8180055: Upgrade the Marlin renderer in Java2D
Summary: added the double-precision variant + MarlinFX backports + Improved MarlinTileGenerator + higher precision of the cubic / quadratic curve
Reviewed-by: flar, pnarayanan
/*
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* 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 sun.java2d.marlin;
import java.util.Arrays;
// TODO: some of the arithmetic here is too verbose and prone to hard to
// debug typos. We should consider making a small Point/Vector class that
// has methods like plus(Point), minus(Point), dot(Point), cross(Point)and such
final class DStroker implements DPathConsumer2D, MarlinConst {
private static final int MOVE_TO = 0;
private static final int DRAWING_OP_TO = 1; // ie. curve, line, or quad
private static final int CLOSE = 2;
/**
* Constant value for join style.
*/
public static final int JOIN_MITER = 0;
/**
* Constant value for join style.
*/
public static final int JOIN_ROUND = 1;
/**
* Constant value for join style.
*/
public static final int JOIN_BEVEL = 2;
/**
* Constant value for end cap style.
*/
public static final int CAP_BUTT = 0;
/**
* Constant value for end cap style.
*/
public static final int CAP_ROUND = 1;
/**
* Constant value for end cap style.
*/
public static final int CAP_SQUARE = 2;
// pisces used to use fixed point arithmetic with 16 decimal digits. I
// didn't want to change the values of the constant below when I converted
// it to floating point, so that's why the divisions by 2^16 are there.
private static final double ROUND_JOIN_THRESHOLD = 1000.0d/65536.0d;
private static final double C = 0.5522847498307933d;
private static final int MAX_N_CURVES = 11;
private DPathConsumer2D out;
private int capStyle;
private int joinStyle;
private double lineWidth2;
private double invHalfLineWidth2Sq;
private final double[] offset0 = new double[2];
private final double[] offset1 = new double[2];
private final double[] offset2 = new double[2];
private final double[] miter = new double[2];
private double miterLimitSq;
private int prev;
// The starting point of the path, and the slope there.
private double sx0, sy0, sdx, sdy;
// the current point and the slope there.
private double cx0, cy0, cdx, cdy; // c stands for current
// vectors that when added to (sx0,sy0) and (cx0,cy0) respectively yield the
// first and last points on the left parallel path. Since this path is
// parallel, it's slope at any point is parallel to the slope of the
// original path (thought they may have different directions), so these
// could be computed from sdx,sdy and cdx,cdy (and vice versa), but that
// would be error prone and hard to read, so we keep these anyway.
private double smx, smy, cmx, cmy;
private final PolyStack reverse;
// This is where the curve to be processed is put. We give it
// enough room to store all curves.
private final double[] middle = new double[MAX_N_CURVES * 6 + 2];
private final double[] lp = new double[8];
private final double[] rp = new double[8];
private final double[] subdivTs = new double[MAX_N_CURVES - 1];
// per-thread renderer context
final DRendererContext rdrCtx;
// dirty curve
final DCurve curve;
/**
* Constructs a <code>DStroker</code>.
* @param rdrCtx per-thread renderer context
*/
DStroker(final DRendererContext rdrCtx) {
this.rdrCtx = rdrCtx;
this.reverse = new PolyStack(rdrCtx);
this.curve = rdrCtx.curve;
}
/**
* Inits the <code>DStroker</code>.
*
* @param pc2d an output <code>DPathConsumer2D</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
* @return this instance
*/
DStroker init(DPathConsumer2D pc2d,
double lineWidth,
int capStyle,
int joinStyle,
double miterLimit)
{
this.out = pc2d;
this.lineWidth2 = lineWidth / 2.0d;
this.invHalfLineWidth2Sq = 1.0d / (2.0d * lineWidth2 * lineWidth2);
this.capStyle = capStyle;
this.joinStyle = joinStyle;
double limit = miterLimit * lineWidth2;
this.miterLimitSq = limit * limit;
this.prev = CLOSE;
rdrCtx.stroking = 1;
return this; // fluent API
}
/**
* Disposes this stroker:
* clean up before reusing this instance
*/
void dispose() {
reverse.dispose();
if (DO_CLEAN_DIRTY) {
// Force zero-fill dirty arrays:
Arrays.fill(offset0, 0.0d);
Arrays.fill(offset1, 0.0d);
Arrays.fill(offset2, 0.0d);
Arrays.fill(miter, 0.0d);
Arrays.fill(middle, 0.0d);
Arrays.fill(lp, 0.0d);
Arrays.fill(rp, 0.0d);
Arrays.fill(subdivTs, 0.0d);
}
}
private static void computeOffset(final double lx, final double ly,
final double w, final double[] m)
{
double len = lx*lx + ly*ly;
if (len == 0.0d) {
m[0] = 0.0d;
m[1] = 0.0d;
} else {
len = Math.sqrt(len);
m[0] = (ly * w) / len;
m[1] = -(lx * w) / len;
}
}
// Returns true if the vectors (dx1, dy1) and (dx2, dy2) are
// clockwise (if dx1,dy1 needs to be rotated clockwise to close
// the smallest angle between it and dx2,dy2).
// This is equivalent to detecting whether a point q is on the right side
// of a line passing through points p1, p2 where p2 = p1+(dx1,dy1) and
// q = p2+(dx2,dy2), which is the same as saying p1, p2, q are in a
// clockwise order.
