/*
* Copyright (c) 2007, 2017, 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 sun.java2d.marlin;
import static java.lang.Math.PI;
import static java.lang.Math.cos;
import static java.lang.Math.sqrt;
import static java.lang.Math.cbrt;
import static java.lang.Math.acos;
import java.util.Arrays;
import static sun.java2d.marlin.MarlinConst.INITIAL_EDGES_COUNT;
import sun.java2d.marlin.stats.Histogram;
import sun.java2d.marlin.stats.StatLong;
final class DHelpers implements MarlinConst {
private DHelpers() {
throw new Error("This is a non instantiable class");
}
static boolean within(final double x, final double y, final double err) {
final double d = y - x;
return (d <= err && d >= -err);
}
static int quadraticRoots(final double a, final double b,
final double c, double[] zeroes, final int off)
{
int ret = off;
double t;
if (a != 0.0d) {
final double dis = b*b - 4*a*c;
if (dis > 0.0d) {
final double sqrtDis = Math.sqrt(dis);
// depending on the sign of b we use a slightly different
// algorithm than the traditional one to find one of the roots
// so we can avoid adding numbers of different signs (which
// might result in loss of precision).
if (b >= 0.0d) {
zeroes[ret++] = (2.0d * c) / (-b - sqrtDis);
zeroes[ret++] = (-b - sqrtDis) / (2.0d * a);
} else {
zeroes[ret++] = (-b + sqrtDis) / (2.0d * a);
zeroes[ret++] = (2.0d * c) / (-b + sqrtDis);
}
} else if (dis == 0.0d) {
t = (-b) / (2.0d * a);
zeroes[ret++] = t;
}
} else {
if (b != 0.0d) {
t = (-c) / b;
zeroes[ret++] = t;
}
}
return ret - off;
}
// find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B)
static int cubicRootsInAB(double d, double a, double b, double c,
double[] pts, final int off,
final double A, final double B)
{
if (d == 0.0d) {
int num = quadraticRoots(a, b, c, pts, off);
return filterOutNotInAB(pts, off, num, A, B) - off;
}
// From Graphics Gems:
// http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
// (also from awt.geom.CubicCurve2D. But here we don't need as
// much accuracy and we don't want to create arrays so we use
// our own customized version).
// normal form: x^3 + ax^2 + bx + c = 0
a /= d;
b /= d;
c /= d;
// substitute x = y - A/3 to eliminate quadratic term:
// x^3 +Px + Q = 0
//
// Since we actually need P/3 and Q/2 for all of the
// calculations that follow, we will calculate
// p = P/3
// q = Q/2
// instead and use those values for simplicity of the code.
double sq_A = a * a;
double p = (1.0d/3.0d) * ((-1.0d/3.0d) * sq_A + b);
double q = (1.0d/2.0d) * ((2.0d/27.0d) * a * sq_A - (1.0d/3.0d) * a * b + c);
// use Cardano's formula
double cb_p = p * p * p;
double D = q * q + cb_p;
int num;
if (D < 0.0d) {
// see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
final double phi = (1.0d/3.0d) * acos(-q / sqrt(-cb_p));
final double t = 2.0d * sqrt(-p);
pts[ off+0 ] = ( t * cos(phi));
pts[ off+1 ] = (-t * cos(phi + (PI / 3.0d)));
pts[ off+2 ] = (-t * cos(phi - (PI / 3.0d)));
num = 3;
} else {
final double sqrt_D = sqrt(D);
final double u = cbrt(sqrt_D - q);
final double v = - cbrt(sqrt_D + q);
pts[ off ] = (u + v);
num = 1;
if (within(D, 0.0d, 1e-8d)) {
pts[off+1] = -(pts[off] / 2.0d);
num = 2;
}
}
final double sub = (1.0d/3.0d) * a;
for (int i = 0; i < num; ++i) {
pts[ off+i ] -= sub;
}
return filterOutNotInAB(pts, off, num, A, B) - off;
}
static double evalCubic(final double a, final double b,
final double c, final double d,
final double t)
{
return t * (t * (t * a + b) + c) + d;
