| /* |
| * 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; |
| } |
| } |
