[type-1]; |
| float dxs = middle[2] - middle[0]; |
| float dys = middle[3] - middle[1]; |
| float dxf = middle[type - 2] - middle[type - 4]; |
| float dyf = middle[type - 1] - middle[type - 3]; |
| switch(type) { |
| case 6: |
| if ((dxs == 0f && dys == 0f) || |
| (dxf == 0f && dyf == 0f)) { |
| dxs = dxf = middle[4] - middle[0]; |
| dys = dyf = middle[5] - middle[1]; |
| } |
| break; |
| case 8: |
| boolean p1eqp2 = (dxs == 0f && dys == 0f); |
| boolean p3eqp4 = (dxf == 0f && dyf == 0f); |
| if (p1eqp2) { |
| dxs = middle[4] - middle[0]; |
| dys = middle[5] - middle[1]; |
| if (dxs == 0f && dys == 0f) { |
| dxs = middle[6] - middle[0]; |
| dys = middle[7] - middle[1]; |
| } |
| } |
| if (p3eqp4) { |
| dxf = middle[6] - middle[2]; |
| dyf = middle[7] - middle[3]; |
| if (dxf == 0f && dyf == 0f) { |
| dxf = middle[6] - middle[0]; |
| dyf = middle[7] - middle[1]; |
| } |
| } |
| } |
| if (dxs == 0f && dys == 0f) { |
| // this happens iff the "curve" is just a point |
| lineTo(middle[0], middle[1]); |
| return; |
| } |
| // if these vectors are too small, normalize them, to avoid future |
| // precision problems. |
| if (Math.abs(dxs) < 0.1f && Math.abs(dys) < 0.1f) { |
| float len = (float) sqrt(dxs*dxs + dys*dys); |
| dxs /= len; |
| dys /= len; |
| } |
| if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { |
| float len = (float) sqrt(dxf*dxf + dyf*dyf); |
| dxf /= len; |
| dyf /= len; |
| } |
| |
| computeOffset(dxs, dys, lineWidth2, offset[0]); |
| final float mx = offset[0][0]; |
| final float my = offset[0][1]; |
| drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, mx, my); |
| |
| int nSplits = findSubdivPoints(middle, subdivTs, type, lineWidth2); |
| |
| int kind = 0; |
| Iterator<Integer> it = Curve.breakPtsAtTs(middle, type, subdivTs, nSplits); |
| while(it.hasNext()) { |
| int curCurveOff = it.next(); |
| |
| switch (type) { |
| case 8: |
| kind = computeOffsetCubic(middle, curCurveOff, lp, rp); |
| break; |
| case 6: |
| kind = computeOffsetQuad(middle, curCurveOff, lp, rp); |
| break; |
| } |
| emitLineTo(lp[0], lp[1]); |
| switch(kind) { |
| case 8: |
| emitCurveTo(lp[0], lp[1], lp[2], lp[3], lp[4], lp[5], lp[6], lp[7], false); |
| emitCurveTo(rp[0], rp[1], rp[2], rp[3], rp[4], rp[5], rp[6], rp[7], true); |
| break; |
| case 6: |
| emitQuadTo(lp[0], lp[1], lp[2], lp[3], lp[4], lp[5], false); |
| emitQuadTo(rp[0], rp[1], rp[2], rp[3], rp[4], rp[5], true); |
| break; |
| case 4: |
| emitLineTo(lp[2], lp[3]); |
| emitLineTo(rp[0], rp[1], true); |
| break; |
| } |
| emitLineTo(rp[kind - 2], rp[kind - 1], true); |
| } |
| |
| this.cmx = (lp[kind - 2] - rp[kind - 2]) / 2; |
| this.cmy = (lp[kind - 1] - rp[kind - 1]) / 2; |
| this.cdx = dxf; |
| this.cdy = dyf; |
| this.cx0 = xf; |
| this.cy0 = yf; |
| this.prev = DRAWING_OP_TO; |
| } |
| ****************************** END WORKAROUND *******************************/ |
| |
| // finds values of t where the curve in pts should be subdivided in order |
| // to get good offset curves a distance of w away from the middle curve. |
| // Stores the points in ts, and returns how many of them there were. |
| private static Curve c = new Curve(); |
| private static int findSubdivPoints(float[] pts, float[] ts, final int type, final float w) |