}
static double evalQuad(final double a, final double b,
final double c, final double t)
{
return t * (t * a + b) + c;
}
// returns the index 1 past the last valid element remaining after filtering
static int filterOutNotInAB(double[] nums, final int off, final int len,
final double a, final double b)
{
int ret = off;
for (int i = off, end = off + len; i < end; i++) {
if (nums[i] >= a && nums[i] < b) {
nums[ret++] = nums[i];
}
}
return ret;
}
static double linelen(double x1, double y1, double x2, double y2) {
final double dx = x2 - x1;
final double dy = y2 - y1;
return Math.sqrt(dx*dx + dy*dy);
}
static void subdivide(double[] src, int srcoff, double[] left, int leftoff,
double[] right, int rightoff, int type)
{
switch(type) {
case 6:
DHelpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff);
return;
case 8:
DHelpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
return;
default:
throw new InternalError("Unsupported curve type");
}
}
static void isort(double[] a, int off, int len) {
for (int i = off + 1, end = off + len; i < end; i++) {
double ai = a[i];
int j = i - 1;
for (; j >= off && a[j] > ai; j--) {
a[j+1] = a[j];
}
a[j+1] = ai;
}
}
// Most of these are copied from classes in java.awt.geom because we need
// both single and double precision variants of these functions, and Line2D,
// CubicCurve2D, QuadCurve2D don't provide them.
/**
* Subdivides the cubic curve specified by the coordinates
* stored in the src array at indices srcoff
* through (srcoff + 7) and stores the
* resulting two subdivided curves into the two result arrays at the
* corresponding indices.
* Either or both of the left and right
* arrays may be null or a reference to the same array
* as the src array.
* Note that the last point in the first subdivided curve is the
* same as the first point in the second subdivided curve. Thus,
* it is possible to pass the same array for left
* and right and to use offsets, such as rightoff
* equals (leftoff + 6), in order
* to avoid allocating extra storage for this common point.
* @param src the array holding the coordinates for the source curve
* @param srcoff the offset into the array of the beginning of the
* the 6 source coordinates
* @param left the array for storing the coordinates for the first
* half of the subdivided curve
* @param leftoff the offset into the array of the beginning of the
* the 6 left coordinates
* @param right the array for storing the coordinates for the second
* half of the subdivided curve
* @param rightoff the offset into the array of the beginning of the
* the 6 right coordinates
* @since 1.7
*/
static void subdivideCubic(double[] src, int srcoff,
double[] left, int leftoff,
double[] right, int rightoff)
{
double x1 = src[srcoff + 0];
double y1 = src[srcoff + 1];
double ctrlx1 = src[srcoff + 2];
double ctrly1 = src[srcoff + 3];
double ctrlx2 = src[srcoff + 4];
double ctrly2 = src[srcoff + 5];
double x2 = src[srcoff + 6];
double y2 = src[srcoff + 7];
if (left != null) {
left[leftoff + 0] = x1;
left[leftoff + 1] = y1;
}
if (right != null) {
right[rightoff + 6] = x2;
right[rightoff + 7] = y2;
}
x1 = (x1 + ctrlx1) / 2.0d;
y1 = (y1 + ctrly1) / 2.0d;
x2 = (x2 + ctrlx2) / 2.0d;
y2 = (y2 + ctrly2) / 2.0d;
double centerx = (ctrlx1 + ctrlx2) / 2.0d;
double centery = (ctrly1 + ctrly2) / 2.0d;
ctrlx1 = (x1 + centerx) / 2.0d;
ctrly1 = (y1 + centery) / 2.0d;
ctrlx2 = (x2 + centerx) / 2.0d;
ctrly2 = (y2 + centery) / 2.0d;