// NOTE: "clockwise" here assumes coordinates with 0,0 at the bottom left.
private static boolean isCW(final double dx1, final double dy1,
final double dx2, final double dy2)
{
return dx1 * dy2 <= dy1 * dx2;
}
private void drawRoundJoin(double x, double y,
double omx, double omy, double mx, double my,
boolean rev,
double threshold)
{
if ((omx == 0.0d && omy == 0.0d) || (mx == 0.0d && my == 0.0d)) {
return;
}
double domx = omx - mx;
double domy = omy - my;
double len = domx*domx + domy*domy;
if (len < threshold) {
return;
}
if (rev) {
omx = -omx;
omy = -omy;
mx = -mx;
my = -my;
}
drawRoundJoin(x, y, omx, omy, mx, my, rev);
}
private void drawRoundJoin(double cx, double cy,
double omx, double omy,
double mx, double my,
boolean rev)
{
// The sign of the dot product of mx,my and omx,omy is equal to the
// the sign of the cosine of ext
// (ext is the angle between omx,omy and mx,my).
final double cosext = omx * mx + omy * my;
// If it is >=0, we know that abs(ext) is <= 90 degrees, so we only
// need 1 curve to approximate the circle section that joins omx,omy
// and mx,my.
final int numCurves = (cosext >= 0.0d) ? 1 : 2;
switch (numCurves) {
case 1:
drawBezApproxForArc(cx, cy, omx, omy, mx, my, rev);
break;
case 2:
// we need to split the arc into 2 arcs spanning the same angle.
// The point we want will be one of the 2 intersections of the
// perpendicular bisector of the chord (omx,omy)->(mx,my) and the
// circle. We could find this by scaling the vector
// (omx+mx, omy+my)/2 so that it has length=lineWidth2 (and thus lies
// on the circle), but that can have numerical problems when the angle
// between omx,omy and mx,my is close to 180 degrees. So we compute a
// normal of (omx,omy)-(mx,my). This will be the direction of the
// perpendicular bisector. To get one of the intersections, we just scale
// this vector that its length is lineWidth2 (this works because the
// perpendicular bisector goes through the origin). This scaling doesn't
// have numerical problems because we know that lineWidth2 divided by
// this normal's length is at least 0.5 and at most sqrt(2)/2 (because
// we know the angle of the arc is > 90 degrees).
double nx = my - omy, ny = omx - mx;
double nlen = Math.sqrt(nx*nx + ny*ny);
double scale = lineWidth2/nlen;
double mmx = nx * scale, mmy = ny * scale;
// if (isCW(omx, omy, mx, my) != isCW(mmx, mmy, mx, my)) then we've
// computed the wrong intersection so we get the other one.
// The test above is equivalent to if (rev).
if (rev) {
mmx = -mmx;
mmy = -mmy;
}
drawBezApproxForArc(cx, cy, omx, omy, mmx, mmy, rev);
drawBezApproxForArc(cx, cy, mmx, mmy, mx, my, rev);
break;
default:
}
}
// the input arc defined by omx,omy and mx,my must span <= 90 degrees.
private void drawBezApproxForArc(final double cx, final double cy,
final double omx, final double omy,
final double mx, final double my,
boolean rev)
{
final double cosext2 = (omx * mx + omy * my) * invHalfLineWidth2Sq;
// check round off errors producing cos(ext) > 1 and a NaN below
// cos(ext) == 1 implies colinear segments and an empty join anyway
if (cosext2 >= 0.5d) {
// just return to avoid generating a flat curve:
return;
}
// cv is the length of P1-P0 and P2-P3 divided by the radius of the arc
// (so, cv assumes the arc has radius 1). P0, P1, P2, P3 are the points that
// define the bezier curve we're computing.
// It is computed using the constraints that P1-P0 and P3-P2 are parallel
// to the arc tangents at the endpoints, and that |P1-P0|=|P3-P2|.
double cv = ((4.0d / 3.0d) * Math.sqrt(0.5d - cosext2) /
(1.0d + Math.sqrt(cosext2 + 0.5d)));
// if clockwise, we need to negate cv.
if (rev) { // rev is equivalent to isCW(omx, omy, mx, my)
cv = -cv;
}
final double x1 = cx + omx;
final double y1 = cy + omy;
final double x2 = x1 - cv * omy;
final double y2 = y1 + cv * omx;
final double x4 = cx + mx;
final double y4 = cy + my;
final double x3 = x4 + cv * my;
final double y3 = y4 - cv * mx;
emitCurveTo(x1, y1, x2, y2, x3, y3, x4, y4, rev);
}
private void drawRoundCap(double cx, double cy, double mx, double my) {
final double Cmx = C * mx;
final double Cmy = C * my;
emitCurveTo(cx + mx - Cmy, cy + my + Cmx,
cx - my + Cmx, cy + mx + Cmy,
cx - my, cy + mx);
emitCurveTo(cx - my - Cmx, cy + mx - Cmy,
cx - mx - Cmy, cy - my + Cmx,
cx - mx, cy - my);
}
// Return the intersection point of the lines (x0, y0) -> (x1, y1)
// and (x0p, y0p) -> (x1p, y1p) in m[off] and m[off+1]
private static void computeMiter(final double x0, final double y0,
final double x1, final double y1,
final double x0p, final double y0p,
final double x1p, final double y1p,
final double[] m, int off)
{
double x10 = x1 - x0;
double y10 = y1 - y0;
double x10p = x1p - x0p;
double y10p = y1p - y0p;
// if this is 0, the lines are parallel. If they go in the
// same direction, there is no intersection so m[off] and
// m[off+1] will contain infinity, so no miter will be drawn.
