/*
 * Copyright (c) 2007, 2015, 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;

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 != 0f) {
            final float dis = b*b - 4*a*c;
            if (dis > 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 >= 0f) {
                    zeroes[ret++] = (2f * c) / (-b - sqrtDis);
                    zeroes[ret++] = (-b - sqrtDis) / (2f * a);
                } else {
                    zeroes[ret++] = (-b + sqrtDis) / (2f * a);
                    zeroes[ret++] = (2f * c) / (-b + sqrtDis);
                }
            } else if (dis == 0f) {
                t = (-b) / (2f * 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 == 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 = (1.0/3.0) * ((-1.0/3.0) * sq_A + b);
        double q = (1.0/2.0) * ((2.0/27.0) * a * sq_A - (1.0/3.0) * a * b + c);

        // use Cardano's formula

        double cb_p = p * p * p;
        double D = q * q + cb_p;

        int num;
        if (D < 0.0) {
            // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
            final double phi = (1.0/3.0) * acos(-q / sqrt(-cb_p));
            final double t = 2.0 * sqrt(-p);

            pts[ off+0 ] =  (float)( t * cos(phi));
            pts[ off+1 ] =  (float)(-t * cos(phi + (PI / 3.0)));
            pts[ off+2 ] =  (float)(-t * cos(phi - (PI / 3.0)));
            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, 0.0, 1e-8)) {
                pts[off+1] = -(pts[off] / 2f);
                num = 2;
            }
        }

        final float sub = (1f/3f) * 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 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);
            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
    // float versions 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) / 2f;
        y1 = (y1 + ctrly1) / 2f;
        x2 = (x2 + ctrlx2) / 2f;
        y2 = (y2 + ctrly2) / 2f;
        float centerx = (ctrlx1 + ctrlx2) / 2f;
        float centery = (ctrly1 + ctrly2) / 2f;
        ctrlx1 = (x1 + centerx) / 2f;
        ctrly1 = (y1 + centery) / 2f;
        ctrlx2 = (x2 + centerx) / 2f;
        ctrly2 = (y2 + centery) / 2f;
        centerx = (ctrlx1 + ctrlx2) / 2f;
        centery = (ctrly1 + ctrly2) / 2f;
        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) / 2f;
        y1 = (y1 + ctrly) / 2f;
        x2 = (x2 + ctrlx) / 2f;
        y2 = (y2 + ctrly) / 2f;
        ctrlx = (x1 + x2) / 2f;
        ctrly = (y1 + y2) / 2f;
        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;
        }
    }
}