centerx = (ctrlx1 + ctrlx2) / 2.0d;
centery = (ctrly1 + ctrly2) / 2.0d;
if (left != null) {
left[leftoff + 2] = x1;
left[leftoff + 3] = y1;
left[leftoff + 4] = ctrlx1;
left[leftoff + 5] = ctrly1;
left[leftoff + 6] = centerx;
left[leftoff + 7] = centery;
}
if (right != null) {
right[rightoff + 0] = centerx;
right[rightoff + 1] = centery;
right[rightoff + 2] = ctrlx2;
right[rightoff + 3] = ctrly2;
right[rightoff + 4] = x2;
right[rightoff + 5] = y2;
}
}
static void subdivideCubicAt(double t, double[] src, int srcoff,
double[] left, int leftoff,
double[] right, int rightoff)
{
double x1 = src[srcoff + 0];
double y1 = src[srcoff + 1];
double ctrlx1 = src[srcoff + 2];
double ctrly1 = src[srcoff + 3];
double ctrlx2 = src[srcoff + 4];
double ctrly2 = src[srcoff + 5];
double x2 = src[srcoff + 6];
double y2 = src[srcoff + 7];
if (left != null) {
left[leftoff + 0] = x1;
left[leftoff + 1] = y1;
}
if (right != null) {
right[rightoff + 6] = x2;
right[rightoff + 7] = y2;
}
x1 = x1 + t * (ctrlx1 - x1);
y1 = y1 + t * (ctrly1 - y1);
x2 = ctrlx2 + t * (x2 - ctrlx2);
y2 = ctrly2 + t * (y2 - ctrly2);
double centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
double centery = ctrly1 + t * (ctrly2 - ctrly1);
ctrlx1 = x1 + t * (centerx - x1);
ctrly1 = y1 + t * (centery - y1);
ctrlx2 = centerx + t * (x2 - centerx);
ctrly2 = centery + t * (y2 - centery);
centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
centery = ctrly1 + t * (ctrly2 - ctrly1);
if (left != null) {
left[leftoff + 2] = x1;
left[leftoff + 3] = y1;
left[leftoff + 4] = ctrlx1;
left[leftoff + 5] = ctrly1;
left[leftoff + 6] = centerx;
left[leftoff + 7] = centery;
}
if (right != null) {
right[rightoff + 0] = centerx;
right[rightoff + 1] = centery;
right[rightoff + 2] = ctrlx2;
right[rightoff + 3] = ctrly2;
right[rightoff + 4] = x2;
right[rightoff + 5] = y2;
}
}
static void subdivideQuad(double[] src, int srcoff,
double[] left, int leftoff,
double[] right, int rightoff)
{
double x1 = src[srcoff + 0];
double y1 = src[srcoff + 1];
double ctrlx = src[srcoff + 2];
double ctrly = src[srcoff + 3];
double x2 = src[srcoff + 4];
double y2 = src[srcoff + 5];
if (left != null) {
left[leftoff + 0] = x1;
left[leftoff + 1] = y1;
}
if (right != null) {
right[rightoff + 4] = x2;
right[rightoff + 5] = y2;
}
x1 = (x1 + ctrlx) / 2.0d;
y1 = (y1 + ctrly) / 2.0d;
x2 = (x2 + ctrlx) / 2.0d;
y2 = (y2 + ctrly) / 2.0d;
ctrlx = (x1 + x2) / 2.0d;
ctrly = (y1 + y2) / 2.0d;
if (left != null) {
left[leftoff + 2] = x1;
left[leftoff + 3] = y1;
left[leftoff + 4] = ctrlx;
left[leftoff + 5] = ctrly;
}
if (right != null) {
right[rightoff + 0] = ctrlx;
right[rightoff + 1] = ctrly;
right[rightoff + 2] = x2;
right[rightoff + 3] = y2;
}
}
static void subdivideQuadAt(double t, double[] src, int srcoff,
double[] left, int leftoff,
double[] right, int rightoff)
{
double x1 = src[srcoff + 0];
double y1 = src[srcoff + 1];
double ctrlx = src[srcoff + 2];
double ctrly = src[srcoff + 3];
double x2 = src[srcoff + 4];
double y2 = src[srcoff + 5];
if (left != null) {
left[leftoff + 0] = x1;
left[leftoff + 1] = y1;
}
if (right != null) {
right[rightoff + 4] = x2;
right[rightoff + 5] = y2;
}
x1 = x1 + t * (ctrlx - x1);
y1 = y1 + t * (ctrly - y1);
x2 = ctrlx + t * (x2 - ctrlx);
y2 = ctrly + t * (y2 - ctrly);
ctrlx = x1 + t * (x2 - x1);
ctrly = y1 + t * (y2 - y1);
if (left != null) {
left[leftoff + 2] = x1;
left[leftoff + 3] = y1;
left[leftoff + 4] = ctrlx;