// If they go in the same direction that means that the start of the
// current segment and the end of the previous segment have the same
// tangent, in which case this method won't even be involved in
// miter drawing because it won't be called by drawMiter (because
// (mx == omx && my == omy) will be true, and drawMiter will return
// immediately).
double den = x10*y10p - x10p*y10;
double t = x10p*(y0-y0p) - y10p*(x0-x0p);
t /= den;
m[off++] = x0 + t*x10;
m[off] = y0 + t*y10;
}
// Return the intersection point of the lines (x0, y0) -> (x1, y1)
// and (x0p, y0p) -> (x1p, y1p) in m[off] and m[off+1]
private static void safeComputeMiter(final double x0, final double y0,
final double x1, final double y1,
final double x0p, final double y0p,
final double x1p, final double y1p,
final double[] m, int off)
{
double x10 = x1 - x0;
double y10 = y1 - y0;
double x10p = x1p - x0p;
double y10p = y1p - y0p;
// if this is 0, the lines are parallel. If they go in the
// same direction, there is no intersection so m[off] and
// m[off+1] will contain infinity, so no miter will be drawn.
// If they go in the same direction that means that the start of the
// current segment and the end of the previous segment have the same
// tangent, in which case this method won't even be involved in
// miter drawing because it won't be called by drawMiter (because
// (mx == omx && my == omy) will be true, and drawMiter will return
// immediately).
double den = x10*y10p - x10p*y10;
if (den == 0.0d) {
m[off++] = (x0 + x0p) / 2.0d;
m[off] = (y0 + y0p) / 2.0d;
return;
}
double t = x10p*(y0-y0p) - y10p*(x0-x0p);
t /= den;
m[off++] = x0 + t*x10;
m[off] = y0 + t*y10;
}
private void drawMiter(final double pdx, final double pdy,
final double x0, final double y0,
final double dx, final double dy,
double omx, double omy, double mx, double my,
boolean rev)
{
if ((mx == omx && my == omy) ||
(pdx == 0.0d && pdy == 0.0d) ||
(dx == 0.0d && dy == 0.0d))
{
return;
}
if (rev) {
omx = -omx;
omy = -omy;
mx = -mx;
my = -my;
}
computeMiter((x0 - pdx) + omx, (y0 - pdy) + omy, x0 + omx, y0 + omy,
(dx + x0) + mx, (dy + y0) + my, x0 + mx, y0 + my,
miter, 0);
final double miterX = miter[0];
final double miterY = miter[1];
double lenSq = (miterX-x0)*(miterX-x0) + (miterY-y0)*(miterY-y0);
// If the lines are parallel, lenSq will be either NaN or +inf
// (actually, I'm not sure if the latter is possible. The important
// thing is that -inf is not possible, because lenSq is a square).
// For both of those values, the comparison below will fail and
// no miter will be drawn, which is correct.
if (lenSq < miterLimitSq) {
emitLineTo(miterX, miterY, rev);
}
}
@Override
public void moveTo(double x0, double y0) {
if (prev == DRAWING_OP_TO) {
finish();
}
this.sx0 = this.cx0 = x0;
this.sy0 = this.cy0 = y0;
this.cdx = this.sdx = 1.0d;
this.cdy = this.sdy = 0.0d;
this.prev = MOVE_TO;
}
@Override
public void lineTo(double x1, double y1) {
double dx = x1 - cx0;
double dy = y1 - cy0;
if (dx == 0.0d && dy == 0.0d) {
dx = 1.0d;
}
computeOffset(dx, dy, lineWidth2, offset0);
final double mx = offset0[0];
final double my = offset0[1];
drawJoin(cdx, cdy, cx0, cy0, dx, dy, cmx, cmy, mx, my);
emitLineTo(cx0 + mx, cy0 + my);
emitLineTo( x1 + mx, y1 + my);
emitLineToRev(cx0 - mx, cy0 - my);
emitLineToRev( x1 - mx, y1 - my);
this.cmx = mx;
this.cmy = my;
this.cdx = dx;
this.cdy = dy;
this.cx0 = x1;
this.cy0 = y1;
this.prev = DRAWING_OP_TO;
}
@Override
public void closePath() {
if (prev != DRAWING_OP_TO) {
if (prev == CLOSE) {
return;
}
emitMoveTo(cx0, cy0 - lineWidth2);
this.cmx = this.smx = 0.0d;
this.cmy = this.smy = -lineWidth2;
this.cdx = this.sdx = 1.0d;
this.cdy = this.sdy = 0.0d;
finish();
return;
}
if (cx0 != sx0 || cy0 != sy0) {
lineTo(sx0, sy0);
}
drawJoin(cdx, cdy, cx0, cy0, sdx, sdy, cmx, cmy, smx, smy);
emitLineTo(sx0 + smx, sy0 + smy);
emitMoveTo(sx0 - smx, sy0 - smy);
emitReverse();
this.prev = CLOSE;
emitClose();
}
private void emitReverse() {
reverse.popAll(out);
}
@Override
public void pathDone() {
if (prev == DRAWING_OP_TO) {
finish();
}
out.pathDone();
// this shouldn't matter since this object won't be used
// after the call to this method.
