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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 static java.lang.Math.PI;
import java.util.Arrays;
import sun.awt.geom.PathConsumer2D;
import sun.java2d.marlin.stats.Histogram;
import sun.java2d.marlin.stats.StatLong;

final class Helpers implements MarlinConst {

    private Helpers() {
        throw new Error("This is a non instantiable class");
    }

    static boolean within(final float x, final float y, final float err) {
        final float d = y - x;
        return (d <= err && d >= -err);
    }

    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 float a, final float b,
                              final float c, float[] zeroes, final int off)
    {
        int ret = off;
        float t;
        if (a != 0.0f) {
            final float dis = b*b - 4*a*c;
            if (dis > 0.0f) {
                final float sqrtDis = (float) 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 >= 0.0f) {
                    zeroes[ret++] = (2.0f * c) / (-b - sqrtDis);
                    zeroes[ret++] = (-b - sqrtDis) / (2.0f * a);
                } else {
                    zeroes[ret++] = (-b + sqrtDis) / (2.0f * a);
                    zeroes[ret++] = (2.0f * c) / (-b + sqrtDis);
                }
            } else if (dis == 0.0f) {
                t = (-b) / (2.0f * a);
                zeroes[ret++] = t;
            }
        } else {
            if (b != 0.0f) {
                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(float d, float a, float b, float c,
                              float[] pts, final int off,
                              final float A, final float B)
    {
        if (d == 0.0f) {
            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) * Math.acos(-q / Math.sqrt(-cb_p));
            final double t = 2.0d * Math.sqrt(-p);

            pts[ off+0 ] = (float) ( t * Math.cos(phi));
            pts[ off+1 ] = (float) (-t * Math.cos(phi + (PI / 3.0d)));
            pts[ off+2 ] = (float) (-t * Math.cos(phi - (PI / 3.0d)));
            num = 3;
        } else {
            final double sqrt_D = Math.sqrt(D);
            final double u =   Math.cbrt(sqrt_D - q);
            final double v = - Math.cbrt(sqrt_D + q);

            pts[ off ] = (float) (u + v);
            num = 1;

            if (within(D, 0.0d, 1e-8d)) {
                pts[off+1] = -(pts[off] / 2.0f);
                num = 2;
            }
        }

        final float sub = (1.0f/3.0f) * a;

        for (int i = 0; i < num; ++i) {
            pts[ off+i ] -= sub;
        }

        return filterOutNotInAB(pts, off, num, A, B) - off;
    }

    static float evalCubic(final float a, final float b,
                           final float c, final float d,
                           final float t)
    {
        return t * (t * (t * a + b) + c) + d;
    }

    static float evalQuad(final float a, final float b,
                          final float c, final float t)
    {
        return t * (t * a + b) + c;
    }

    // returns the index 1 past the last valid element remaining after filtering
    static int filterOutNotInAB(float[] nums, final int off, final int len,
                                final float a, final float 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 float linelen(float x1, float y1, float x2, float y2) {
        final float dx = x2 - x1;
        final float dy = y2 - y1;
        return (float) Math.sqrt(dx*dx + dy*dy);
    }

    static void subdivide(float[] src, int srcoff, float[] left, int leftoff,
                          float[] right, int rightoff, int type)
    {
        switch(type) {
        case 6:
            Helpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff);
            return;
        case 8:
            Helpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
            return;
        default:
            throw new InternalError("Unsupported curve type");
        }
    }

