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