this.prev = CLOSE;
// Dispose this instance:
dispose();
}
private void finish() {
if (capStyle == CAP_ROUND) {
drawRoundCap(cx0, cy0, cmx, cmy);
} else if (capStyle == CAP_SQUARE) {
emitLineTo(cx0 - cmy + cmx, cy0 + cmx + cmy);
emitLineTo(cx0 - cmy - cmx, cy0 + cmx - cmy);
}
emitReverse();
if (capStyle == CAP_ROUND) {
drawRoundCap(sx0, sy0, -smx, -smy);
} else if (capStyle == CAP_SQUARE) {
emitLineTo(sx0 + smy - smx, sy0 - smx - smy);
emitLineTo(sx0 + smy + smx, sy0 - smx + smy);
}
emitClose();
}
private void emitMoveTo(final double x0, final double y0) {
out.moveTo(x0, y0);
}
private void emitLineTo(final double x1, final double y1) {
out.lineTo(x1, y1);
}
private void emitLineToRev(final double x1, final double y1) {
reverse.pushLine(x1, y1);
}
private void emitLineTo(final double x1, final double y1,
final boolean rev)
{
if (rev) {
emitLineToRev(x1, y1);
} else {
emitLineTo(x1, y1);
}
}
private void emitQuadTo(final double x1, final double y1,
final double x2, final double y2)
{
out.quadTo(x1, y1, x2, y2);
}
private void emitQuadToRev(final double x0, final double y0,
final double x1, final double y1)
{
reverse.pushQuad(x0, y0, x1, y1);
}
private void emitCurveTo(final double x1, final double y1,
final double x2, final double y2,
final double x3, final double y3)
{
out.curveTo(x1, y1, x2, y2, x3, y3);
}
private void emitCurveToRev(final double x0, final double y0,
final double x1, final double y1,
final double x2, final double y2)
{
reverse.pushCubic(x0, y0, x1, y1, x2, y2);
}
private void emitCurveTo(final double x0, final double y0,
final double x1, final double y1,
final double x2, final double y2,
final double x3, final double y3, final boolean rev)
{
if (rev) {
reverse.pushCubic(x0, y0, x1, y1, x2, y2);
} else {
out.curveTo(x1, y1, x2, y2, x3, y3);
}
}
private void emitClose() {
out.closePath();
}
private void drawJoin(double pdx, double pdy,
double x0, double y0,
double dx, double dy,
double omx, double omy,
double mx, double my)
{
if (prev != DRAWING_OP_TO) {
emitMoveTo(x0 + mx, y0 + my);
this.sdx = dx;
this.sdy = dy;
this.smx = mx;
this.smy = my;
} else {
boolean cw = isCW(pdx, pdy, dx, dy);
if (joinStyle == JOIN_MITER) {
drawMiter(pdx, pdy, x0, y0, dx, dy, omx, omy, mx, my, cw);
} else if (joinStyle == JOIN_ROUND) {
drawRoundJoin(x0, y0,
omx, omy,
mx, my, cw,
ROUND_JOIN_THRESHOLD);
}
emitLineTo(x0, y0, !cw);
}
prev = DRAWING_OP_TO;
}
private static boolean within(final double x1, final double y1,
final double x2, final double y2,
final double ERR)
{
assert ERR > 0 : "";
// compare taxicab distance. ERR will always be small, so using
// true distance won't give much benefit
return (DHelpers.within(x1, x2, ERR) && // we want to avoid calling Math.abs
DHelpers.within(y1, y2, ERR)); // this is just as good.
}
private void getLineOffsets(double x1, double y1,
double x2, double y2,
double[] left, double[] right) {
computeOffset(x2 - x1, y2 - y1, lineWidth2, offset0);
final double mx = offset0[0];
final double my = offset0[1];
left[0] = x1 + mx;
left[1] = y1 + my;
left[2] = x2 + mx;
left[3] = y2 + my;
right[0] = x1 - mx;
right[1] = y1 - my;
right[2] = x2 - mx;
right[3] = y2 - my;
}
private int computeOffsetCubic(double[] pts, final int off,
double[] leftOff, double[] rightOff)
{
// if p1=p2 or p3=p4 it means that the derivative at the endpoint
// vanishes, which creates problems with computeOffset. Usually
// this happens when this stroker object is trying to widen
// a curve with a cusp. What happens is that curveTo splits
// the input curve at the cusp, and passes it to this function.
// because of inaccuracies in the splitting, we consider points
// equal if they're very close to each other.
final double x1 = pts[off + 0], y1 = pts[off + 1];
final double x2 = pts[off + 2], y2 = pts[off + 3];
final double x3 = pts[off + 4], y3 = pts[off + 5];
final double x4 = pts[off + 6], y4 = pts[off + 7];
double dx4 = x4 - x3;
double dy4 = y4 - y3;
double dx1 = x2 - x1;
double dy1 = y2 - y1;
// if p1 == p2 && p3 == p4: draw line from p1->p4, unless p1 == p4,
// in which case ignore if p1 == p2
final boolean p1eqp2 = within(x1, y1, x2, y2, 6.0d * Math.ulp(y2));
final boolean p3eqp4 = within(x3, y3, x4, y4, 6.0d * Math.ulp(y4));
if (p1eqp2 && p3eqp4) {
getLineOffsets(x1, y1, x4, y4, leftOff, rightOff);
return 4;
} else if (p1eqp2) {
dx1 = x3 - x1;
dy1 = y3 - y1;
} else if (p3eqp4) {
dx4 = x4 - x2;
dy4 = y4 - y2;
}
// if p2-p1 and p4-p3 are parallel, that must mean this curve is a line
double dotsq = (dx1 * dx4 + dy1 * dy4);
dotsq *= dotsq;
double l1sq = dx1 * dx1 + dy1 * dy1, l4sq = dx4 * dx4 + dy4 * dy4;
if (DHelpers.within(dotsq, l1sq * l4sq, 4.0d * Math.ulp(dotsq))) {
getLineOffsets(x1, y1, x4, y4, leftOff, rightOff);
return 4;
}
// What we're trying to do in this function is to approximate an ideal
// offset curve (call it I) of the input curve B using a bezier curve Bp.
// The constraints I use to get the equations are:
//
// 1. The computed curve Bp should go through I(0) and I(1). These are
// x1p, y1p, x4p, y4p, which are p1p and p4p. We still need to find
// 4 variables: the x and y components of p2p and p3p (i.e. x2p, y2p, x3p, y3p).
//
// 2. Bp should have slope equal in absolute value to I at the endpoints. So,
// (by the way, the operator || in the comments below means "aligned with".