    static void isort(float[] a, int off, int len) {
        for (int i = off + 1, end = off + len; i < end; i++) {
            float 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.
Params:
  • src – the array holding the coordinates for the source curve
  • srcoff – the offset into the array of the beginning of the the 6 source coordinates
  • left – the array for storing the coordinates for the first half of the subdivided curve
  • leftoff – the offset into the array of the beginning of the the 6 left coordinates
  • right – the array for storing the coordinates for the second half of the subdivided curve
  • rightoff – the offset into the array of the beginning of the the 6 right coordinates
Since:1.7
/** * Subdivides the cubic curve specified by the coordinates * stored in the <code>src</code> array at indices <code>srcoff</code> * through (<code>srcoff</code>&nbsp;+&nbsp;7) and stores the * resulting two subdivided curves into the two result arrays at the * corresponding indices. * Either or both of the <code>left</code> and <code>right</code> * arrays may be <code>null</code> or a reference to the same array * as the <code>src</code> 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 <code>left</code> * and <code>right</code> and to use offsets, such as <code>rightoff</code> * equals (<code>leftoff</code> + 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(float[] src, int srcoff, float[] left, int leftoff, float[] right, int rightoff) { float x1 = src[srcoff + 0]; float y1 = src[srcoff + 1]; float ctrlx1 = src[srcoff + 2]; float ctrly1 = src[srcoff + 3]; float ctrlx2 = src[srcoff + 4]; float ctrly2 = src[srcoff + 5]; float x2 = src[srcoff + 6]; float 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) / 2.0f; y1 = (y1 + ctrly1) / 2.0f; x2 = (x2 + ctrlx2) / 2.0f; y2 = (y2 + ctrly2) / 2.0f; float centerx = (ctrlx1 + ctrlx2) / 2.0f; float centery = (ctrly1 + ctrly2) / 2.0f; ctrlx1 = (x1 + centerx) / 2.0f; ctrly1 = (y1 + centery) / 2.0f; ctrlx2 = (x2 + centerx) / 2.0f; ctrly2 = (y2 + centery) / 2.0f; centerx = (ctrlx1 + ctrlx2) / 2.0f; centery = (ctrly1 + ctrly2) / 2.0f; 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(float t, float[] src, int srcoff, float[] left, int leftoff, float[] right, int rightoff) { float x1 = src[srcoff + 0]; float y1 = src[srcoff + 1]; float ctrlx1 = src[srcoff + 2]; float ctrly1 = src[srcoff + 3]; float ctrlx2 = src[srcoff + 4]; float ctrly2 = src[srcoff + 5]; float x2 = src[srcoff + 6]; float 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); float centerx = ctrlx1 + t * (ctrlx2 - ctrlx1); float 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(float[] src, int srcoff, float[] left, int leftoff, float[] right, int rightoff) { float x1 = src[srcoff + 0]; float y1 = src[srcoff + 1]; float ctrlx = src[srcoff + 2]; float ctrly = src[srcoff + 3]; float x2 = src[srcoff + 4]; float 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) / 2.0f; y1 = (y1 + ctrly) / 2.0f; x2 = (x2 + ctrlx) / 2.0f; y2 = (y2 + ctrly) / 2.0f; ctrlx = (x1 + x2) / 2.0f; ctrly = (y1 + y2) / 2.0f; 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(float t, float[] src, int srcoff, float[] left, int leftoff, float[] right, int rightoff) { float x1 = src[srcoff + 0]; float y1 = src[srcoff + 1]; float ctrlx = src[srcoff + 2]; float ctrly = src[srcoff + 3]; float x2 = src[srcoff + 4]; float 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(float t, float[] src, int srcoff, float[] left, int leftoff, float[] 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 int outcode(final float x, final float y, final float[] 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; float[] curves; int end; byte[] curveTypes; int numCurves; // curves ref (dirty) final FloatArrayCache.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 RendererContext rdrCtx) { this(rdrCtx, null, null, null, null, null); } PolyStack(final RendererContext 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.newDirtyFloatArrayRef(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
/** * 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(float x0, float y0, float x1, float y1, float x2, float y2) { ensureSpace(6); curveTypes[numCurves++] = TYPE_CUBICTO; // we reverse the coordinate order to make popping easier final float[] _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(float x0, float y0, float x1, float y1) { ensureSpace(4); curveTypes[numCurves++] = TYPE_QUADTO; final float[] _curves = curves; int e = end; _curves[e++] = x1; _curves[e++] = y1; _curves[e++] = x0; _curves[e++] = y0; end = e; } void pushLine(float x, float y) { ensureSpace(2); curveTypes[numCurves++] = TYPE_LINETO; curves[end++] = x; curves[end++] = y; } void pullAll(final PathConsumer2D 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 float[] _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 PathConsumer2D 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 float[] _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; } } // a stack of integer indices static final class IndexStack { // integer capacity = edges count / 4 ~ 1024 private static final int INITIAL_COUNT = INITIAL_EDGES_COUNT >> 2; private int end; private int[] indices; // indices ref (dirty) private final IntArrayCache.Reference indices_ref; // used marks (stats only) private int indicesUseMark; private final StatLong stat_idxstack_indices; private final Histogram hist_idxstack_indices; private final StatLong stat_array_idxstack_indices; IndexStack(final RendererContext rdrCtx) { this(rdrCtx, null, null, null); } IndexStack(final RendererContext rdrCtx, final StatLong stat_idxstack_indices, final Histogram hist_idxstack_indices, final StatLong stat_array_idxstack_indices) { indices_ref = rdrCtx.newDirtyIntArrayRef(INITIAL_COUNT); // 4K indices = indices_ref.initial; end = 0; if (DO_STATS) { indicesUseMark = 0; } this.stat_idxstack_indices = stat_idxstack_indices; this.hist_idxstack_indices = hist_idxstack_indices; this.stat_array_idxstack_indices = stat_array_idxstack_indices; }
Disposes this PolyStack: clean up before reusing this instance
/** * Disposes this PolyStack: * clean up before reusing this instance */
void dispose() { end = 0; if (DO_STATS) { stat_idxstack_indices.add(indicesUseMark); hist_idxstack_indices.add(indicesUseMark); // reset marks indicesUseMark = 0; } // Return arrays: // values is kept dirty indices = indices_ref.putArray(indices); } boolean isEmpty() { return (end == 0); } void reset() { end = 0; } void push(final int v) { // remove redundant values (reverse order): int[] _values = indices; final int nc = end; if (nc != 0) { if (_values[nc - 1] == v) { // remove both duplicated values: end--; return; } } if (_values.length <= nc) { if (DO_STATS) { stat_array_idxstack_indices.add(nc + 1); } indices = _values = indices_ref.widenArray(_values, nc, nc + 1); } _values[end++] = v; if (DO_STATS) { // update used marks: if (end > indicesUseMark) { indicesUseMark = end; } } } void pullAll(final float[] points, final PathConsumer2D io) { final int nc = end; if (nc == 0) { return; } final int[] _values = indices; for (int i = 0, j; i < nc; i++) { j = _values[i] << 1; io.lineTo(points[j], points[j + 1]); } end = 0; } } }