| { |
| final float x12 = pts[2] - pts[0]; |
| final float y12 = pts[3] - pts[1]; |
| // if the curve is already parallel to either axis we gain nothing |
| // from rotating it. |
| if (y12 != 0f && x12 != 0f) { |
| // we rotate it so that the first vector in the control polygon is |
| // parallel to the x-axis. This will ensure that rotated quarter |
| // circles won't be subdivided. |
| final float hypot = (float) sqrt(x12 * x12 + y12 * y12); |
| final float cos = x12 / hypot; |
| final float sin = y12 / hypot; |
| final float x1 = cos * pts[0] + sin * pts[1]; |
| final float y1 = cos * pts[1] - sin * pts[0]; |
| final float x2 = cos * pts[2] + sin * pts[3]; |
| final float y2 = cos * pts[3] - sin * pts[2]; |
| final float x3 = cos * pts[4] + sin * pts[5]; |
| final float y3 = cos * pts[5] - sin * pts[4]; |
| switch(type) { |
| case 8: |
| final float x4 = cos * pts[6] + sin * pts[7]; |
| final float y4 = cos * pts[7] - sin * pts[6]; |
| c.set(x1, y1, x2, y2, x3, y3, x4, y4); |
| break; |
| case 6: |
| c.set(x1, y1, x2, y2, x3, y3); |
| break; |
| } |
| } else { |
| c.set(pts, type); |
| } |
| |
| int ret = 0; |
| // we subdivide at values of t such that the remaining rotated |
| // curves are monotonic in x and y. |
| ret += c.dxRoots(ts, ret); |
| ret += c.dyRoots(ts, ret); |
| // subdivide at inflection points. |
| if (type == 8) { |
| // quadratic curves can't have inflection points |
| ret += c.infPoints(ts, ret); |
| } |
| |
| // now we must subdivide at points where one of the offset curves will have |
| // a cusp. This happens at ts where the radius of curvature is equal to w. |
| ret += c.rootsOfROCMinusW(ts, ret, w, 0.0001f); |
| |
| ret = Helpers.filterOutNotInAB(ts, 0, ret, 0.0001f, 0.9999f); |
| Helpers.isort(ts, 0, ret); |
| return ret; |
| } |
| |
| @Override public void curveTo(float x1, float y1, |
| float x2, float y2, |
| float x3, float y3) |
| { |
| middle[0] = cx0; middle[1] = cy0; |
| middle[2] = x1; middle[3] = y1; |
| middle[4] = x2; middle[5] = y2; |
| middle[6] = x3; middle[7] = y3; |
| |
| // inlined version of somethingTo(8); |
| // See the TODO on somethingTo |
| |
| // need these so we can update the state at the end of this method |
| final float xf = middle[6], yf = middle[7]; |
| float dxs = middle[2] - middle[0]; |
| float dys = middle[3] - middle[1]; |
| float dxf = middle[6] - middle[4]; |
| float dyf = middle[7] - middle[5]; |
| |
| boolean p1eqp2 = (dxs == 0f && dys == 0f); |
| boolean p3eqp4 = (dxf == 0f && dyf == 0f); |
| if (p1eqp2) { |
| dxs = middle[4] - middle[0]; |
| dys = middle[5] - middle[1]; |
| if (dxs == 0f && dys == 0f) { |
| dxs = middle[6] - middle[0]; |
| dys = middle[7] - middle[1]; |
| } |
| } |
| if (p3eqp4) { |
| dxf = middle[6] - middle[2]; |
| dyf = middle[7] - middle[3]; |
| if (dxf == 0f && dyf == 0f) { |
| dxf = middle[6] - middle[0]; |
| dyf = middle[7] - middle[1]; |
| } |
| } |
| if (dxs == 0f && dys == 0f) { |
| // this happens iff the "curve" is just a point |
| lineTo(middle[0], middle[1]); |
| return; |
| } |
| |
| // if these vectors are too small, normalize them, to avoid future |
| // precision problems. |
| if (Math.abs(dxs) < 0.1f && Math.abs(dys) < 0.1f) { |
| float len = (float) sqrt(dxs*dxs + dys*dys); |