// It is defined on vectors, so when we say I'(0) || Bp'(0) we mean that
// vectors I'(0) and Bp'(0) are aligned, which is the same as saying
// that the tangent lines of I and Bp at 0 are parallel. Mathematically
// this means (I'(t) || Bp'(t)) <==> (I'(t) = c * Bp'(t)) where c is some
// nonzero constant.)
// I'(0) || Bp'(0) and I'(1) || Bp'(1). Obviously, I'(0) || B'(0) and
// I'(1) || B'(1); therefore, Bp'(0) || B'(0) and Bp'(1) || B'(1).
// We know that Bp'(0) || (p2p-p1p) and Bp'(1) || (p4p-p3p) and the same
// is true for any bezier curve; therefore, we get the equations
// (1) p2p = c1 * (p2-p1) + p1p
// (2) p3p = c2 * (p4-p3) + p4p
// We know p1p, p4p, p2, p1, p3, and p4; therefore, this reduces the number
// of unknowns from 4 to 2 (i.e. just c1 and c2).
// To eliminate these 2 unknowns we use the following constraint:
//
// 3. Bp(0.5) == I(0.5). Bp(0.5)=(x,y) and I(0.5)=(xi,yi), and I should note
// that I(0.5) is *the only* reason for computing dxm,dym. This gives us
// (3) Bp(0.5) = (p1p + 3 * (p2p + p3p) + p4p)/8, which is equivalent to
// (4) p2p + p3p = (Bp(0.5)*8 - p1p - p4p) / 3
// We can substitute (1) and (2) from above into (4) and we get:
// (5) c1*(p2-p1) + c2*(p4-p3) = (Bp(0.5)*8 - p1p - p4p)/3 - p1p - p4p
// which is equivalent to
// (6) c1*(p2-p1) + c2*(p4-p3) = (4/3) * (Bp(0.5) * 2 - p1p - p4p)
//
// The right side of this is a 2D vector, and we know I(0.5), which gives us
// Bp(0.5), which gives us the value of the right side.
// The left side is just a matrix vector multiplication in disguise. It is
//
// [x2-x1, x4-x3][c1]
// [y2-y1, y4-y3][c2]
// which, is equal to
// [dx1, dx4][c1]
// [dy1, dy4][c2]
// At this point we are left with a simple linear system and we solve it by
// getting the inverse of the matrix above. Then we use [c1,c2] to compute
// p2p and p3p.
double x = (x1 + 3.0d * (x2 + x3) + x4) / 8.0d;
double y = (y1 + 3.0d * (y2 + y3) + y4) / 8.0d;
// (dxm,dym) is some tangent of B at t=0.5. This means it's equal to
// c*B'(0.5) for some constant c.
double dxm = x3 + x4 - x1 - x2, dym = y3 + y4 - y1 - y2;
// this computes the offsets at t=0, 0.5, 1, using the property that
// for any bezier curve the vectors p2-p1 and p4-p3 are parallel to
// the (dx/dt, dy/dt) vectors at the endpoints.
computeOffset(dx1, dy1, lineWidth2, offset0);
computeOffset(dxm, dym, lineWidth2, offset1);
computeOffset(dx4, dy4, lineWidth2, offset2);
double x1p = x1 + offset0[0]; // start
double y1p = y1 + offset0[1]; // point
double xi = x + offset1[0]; // interpolation
double yi = y + offset1[1]; // point
double x4p = x4 + offset2[0]; // end
double y4p = y4 + offset2[1]; // point
double invdet43 = 4.0d / (3.0d * (dx1 * dy4 - dy1 * dx4));
double two_pi_m_p1_m_p4x = 2.0d * xi - x1p - x4p;
double two_pi_m_p1_m_p4y = 2.0d * yi - y1p - y4p;
double c1 = invdet43 * (dy4 * two_pi_m_p1_m_p4x - dx4 * two_pi_m_p1_m_p4y);
double c2 = invdet43 * (dx1 * two_pi_m_p1_m_p4y - dy1 * two_pi_m_p1_m_p4x);
double x2p, y2p, x3p, y3p;
x2p = x1p + c1*dx1;
y2p = y1p + c1*dy1;
x3p = x4p + c2*dx4;
y3p = y4p + c2*dy4;
leftOff[0] = x1p; leftOff[1] = y1p;
leftOff[2] = x2p; leftOff[3] = y2p;
leftOff[4] = x3p; leftOff[5] = y3p;
leftOff[6] = x4p; leftOff[7] = y4p;
x1p = x1 - offset0[0]; y1p = y1 - offset0[1];
xi = xi - 2.0d * offset1[0]; yi = yi - 2.0d * offset1[1];
x4p = x4 - offset2[0]; y4p = y4 - offset2[1];
two_pi_m_p1_m_p4x = 2.0d * xi - x1p - x4p;
two_pi_m_p1_m_p4y = 2.0d * yi - y1p - y4p;
c1 = invdet43 * (dy4 * two_pi_m_p1_m_p4x - dx4 * two_pi_m_p1_m_p4y);
c2 = invdet43 * (dx1 * two_pi_m_p1_m_p4y - dy1 * two_pi_m_p1_m_p4x);
x2p = x1p + c1*dx1;
y2p = y1p + c1*dy1;
x3p = x4p + c2*dx4;
y3p = y4p + c2*dy4;
rightOff[0] = x1p; rightOff[1] = y1p;
rightOff[2] = x2p; rightOff[3] = y2p;
rightOff[4] = x3p; rightOff[5] = y3p;
rightOff[6] = x4p; rightOff[7] = y4p;
return 8;
}
// compute offset curves using bezier spline through t=0.5 (i.e.
