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/*
* Copyright (c) 2007, 2013, 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
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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.
*/
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 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.
*
* @param pc2d an output PathConsumer2D.
* @param lineWidth the desired line width in pixels
* @param capStyle the desired end cap style, one of
* CAP_BUTT, CAP_ROUND or
* CAP_SQUARE.
* @param joinStyle the desired line join style, one of
* JOIN_MITER, JOIN_ROUND or
* JOIN_BEVEL.
* @param miterLimit the desired miter limit
*/
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 *******************************/
// 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;
}
}
}
