/* * Copyright (c) 1997, 2003, 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 * or visit www.oracle.com if you need additional information or have any * questions. */ package java.awt.geom; import java.util.*; /** * A utility class to iterate over the path segments of an arc * through the PathIterator interface. * * @author      Jim Graham */class ArcIterator implements PathIterator {    double x, y, w, h, angStRad, increment, cv;    AffineTransform affine;    int index;    int arcSegs;    int lineSegs;     ArcIterator(Arc2D a, AffineTransform at) {        this.w = a.getWidth() / 2;        this.h = a.getHeight() / 2;        this.x = a.getX() + w;        this.y = a.getY() + h;        this.angStRad = -Math.toRadians(a.getAngleStart());        this.affine = at;        double ext = -a.getAngleExtent();        if (ext >= 360.0 || ext <= -360) {            arcSegs = 4;            this.increment = Math.PI / 2;            // btan(Math.PI / 2);            this.cv = 0.5522847498307933;            if (ext < 0) {                increment = -increment;                cv = -cv;            }        } else {            arcSegs = (int) Math.ceil(Math.abs(ext) / 90.0);            this.increment = Math.toRadians(ext / arcSegs);            this.cv = btan(increment);            if (cv == 0) {                arcSegs = 0;            }        }        switch (a.getArcType()) {        case Arc2D.OPEN:            lineSegs = 0;            break;        case Arc2D.CHORD:            lineSegs = 1;            break;        case Arc2D.PIE:            lineSegs = 2;            break;        }        if (w < 0 || h < 0) {            arcSegs = lineSegs = -1;        }    }     /**     * Return the winding rule for determining the insideness of the     * path.     * @see #WIND_EVEN_ODD     * @see #WIND_NON_ZERO     */    public int getWindingRule() {        return WIND_NON_ZERO;    }     /**     * Tests if there are more points to read.     * @return true if there are more points to read     */    public boolean isDone() {        return index > arcSegs + lineSegs;    }     /**     * Moves the iterator to the next segment of the path forwards     * along the primary direction of traversal as long as there are     * more points in that direction.     */    public void next() {        index++;    }     /*     * btan computes the length (k) of the control segments at     * the beginning and end of a cubic bezier that approximates     * a segment of an arc with extent less than or equal to     * 90 degrees.  This length (k) will be used to generate the     * 2 bezier control points for such a segment.     *     *   Assumptions:     *     a) arc is centered on 0,0 with radius of 1.0     *     b) arc extent is less than 90 degrees     *     c) control points should preserve tangent     *     d) control segments should have equal length     *     *   Initial data:     *     start angle: ang1     *     end angle:   ang2 = ang1 + extent     *     start point: P1 = (x1, y1) = (cos(ang1), sin(ang1))     *     end point:   P4 = (x4, y4) = (cos(ang2), sin(ang2))     *     *   Control points:     *     P2 = (x2, y2)     *     | x2 = x1 - k * sin(ang1) = cos(ang1) - k * sin(ang1)     *     | y2 = y1 + k * cos(ang1) = sin(ang1) + k * cos(ang1)     *     *     P3 = (x3, y3)     *     | x3 = x4 + k * sin(ang2) = cos(ang2) + k * sin(ang2)     *     | y3 = y4 - k * cos(ang2) = sin(ang2) - k * cos(ang2)     *     * The formula for this length (k) can be found using the     * following derivations:     *     *   Midpoints:     *     a) bezier (t = 1/2)     *        bPm = P1 * (1-t)^3 +     *              3 * P2 * t * (1-t)^2 +     *              3 * P3 * t^2 * (1-t) +     *              P4 * t^3 =     *            = (P1 + 3P2 + 3P3 + P4)/8     *     *     b) arc     *        aPm = (cos((ang1 + ang2)/2), sin((ang1 + ang2)/2))     *     *   Let angb = (ang2 - ang1)/2; angb is half of the angle     *   between ang1 and ang2.     *     *   Solve the equation bPm == aPm     *     *     a) For xm coord:     *        x1 + 3*x2 + 3*x3 + x4 = 8*cos((ang1 + ang2)/2)     *     *        cos(ang1) + 3*cos(ang1) - 3*k*sin(ang1) +     *        3*cos(ang2) + 3*k*sin(ang2) + cos(ang2) =     *        = 8*cos((ang1 + ang2)/2)     *     *        4*cos(ang1) + 4*cos(ang2) + 3*k*(sin(ang2) - sin(ang1)) =     *        = 8*cos((ang1 + ang2)/2)     *     *        8*cos((ang1 + ang2)/2)*cos((ang2 - ang1)/2) +     *        6*k*sin((ang2 - ang1)/2)*cos((ang1 + ang2)/2) =     *        = 8*cos((ang1 + ang2)/2)     *     *        4*cos(angb) + 3*k*sin(angb) = 4     *     *        k = 4 / 3 * (1 - cos(angb)) / sin(angb)     *     *     b) For ym coord we derive the same formula.     *     * Since this formula can generate "NaN" values for small     * angles, we will derive a safer form that does not involve     * dividing by very small values:     *     (1 - cos(angb)) / sin(angb) =     *     = (1 - cos(angb))*(1 + cos(angb)) / sin(angb)*(1 + cos(angb)) =     *     = (1 - cos(angb)^2) / sin(angb)*(1 + cos(angb)) =     *     = sin(angb)^2 / sin(angb)*(1 + cos(angb)) =     *     = sin(angb) / (1 + cos(angb))     *     */    private static double btan(double increment) {        increment /= 2.0;        return 4.0 / 3.0 * Math.sin(increment) / (1.0 + Math.cos(increment));    }     /**     * Returns the coordinates and type of the current path segment in     * the iteration.     * The return value is the path segment type:     * SEG_MOVETO, SEG_LINETO, SEG_QUADTO, SEG_CUBICTO, or SEG_CLOSE.     * A float array of length 6 must be passed in and may be used to     * store the coordinates of the point(s).     * Each point is stored as a pair of float x,y coordinates.     * SEG_MOVETO and SEG_LINETO types will return one point,     * SEG_QUADTO will return two points,     * SEG_CUBICTO will return 3 points     * and SEG_CLOSE will not return any points.     * @see #SEG_MOVETO     * @see #SEG_LINETO     * @see #SEG_QUADTO     * @see #SEG_CUBICTO     * @see #SEG_CLOSE     */    public int currentSegment(float[] coords) {        if (isDone()) {            throw new NoSuchElementException("arc iterator out of bounds");        }        double angle = angStRad;        if (index == 0) {            coords[0] = (float) (x + Math.cos(angle) * w);            coords[1] = (float) (y + Math.sin(angle) * h);            if (affine != null) {                affine.transform(coords, 0, coords, 0, 1);            }            return SEG_MOVETO;        }        if (index > arcSegs) {            if (index == arcSegs + lineSegs) {                return SEG_CLOSE;            }            coords[0] = (float) x;            coords[1] = (float) y;            if (affine != null) {                affine.transform(coords, 0, coords, 0, 1);            }            return SEG_LINETO;        }        angle += increment * (index - 1);        double relx = Math.cos(angle);        double rely = Math.sin(angle);        coords[0] = (float) (x + (relx - cv * rely) * w);        coords[1] = (float) (y + (rely + cv * relx) * h);        angle += increment;        relx = Math.cos(angle);        rely = Math.sin(angle);        coords[2] = (float) (x + (relx + cv * rely) * w);        coords[3] = (float) (y + (rely - cv * relx) * h);        coords[4] = (float) (x + relx * w);        coords[5] = (float) (y + rely * h);        if (affine != null) {            affine.transform(coords, 0, coords, 0, 3);        }        return SEG_CUBICTO;    }     /**     * Returns the coordinates and type of the current path segment in     * the iteration.     * The return value is the path segment type:     * SEG_MOVETO, SEG_LINETO, SEG_QUADTO, SEG_CUBICTO, or SEG_CLOSE.     * A double array of length 6 must be passed in and may be used to     * store the coordinates of the point(s).     * Each point is stored as a pair of double x,y coordinates.     * SEG_MOVETO and SEG_LINETO types will return one point,     * SEG_QUADTO will return two points,     * SEG_CUBICTO will return 3 points     * and SEG_CLOSE will not return any points.     * @see #SEG_MOVETO     * @see #SEG_LINETO     * @see #SEG_QUADTO     * @see #SEG_CUBICTO     * @see #SEG_CLOSE     */    public int currentSegment(double[] coords) {        if (isDone()) {            throw new NoSuchElementException("arc iterator out of bounds");        }        double angle = angStRad;        if (index == 0) {            coords[0] = x + Math.cos(angle) * w;            coords[1] = y + Math.sin(angle) * h;            if (affine != null) {                affine.transform(coords, 0, coords, 0, 1);            }            return SEG_MOVETO;        }        if (index > arcSegs) {            if (index == arcSegs + lineSegs) {                return SEG_CLOSE;            }            coords[0] = x;            coords[1] = y;            if (affine != null) {                affine.transform(coords, 0, coords, 0, 1);            }            return SEG_LINETO;        }        angle += increment * (index - 1);        double relx = Math.cos(angle);        double rely = Math.sin(angle);        coords[0] = x + (relx - cv * rely) * w;        coords[1] = y + (rely + cv * relx) * h;        angle += increment;        relx = Math.cos(angle);        rely = Math.sin(angle);        coords[2] = x + (relx + cv * rely) * w;        coords[3] = y + (rely - cv * relx) * h;        coords[4] = x + relx * w;        coords[5] = y + rely * h;        if (affine != null) {            affine.transform(coords, 0, coords, 0, 3);        }        return SEG_CUBICTO;    }}