| dxs /= len; |
| dys /= len; |
| } |
| if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { |
| float len = (float) sqrt(dxf*dxf + dyf*dyf); |
| dxf /= len; |
| dyf /= len; |
| } |
| |
| computeOffset(dxs, dys, lineWidth2, offset[0]); |
| final float mx = offset[0][0]; |
| final float my = offset[0][1]; |
| drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, mx, my); |
| |
| int nSplits = findSubdivPoints(middle, subdivTs, 8, lineWidth2); |
| |
| int kind = 0; |
| Iterator<Integer> it = Curve.breakPtsAtTs(middle, 8, subdivTs, nSplits); |
| while(it.hasNext()) { |
| int curCurveOff = it.next(); |
| |
| kind = computeOffsetCubic(middle, curCurveOff, lp, rp); |
| emitLineTo(lp[0], lp[1]); |
| switch(kind) { |
| case 8: |
| emitCurveTo(lp[0], lp[1], lp[2], lp[3], lp[4], lp[5], lp[6], lp[7], false); |
| emitCurveTo(rp[0], rp[1], rp[2], rp[3], rp[4], rp[5], rp[6], rp[7], true); |
| break; |
| case 4: |
| emitLineTo(lp[2], lp[3]); |
| emitLineTo(rp[0], rp[1], true); |
| break; |
| } |
| emitLineTo(rp[kind - 2], rp[kind - 1], true); |
| } |
| |
| this.cmx = (lp[kind - 2] - rp[kind - 2]) / 2; |
| this.cmy = (lp[kind - 1] - rp[kind - 1]) / 2; |
| this.cdx = dxf; |
| this.cdy = dyf; |
| this.cx0 = xf; |
| this.cy0 = yf; |
| this.prev = DRAWING_OP_TO; |
| } |
| |
| @Override public void quadTo(float x1, float y1, float x2, float y2) { |
| middle[0] = cx0; middle[1] = cy0; |
| middle[2] = x1; middle[3] = y1; |
| middle[4] = x2; middle[5] = y2; |
| |
| // inlined version of somethingTo(8); |
| // See the TODO on somethingTo |
| |
| // need these so we can update the state at the end of this method |
| final float xf = middle[4], yf = middle[5]; |
| float dxs = middle[2] - middle[0]; |
| float dys = middle[3] - middle[1]; |
| float dxf = middle[4] - middle[2]; |
| float dyf = middle[5] - middle[3]; |
| if ((dxs == 0f && dys == 0f) || (dxf == 0f && dyf == 0f)) { |
| dxs = dxf = middle[4] - middle[0]; |
| dys = dyf = middle[5] - middle[1]; |
| } |
| if (dxs == 0f && dys == 0f) { |
| // this happens iff the "curve" is just a point |
| lineTo(middle[0], middle[1]); |
| return; |
| } |
| // if these vectors are too small, normalize them, to avoid future |
| // precision problems. |
| if (Math.abs(dxs) < 0.1f && Math.abs(dys) < 0.1f) { |
| float len = (float) sqrt(dxs*dxs + dys*dys); |
| dxs /= len; |
| dys /= len; |
| } |
| if (Math.abs(dxf) < 0.1f && Math.abs(dyf) < 0.1f) { |
| float len = (float) sqrt(dxf*dxf + dyf*dyf); |
| dxf /= len; |
| dyf /= len; |
| } |
| |
| computeOffset(dxs, dys, lineWidth2, offset[0]); |
| final float mx = offset[0][0]; |
| final float my = offset[0][1]; |
| drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, mx, my); |
| |
| int nSplits = findSubdivPoints(middle, subdivTs, 6, lineWidth2); |
| |
| int kind = 0; |
| Iterator<Integer> it = Curve.breakPtsAtTs(middle, 6, subdivTs, nSplits); |
| while(it.hasNext()) { |
| int curCurveOff = it.next(); |
| |
| kind = computeOffsetQuad(middle, curCurveOff, lp, rp); |
| emitLineTo(lp[0], lp[1]); |
| switch(kind) { |
| case 6: |
| emitQuadTo(lp[0], lp[1], lp[2], lp[3], lp[4], lp[5], false); |
| emitQuadTo(rp[0], rp[1], rp[2], rp[3], rp[4], rp[5], true); |
| break; |
| case 4: |
| emitLineTo(lp[2], lp[3]); |