// ComputedCurve(0.5) == IdealParallelCurve(0.5))
// return the kind of curve in the right and left arrays.
private int computeOffsetQuad(double[] pts, final int off,
double[] leftOff, double[] rightOff)
{
final double x1 = pts[off + 0], y1 = pts[off + 1];
final double x2 = pts[off + 2], y2 = pts[off + 3];
final double x3 = pts[off + 4], y3 = pts[off + 5];
final double dx3 = x3 - x2;
final double dy3 = y3 - y2;
final double dx1 = x2 - x1;
final double dy1 = y2 - y1;
// if p1=p2 or p3=p4 it means that the derivative at the endpoint
// vanishes, which creates problems with computeOffset. Usually
// this happens when this stroker object is trying to widen
// a curve with a cusp. What happens is that curveTo splits
// the input curve at the cusp, and passes it to this function.
// because of inaccuracies in the splitting, we consider points
// equal if they're very close to each other.
// if p1 == p2 && p3 == p4: draw line from p1->p4, unless p1 == p4,
// in which case ignore.
final boolean p1eqp2 = within(x1, y1, x2, y2, 6.0d * Math.ulp(y2));
final boolean p2eqp3 = within(x2, y2, x3, y3, 6.0d * Math.ulp(y3));
if (p1eqp2 || p2eqp3) {
getLineOffsets(x1, y1, x3, y3, leftOff, rightOff);
return 4;
}
// if p2-p1 and p4-p3 are parallel, that must mean this curve is a line
double dotsq = (dx1 * dx3 + dy1 * dy3);
dotsq *= dotsq;
double l1sq = dx1 * dx1 + dy1 * dy1, l3sq = dx3 * dx3 + dy3 * dy3;
if (DHelpers.within(dotsq, l1sq * l3sq, 4.0d * Math.ulp(dotsq))) {
getLineOffsets(x1, y1, x3, y3, leftOff, rightOff);
return 4;
}
// this computes the offsets at t=0, 0.5, 1, using the property that
// for any bezier curve the vectors p2-p1 and p4-p3 are parallel to
// the (dx/dt, dy/dt) vectors at the endpoints.
computeOffset(dx1, dy1, lineWidth2, offset0);
computeOffset(dx3, dy3, lineWidth2, offset1);
double x1p = x1 + offset0[0]; // start
double y1p = y1 + offset0[1]; // point
double x3p = x3 + offset1[0]; // end
double y3p = y3 + offset1[1]; // point
safeComputeMiter(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, leftOff, 2);
leftOff[0] = x1p; leftOff[1] = y1p;
leftOff[4] = x3p; leftOff[5] = y3p;
x1p = x1 - offset0[0]; y1p = y1 - offset0[1];
x3p = x3 - offset1[0]; y3p = y3 - offset1[1];
safeComputeMiter(x1p, y1p, x1p+dx1, y1p+dy1, x3p, y3p, x3p-dx3, y3p-dy3, rightOff, 2);
rightOff[0] = x1p; rightOff[1] = y1p;
rightOff[4] = x3p; rightOff[5] = y3p;
return 6;
}
// finds values of t where the curve in pts should be subdivided in order
// to get good offset curves a distance of w away from the middle curve.
// Stores the points in ts, and returns how many of them there were.
private static int findSubdivPoints(final DCurve c, double[] pts, double[] ts,
final int type, final double w)
{
final double x12 = pts[2] - pts[0];
final double y12 = pts[3] - pts[1];
// if the curve is already parallel to either axis we gain nothing
// from rotating it.
if (y12 != 0.0d && x12 != 0.0d) {
// we rotate it so that the first vector in the control polygon is
// parallel to the x-axis. This will ensure that rotated quarter
// circles won't be subdivided.
final double hypot = Math.sqrt(x12 * x12 + y12 * y12);
final double cos = x12 / hypot;
final double sin = y12 / hypot;
final double x1 = cos * pts[0] + sin * pts[1];
final double y1 = cos * pts[1] - sin * pts[0];
final double x2 = cos * pts[2] + sin * pts[3];
final double y2 = cos * pts[3] - sin * pts[2];
final double x3 = cos * pts[4] + sin * pts[5];
final double y3 = cos * pts[5] - sin * pts[4];
switch(type) {
case 8:
final double x4 = cos * pts[6] + sin * pts[7];
final double y4 = cos * pts[7] - sin * pts[6];
c.set(x1, y1, x2, y2, x3, y3, x4, y4);
break;
case 6:
c.set(x1, y1, x2, y2, x3, y3);
break;
default:
}
} else {
c.set(pts, type);
}
int ret = 0;
// we subdivide at values of t such that the remaining rotated
// curves are monotonic in x and y.
ret += c.dxRoots(ts, ret);
ret += c.dyRoots(ts, ret);
// subdivide at inflection points.
if (type == 8) {
// quadratic curves can't have inflection points
ret += c.infPoints(ts, ret);
}
// now we must subdivide at points where one of the offset curves will have
// a cusp. This happens at ts where the radius of curvature is equal to w.