left[leftoff + 5] = ctrly;
}
if (right != null) {
right[rightoff + 0] = ctrlx;
right[rightoff + 1] = ctrly;
right[rightoff + 2] = x2;
right[rightoff + 3] = y2;
}
}
static void subdivideAt(double t, double[] src, int srcoff,
double[] left, int leftoff,
double[] right, int rightoff, int size)
{
switch(size) {
case 8:
subdivideCubicAt(t, src, srcoff, left, leftoff, right, rightoff);
return;
case 6:
subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
return;
}
}
// From sun.java2d.loops.GeneralRenderer:
static final int OUTCODE_TOP = 1;
static final int OUTCODE_BOTTOM = 2;
static final int OUTCODE_LEFT = 4;
static final int OUTCODE_RIGHT = 8;
static int outcode(final double x, final double y,
final double[] clipRect)
{
int code;
if (y < clipRect[0]) {
code = OUTCODE_TOP;
} else if (y >= clipRect[1]) {
code = OUTCODE_BOTTOM;
} else {
code = 0;
}
if (x < clipRect[2]) {
code |= OUTCODE_LEFT;
} else if (x >= clipRect[3]) {
code |= OUTCODE_RIGHT;
}
return code;
}
// 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;
// curves ref (dirty)
final DoubleArrayCache.Reference curves_ref;
// curveTypes ref (dirty)
final ByteArrayCache.Reference curveTypes_ref;
// used marks (stats only)
int curveTypesUseMark;
int curvesUseMark;
private final StatLong stat_polystack_types;
private final StatLong stat_polystack_curves;
private final Histogram hist_polystack_curves;
private final StatLong stat_array_polystack_curves;
private final StatLong stat_array_polystack_curveTypes;
PolyStack(final DRendererContext rdrCtx) {
this(rdrCtx, null, null, null, null, null);
}
PolyStack(final DRendererContext rdrCtx,
final StatLong stat_polystack_types,
final StatLong stat_polystack_curves,
final Histogram hist_polystack_curves,
final StatLong stat_array_polystack_curves,
final StatLong stat_array_polystack_curveTypes)
{
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;
}
this.stat_polystack_types = stat_polystack_types;
this.stat_polystack_curves = stat_polystack_curves;
this.hist_polystack_curves = hist_polystack_curves;
this.stat_array_polystack_curves = stat_array_polystack_curves;
this.stat_array_polystack_curveTypes = stat_array_polystack_curveTypes;
}
/**
* Disposes this PolyStack:
* clean up before reusing this instance
*/
void dispose() {
end = 0;
numCurves = 0;
if (DO_STATS) {
stat_polystack_types.add(curveTypesUseMark);
stat_polystack_curves.add(curvesUseMark);
hist_polystack_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) {
stat_array_polystack_curves.add(end + n);
}
curves = curves_ref.widenArray(curves, end, end + n);
}
if (curveTypes.length <= numCurves) {
if (DO_STATS) {
stat_array_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 pullAll(final DPathConsumer2D io) {
final int nc = numCurves;
if (nc == 0) {
return;
}
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 e = 0;
for (int i = 0; i < nc; i++) {
switch(_curveTypes[i]) {
case TYPE_LINETO:
io.lineTo(_curves[e], _curves[e+1]);
e += 2;
continue;
case TYPE_QUADTO:
io.quadTo(_curves[e+0], _curves[e+1],
_curves[e+2], _curves[e+3]);
e += 4;
continue;
case TYPE_CUBICTO:
io.curveTo(_curves[e+0], _curves[e+1],
_curves[e+2], _curves[e+3],
_curves[e+4], _curves[e+5]);
e += 6;
continue;
default:
}
}
numCurves = 0;
end = 0;
}
void popAll(final DPathConsumer2D io) {
int nc = numCurves;
if (nc == 0) {
return;
}
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 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;
}
}
}