| emitLineTo(rp[0], rp[1], true); |
| break; |
| } |
| emitLineTo(rp[kind - 2], rp[kind - 1], true); |
| } |
| |
| this.cmx = (lp[kind - 2] - rp[kind - 2]) / 2; |
| this.cmy = (lp[kind - 1] - rp[kind - 1]) / 2; |
| this.cdx = dxf; |
| this.cdy = dyf; |
| this.cx0 = xf; |
| this.cy0 = yf; |
| this.prev = DRAWING_OP_TO; |
| } |
| |
| @Override public long getNativeConsumer() { |
| throw new InternalError("Stroker doesn't use a native consumer"); |
| } |
| |
| // a stack of polynomial curves where each curve shares endpoints with |
| // adjacent ones. |
| private static final class PolyStack { |
| float[] curves; |
| int end; |
| int[] curveTypes; |
| int numCurves; |
| |
| private static final int INIT_SIZE = 50; |
| |
| PolyStack() { |
| curves = new float[8 * INIT_SIZE]; |
| curveTypes = new int[INIT_SIZE]; |
| end = 0; |
| numCurves = 0; |
| } |
| |
| public boolean isEmpty() { |
| return numCurves == 0; |
| } |
| |
| private void ensureSpace(int n) { |
| if (end + n >= curves.length) { |
| int newSize = (end + n) * 2; |
| curves = Arrays.copyOf(curves, newSize); |
| } |
| if (numCurves >= curveTypes.length) { |
| int newSize = numCurves * 2; |
| curveTypes = Arrays.copyOf(curveTypes, newSize); |
| } |
| } |
| |
| public void pushCubic(float x0, float y0, |
| float x1, float y1, |
| float x2, float y2) |
| { |
| ensureSpace(6); |
| curveTypes[numCurves++] = 8; |
| // assert(x0 == lastX && y0 == lastY) |
| |
| // we reverse the coordinate order to make popping easier |
| curves[end++] = x2; curves[end++] = y2; |
| curves[end++] = x1; curves[end++] = y1; |
| curves[end++] = x0; curves[end++] = y0; |
| } |
| |
| public void pushQuad(float x0, float y0, |
| float x1, float y1) |
| { |
| ensureSpace(4); |
| curveTypes[numCurves++] = 6; |
| // assert(x0 == lastX && y0 == lastY) |
| curves[end++] = x1; curves[end++] = y1; |
| curves[end++] = x0; curves[end++] = y0; |
| } |
| |
| public void pushLine(float x, float y) { |
| ensureSpace(2); |
| curveTypes[numCurves++] = 4; |
| // assert(x0 == lastX && y0 == lastY) |
| curves[end++] = x; curves[end++] = y; |
| } |
| |
| @SuppressWarnings("unused") |
| public int pop(float[] pts) { |
| int ret = curveTypes[numCurves - 1]; |
| numCurves--; |
| end -= (ret - 2); |
| System.arraycopy(curves, end, pts, 0, ret - 2); |
| return ret; |
| } |
| |
| public void pop(PathConsumer2D io) { |
| numCurves--; |
| int type = curveTypes[numCurves]; |
| end -= (type - 2); |
| switch(type) { |
| case 8: |
| io.curveTo(curves[end+0], curves[end+1], |
| curves[end+2], curves[end+3], |
| curves[end+4], curves[end+5]); |
| break; |
| case 6: |
| io.quadTo(curves[end+0], curves[end+1], |
| curves[end+2], curves[end+3]); |
| break; |
| case 4: |
| io.lineTo(curves[end], curves[end+1]); |
| } |
| } |
| |
| @Override |
| public String toString() { |
| String ret = ""; |
| int nc = numCurves; |
| int end = this.end; |
| while (nc > 0) { |
| nc--; |
| int type = curveTypes[numCurves]; |
| end -= (type - 2); |
| switch(type) { |
| case 8: |
| ret += "cubic: "; |
| break; |
| case 6: |
| ret += "quad: "; |
| break; |
| case 4: |
| ret += "line: "; |
| break; |
| } |
| ret += Arrays.toString(Arrays.copyOfRange(curves, end, end+type-2)) + "\n"; |
| } |
| return ret; |
| } |
| } |
| } |