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 *

 * 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.pisces;

import java.util.Arrays;

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;

final class Helpers {

    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 != 0f) {

            final float dis = b*b - 4*a*c;

            if (dis > 0) {

                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) {

                    zeroes[ret++] = (2 * c) / (-b - sqrtDis);

                    zeroes[ret++] = (-b - sqrtDis) / (2 * a);

                } else {

                    zeroes[ret++] = (-b + sqrtDis) / (2 * a);

                    zeroes[ret++] = (2 * c) / (-b + sqrtDis);

                }

            } else if (dis == 0f) {

                t = (-b) / (2 * a);

                zeroes[ret++] = t;

            }

        } else {

            if (b != 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) {

            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 = 1.0/3 * (-1.0/3 * sq_A + b);

        double q = 1.0/2 * (2.0/27 * a * sq_A - 1.0/3 * a * b + c);

        /* use Cardano's formula */

        double cb_p = p * p * p;

        double D = q * q + cb_p;

        int num;

        if (D < 0) {

            // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method

            final double phi = 1.0/3 * acos(-q / sqrt(-cb_p));

            final double t = 2 * sqrt(-p);

            pts[ off+0 ] =  (float)( t * cos(phi));

            pts[ off+1 ] =  (float)(-t * cos(phi + PI / 3));

            pts[ off+2 ] =  (float)(-t * cos(phi - PI / 3));

            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 ] = (float)(u + v);

            num = 1;

            if (within(D, 0, 1e-8)) {

                pts[off+1] = -(pts[off] / 2);

                num = 2;

            }

        }

        final float sub = 1.0f/3 * a;

        for (int i = 0; i < num; ++i) {

            pts[ off+i ] -= sub;

        }

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

    }

    // These use a hardcoded factor of 2 for increasing sizes. Perhaps this

    // should be provided as an argument.

    static float[] widenArray(float[] in, final int cursize, final int numToAdd) {

        if (in.length >= cursize + numToAdd) {

            return in;

        }

        return Arrays.copyOf(in, 2 * (cursize + numToAdd));

    }

    static int[] widenArray(int[] in, final int cursize, final int numToAdd) {

        if (in.length >= cursize + numToAdd) {

            return in;

        }

        return Arrays.copyOf(in, 2 * (cursize + numToAdd));

    }

    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; i < off + len; i++) {

            if (nums[i] >= a && nums[i] < b) {

                nums[ret++] = nums[i];

            }

        }

        return ret;

    }

    static float polyLineLength(float[] poly, final int off, final int nCoords) {

        assert nCoords % 2 == 0 && poly.length >= off + nCoords : "";

        float acc = 0;

        for (int i = off + 2; i < off + nCoords; i += 2) {

            acc += linelen(poly[i], poly[i+1], poly[i-2], poly[i-1]);

        }

        return acc;

    }

    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);

            break;

        case 8:

            Helpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);

            break;

        default:

            throw new InternalError("Unsupported curve type");

        }

    }

    static void isort(float[] a, int off, int len) {

        for (int i = off + 1; i < off + len; 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

    // float versions of these functions, and Line2D, CubicCurve2D,

    // QuadCurve2D don't provide them.

    /**

     * 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);

            break;

        case 6:

            subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);

            break;

        }

    }

}