ret += c.rootsOfROCMinusW(ts, ret, w, 0.0001d);
ret = DHelpers.filterOutNotInAB(ts, 0, ret, 0.0001d, 0.9999d);
DHelpers.isort(ts, 0, ret);
return ret;
}
@Override public void curveTo(double x1, double y1,
double x2, double y2,
double x3, double y3)
{
final double[] mid = middle;
mid[0] = cx0; mid[1] = cy0;
mid[2] = x1; mid[3] = y1;
mid[4] = x2; mid[5] = y2;
mid[6] = x3; mid[7] = y3;
// need these so we can update the state at the end of this method
final double xf = mid[6], yf = mid[7];
double dxs = mid[2] - mid[0];
double dys = mid[3] - mid[1];
double dxf = mid[6] - mid[4];
double dyf = mid[7] - mid[5];
boolean p1eqp2 = (dxs == 0.0d && dys == 0.0d);
boolean p3eqp4 = (dxf == 0.0d && dyf == 0.0d);
if (p1eqp2) {
dxs = mid[4] - mid[0];
dys = mid[5] - mid[1];
if (dxs == 0.0d && dys == 0.0d) {
dxs = mid[6] - mid[0];
dys = mid[7] - mid[1];
}
}
if (p3eqp4) {
dxf = mid[6] - mid[2];
dyf = mid[7] - mid[3];
if (dxf == 0.0d && dyf == 0.0d) {
dxf = mid[6] - mid[0];
dyf = mid[7] - mid[1];
}
}
if (dxs == 0.0d && dys == 0.0d) {
// this happens if the "curve" is just a point
lineTo(mid[0], mid[1]);
return;
}
// if these vectors are too small, normalize them, to avoid future
// precision problems.
if (Math.abs(dxs) < 0.1d && Math.abs(dys) < 0.1d) {
double len = Math.sqrt(dxs*dxs + dys*dys);
dxs /= len;
dys /= len;
}
if (Math.abs(dxf) < 0.1d && Math.abs(dyf) < 0.1d) {
double len = Math.sqrt(dxf*dxf + dyf*dyf);
dxf /= len;
dyf /= len;
}
computeOffset(dxs, dys, lineWidth2, offset0);
drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, offset0[0], offset0[1]);
final int nSplits = findSubdivPoints(curve, mid, subdivTs, 8, lineWidth2);
double prevT = 0.0d;
for (int i = 0, off = 0; i < nSplits; i++, off += 6) {
final double t = subdivTs[i];
DHelpers.subdivideCubicAt((t - prevT) / (1.0d - prevT),
mid, off, mid, off, mid, off + 6);
prevT = t;
}
final double[] l = lp;
final double[] r = rp;
int kind = 0;
for (int i = 0, off = 0; i <= nSplits; i++, off += 6) {
kind = computeOffsetCubic(mid, off, l, r);
emitLineTo(l[0], l[1]);
switch(kind) {
case 8:
emitCurveTo(l[2], l[3], l[4], l[5], l[6], l[7]);
emitCurveToRev(r[0], r[1], r[2], r[3], r[4], r[5]);
break;
case 4:
emitLineTo(l[2], l[3]);
emitLineToRev(r[0], r[1]);
break;
default:
}
emitLineToRev(r[kind - 2], r[kind - 1]);
}
this.cmx = (l[kind - 2] - r[kind - 2]) / 2.0d;
this.cmy = (l[kind - 1] - r[kind - 1]) / 2.0d;
this.cdx = dxf;
this.cdy = dyf;
this.cx0 = xf;
this.cy0 = yf;
this.prev = DRAWING_OP_TO;
}
@Override public void quadTo(double x1, double y1, double x2, double y2) {
final double[] mid = middle;
mid[0] = cx0; mid[1] = cy0;
mid[2] = x1; mid[3] = y1;
mid[4] = x2; mid[5] = y2;
// need these so we can update the state at the end of this method
final double xf = mid[4], yf = mid[5];
double dxs = mid[2] - mid[0];
double dys = mid[3] - mid[1];
double dxf = mid[4] - mid[2];
double dyf = mid[5] - mid[3];
if ((dxs == 0.0d && dys == 0.0d) || (dxf == 0.0d && dyf == 0.0d)) {
dxs = dxf = mid[4] - mid[0];
dys = dyf = mid[5] - mid[1];
}
if (dxs == 0.0d && dys == 0.0d) {
// this happens if the "curve" is just a point
lineTo(mid[0], mid[1]);
return;
}
// if these vectors are too small, normalize them, to avoid future
// precision problems.
if (Math.abs(dxs) < 0.1d && Math.abs(dys) < 0.1d) {
double len = Math.sqrt(dxs*dxs + dys*dys);
dxs /= len;
dys /= len;
}
if (Math.abs(dxf) < 0.1d && Math.abs(dyf) < 0.1d) {
double len = Math.sqrt(dxf*dxf + dyf*dyf);
dxf /= len;
dyf /= len;
}
computeOffset(dxs, dys, lineWidth2, offset0);
drawJoin(cdx, cdy, cx0, cy0, dxs, dys, cmx, cmy, offset0[0], offset0[1]);
int nSplits = findSubdivPoints(curve, mid, subdivTs, 6, lineWidth2);
double prevt = 0.0d;
for (int i = 0, off = 0; i < nSplits; i++, off += 4) {
final double t = subdivTs[i];
DHelpers.subdivideQuadAt((t - prevt) / (1.0d - prevt),
mid, off, mid, off, mid, off + 4);
prevt = t;
}
final double[] l = lp;
final double[] r = rp;
int kind = 0;
for (int i = 0, off = 0; i <= nSplits; i++, off += 4) {
kind = computeOffsetQuad(mid, off, l, r);
emitLineTo(l[0], l[1]);
switch(kind) {
case 6:
emitQuadTo(l[2], l[3], l[4], l[5]);
emitQuadToRev(r[0], r[1], r[2], r[3]);
break;
case 4:
emitLineTo(l[2], l[3]);
emitLineToRev(r[0], r[1]);
break;
default:
}
emitLineToRev(r[kind - 2], r[kind - 1]);
}
this.cmx = (l[kind - 2] - r[kind - 2]) / 2.0d;
this.cmy = (l[kind - 1] - r[kind - 1]) / 2.0d;
this.cdx = dxf;
this.cdy = dyf;
this.cx0 = xf;
this.cy0 = yf;
this.prev = DRAWING_OP_TO;
}
@Override public long getNativeConsumer() {
throw new InternalError("Stroker doesn't use a native consumer");
}
// a stack of polynomial curves where each curve shares endpoints with
// adjacent ones.
static final class PolyStack {
private static final byte TYPE_LINETO = (byte) 0;
private static final byte TYPE_QUADTO = (byte) 1;
private static final byte TYPE_CUBICTO = (byte) 2;
// curves capacity = edges count (8192) = edges x 2 (coords)
private static final int INITIAL_CURVES_COUNT = INITIAL_EDGES_COUNT << 1;
// types capacity = edges count (4096)
private static final int INITIAL_TYPES_COUNT = INITIAL_EDGES_COUNT;
double[] curves;
int end;
byte[] curveTypes;
int numCurves;
// per-thread renderer context
final DRendererContext rdrCtx;
// curves ref (dirty)
final DoubleArrayCache.Reference curves_ref;
// curveTypes ref (dirty)
final ByteArrayCache.Reference curveTypes_ref;
// used marks (stats only)
int curveTypesUseMark;
int curvesUseMark;
/**
* Constructor
* @param rdrCtx per-thread renderer context
*/
PolyStack(final DRendererContext rdrCtx) {
this.rdrCtx = rdrCtx;
curves_ref = rdrCtx.newDirtyDoubleArrayRef(INITIAL_CURVES_COUNT); // 32K
curves = curves_ref.initial;
curveTypes_ref = rdrCtx.newDirtyByteArrayRef(INITIAL_TYPES_COUNT); // 4K
curveTypes = curveTypes_ref.initial;
numCurves = 0;
end = 0;
if (DO_STATS) {
curveTypesUseMark = 0;
curvesUseMark = 0;
}
}
/**
* Disposes this PolyStack:
* clean up before reusing this instance
*/
void dispose() {
end = 0;
numCurves = 0;
if (DO_STATS) {
rdrCtx.stats.stat_rdr_poly_stack_types.add(curveTypesUseMark);
rdrCtx.stats.stat_rdr_poly_stack_curves.add(curvesUseMark);
rdrCtx.stats.hist_rdr_poly_stack_curves.add(curvesUseMark);
// reset marks
curveTypesUseMark = 0;
curvesUseMark = 0;
}
// Return arrays:
// curves and curveTypes are kept dirty
curves = curves_ref.putArray(curves);
curveTypes = curveTypes_ref.putArray(curveTypes);
}
private void ensureSpace(final int n) {
// use substraction to avoid integer overflow:
if (curves.length - end < n) {
if (DO_STATS) {
rdrCtx.stats.stat_array_stroker_polystack_curves
.add(end + n);
}
curves = curves_ref.widenArray(curves, end, end + n);
}
if (curveTypes.length <= numCurves) {
if (DO_STATS) {
rdrCtx.stats.stat_array_stroker_polystack_curveTypes
.add(numCurves + 1);
}
curveTypes = curveTypes_ref.widenArray(curveTypes,
numCurves,
numCurves + 1);
}
}
void pushCubic(double x0, double y0,
double x1, double y1,
double x2, double y2)
{
ensureSpace(6);
curveTypes[numCurves++] = TYPE_CUBICTO;
// we reverse the coordinate order to make popping easier
final double[] _curves = curves;
int e = end;
_curves[e++] = x2; _curves[e++] = y2;
_curves[e++] = x1; _curves[e++] = y1;
_curves[e++] = x0; _curves[e++] = y0;
end = e;
}
void pushQuad(double x0, double y0,
double x1, double y1)
{
ensureSpace(4);
curveTypes[numCurves++] = TYPE_QUADTO;
final double[] _curves = curves;
int e = end;
_curves[e++] = x1; _curves[e++] = y1;
_curves[e++] = x0; _curves[e++] = y0;
end = e;
}
void pushLine(double x, double y) {
ensureSpace(2);
curveTypes[numCurves++] = TYPE_LINETO;
curves[end++] = x; curves[end++] = y;
}
void popAll(DPathConsumer2D io) {
if (DO_STATS) {
// update used marks:
if (numCurves > curveTypesUseMark) {
curveTypesUseMark = numCurves;
}
if (end > curvesUseMark) {
curvesUseMark = end;
}
}
final byte[] _curveTypes = curveTypes;
final double[] _curves = curves;
int nc = numCurves;
int e = end;
while (nc != 0) {
switch(_curveTypes[--nc]) {
case TYPE_LINETO:
e -= 2;
io.lineTo(_curves[e], _curves[e+1]);
continue;
case TYPE_QUADTO:
e -= 4;
io.quadTo(_curves[e+0], _curves[e+1],
_curves[e+2], _curves[e+3]);
continue;
case TYPE_CUBICTO:
e -= 6;
io.curveTo(_curves[e+0], _curves[e+1],
_curves[e+2], _curves[e+3],
_curves[e+4], _curves[e+5]);
continue;
default:
}
}
numCurves = 0;
end = 0;
}
@Override
public String toString() {
String ret = "";
int nc = numCurves;
int last = end;
int len;
while (nc != 0) {
switch(curveTypes[--nc]) {
case TYPE_LINETO:
len = 2;
ret += "line: ";
break;
case TYPE_QUADTO:
len = 4;
ret += "quad: ";
break;
case TYPE_CUBICTO:
len = 6;
ret += "cubic: ";
break;
default:
len = 0;
}
last -= len;
ret += Arrays.toString(Arrays.copyOfRange(curves, last, last+len))
+ "\n";
}
return ret;
}
}
}