1. /*

  2.  * @(#)ArcIterator.java	1.16 03/12/19

  3.  *

  4.  * Copyright 2004 Sun Microsystems, Inc. All rights reserved.

  5.  * SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.

  6.  */

  7. 

  8. package java.awt.geom;

  9. 

  10. import java.util.*;

  11. 

  12. /**

  13.  * A utility class to iterate over the path segments of an arc

  14.  * through the PathIterator interface.

  15.  *

  16.  * @version 10 Feb 1997

  17.  * @author	Jim Graham

  18.  */

  19. class ArcIterator implements PathIterator {

  20.     double x, y, w, h, angStRad, increment, cv;

  21.     AffineTransform affine;

  22.     int index;

  23.     int arcSegs;

  24.     int lineSegs;

  25. 

  26.     ArcIterator(Arc2D a, AffineTransform at) {

  27. 	this.w = a.getWidth() / 2;

  28. 	this.h = a.getHeight() / 2;

  29. 	this.x = a.getX() + w;

  30. 	this.y = a.getY() + h;

  31. 	this.angStRad = -Math.toRadians(a.getAngleStart());

  32. 	this.affine = at;

  33. 	double ext = -a.getAngleExtent();

  34. 	if (ext >= 360.0 || ext <= -360) {

  35. 	    arcSegs = 4;

  36. 	    this.increment = Math.PI / 2;

  37. 	    // btan(Math.PI / 2);

  38. 	    this.cv = 0.5522847498307933;

  39. 	    if (ext < 0) {

  40. 		increment = -increment;

  41. 		cv = -cv;

  42. 	    }

  43. 	} else {

  44. 	    arcSegs = (int) Math.ceil(Math.abs(ext) / 90.0);

  45. 	    this.increment = Math.toRadians(ext / arcSegs);

  46. 	    this.cv = btan(increment);

  47. 	    if (cv == 0) {

  48. 		arcSegs = 0;

  49. 	    }

  50. 	}

  51. 	switch (a.getArcType()) {

  52. 	case Arc2D.OPEN:

  53. 	    lineSegs = 0;

  54. 	    break;

  55. 	case Arc2D.CHORD:

  56. 	    lineSegs = 1;

  57. 	    break;

  58. 	case Arc2D.PIE:

  59. 	    lineSegs = 2;

  60. 	    break;

  61. 	}

  62. 	if (w < 0 || h < 0) {

  63. 	    arcSegs = lineSegs = -1;

  64. 	}

  65.     }

  66. 

  67.     /**

  68.      * Return the winding rule for determining the insideness of the

  69.      * path.

  70.      * @see #WIND_EVEN_ODD

  71.      * @see #WIND_NON_ZERO

  72.      */

  73.     public int getWindingRule() {

  74. 	return WIND_NON_ZERO;

  75.     }

  76. 

  77.     /**

  78.      * Tests if there are more points to read.

  79.      * @return true if there are more points to read

  80.      */

  81.     public boolean isDone() {

  82. 	return index > arcSegs + lineSegs;

  83.     }

  84. 

  85.     /**

  86.      * Moves the iterator to the next segment of the path forwards

  87.      * along the primary direction of traversal as long as there are

  88.      * more points in that direction.

  89.      */

  90.     public void next() {

  91. 	index++;

  92.     }

  93. 

  94.     /*

  95.      * btan computes the length (k) of the control segments at

  96.      * the beginning and end of a cubic bezier that approximates

  97.      * a segment of an arc with extent less than or equal to

  98.      * 90 degrees.  This length (k) will be used to generate the

  99.      * 2 bezier control points for such a segment.

  100.      *

  101.      *   Assumptions:

  102.      *     a) arc is centered on 0,0 with radius of 1.0

  103.      *     b) arc extent is less than 90 degrees

  104.      *     c) control points should preserve tangent

  105.      *     d) control segments should have equal length

  106.      *

  107.      *   Initial data:

  108.      *     start angle: ang1

  109.      *     end angle:   ang2 = ang1 + extent

  110.      *     start point: P1 = (x1, y1) = (cos(ang1), sin(ang1))

  111.      *     end point:   P4 = (x4, y4) = (cos(ang2), sin(ang2))

  112.      *

  113.      *   Control points:

  114.      *     P2 = (x2, y2)

  115.      *     | x2 = x1 - k * sin(ang1) = cos(ang1) - k * sin(ang1)

  116.      *     | y2 = y1 + k * cos(ang1) = sin(ang1) + k * cos(ang1)

  117.      *

  118.      *     P3 = (x3, y3)

  119.      *     | x3 = x4 + k * sin(ang2) = cos(ang2) + k * sin(ang2)

  120.      *     | y3 = y4 - k * cos(ang2) = sin(ang2) - k * cos(ang2)

  121.      *

  122.      * The formula for this length (k) can be found using the

  123.      * following derivations:

  124.      *

  125.      *   Midpoints:

  126.      *     a) bezier (t = 1/2)

  127.      *        bPm = P1 * (1-t)^3 +

  128.      *              3 * P2 * t * (1-t)^2 + 

  129.      *              3 * P3 * t^2 * (1-t) +

  130.      *              P4 * t^3 =

  131.      *            = (P1 + 3P2 + 3P3 + P4)/8

  132.      *

  133.      *     b) arc

  134.      *        aPm = (cos((ang1 + ang2)/2), sin((ang1 + ang2)/2))

  135.      *

  136.      *   Let angb = (ang2 - ang1)/2; angb is half of the angle

  137.      *   between ang1 and ang2.

  138.      *

  139.      *   Solve the equation bPm == aPm

  140.      *

  141.      *     a) For xm coord:

  142.      *        x1 + 3*x2 + 3*x3 + x4 = 8*cos((ang1 + ang2)/2)

  143.      *

  144.      *        cos(ang1) + 3*cos(ang1) - 3*k*sin(ang1) +

  145.      *        3*cos(ang2) + 3*k*sin(ang2) + cos(ang2) =

  146.      *        = 8*cos((ang1 + ang2)/2)

  147.      *

  148.      *        4*cos(ang1) + 4*cos(ang2) + 3*k*(sin(ang2) - sin(ang1)) =

  149.      *        = 8*cos((ang1 + ang2)/2)

  150.      *

  151.      *        8*cos((ang1 + ang2)/2)*cos((ang2 - ang1)/2) +

  152.      *        6*k*sin((ang2 - ang1)/2)*cos((ang1 + ang2)/2) =

  153.      *        = 8*cos((ang1 + ang2)/2)

  154.      *

  155.      *        4*cos(angb) + 3*k*sin(angb) = 4

  156.      *

  157.      *        k = 4 / 3 * (1 - cos(angb)) / sin(angb)

  158.      *

  159.      *     b) For ym coord we derive the same formula.

  160.      *

  161.      * Since this formula can generate "NaN" values for small

  162.      * angles, we will derive a safer form that does not involve

  163.      * dividing by very small values:

  164.      *     (1 - cos(angb)) / sin(angb) =

  165.      *     = (1 - cos(angb))*(1 + cos(angb)) / sin(angb)*(1 + cos(angb)) =

  166.      *     = (1 - cos(angb)^2) / sin(angb)*(1 + cos(angb)) =

  167.      *     = sin(angb)^2 / sin(angb)*(1 + cos(angb)) =

  168.      *     = sin(angb) / (1 + cos(angb))

  169.      *

  170.      */

  171.     private static double btan(double increment) {

  172. 	increment /= 2.0;

  173. 	return 4.0 / 3.0 * Math.sin(increment) / (1.0 + Math.cos(increment));

  174.     }

  175. 

  176.     /**

  177.      * Returns the coordinates and type of the current path segment in

  178.      * the iteration.

  179.      * The return value is the path segment type:

  180.      * SEG_MOVETO, SEG_LINETO, SEG_QUADTO, SEG_CUBICTO, or SEG_CLOSE.

  181.      * A float array of length 6 must be passed in and may be used to

  182.      * store the coordinates of the point(s).

  183.      * Each point is stored as a pair of float x,y coordinates.

  184.      * SEG_MOVETO and SEG_LINETO types will return one point,

  185.      * SEG_QUADTO will return two points,

  186.      * SEG_CUBICTO will return 3 points

  187.      * and SEG_CLOSE will not return any points.

  188.      * @see #SEG_MOVETO

  189.      * @see #SEG_LINETO

  190.      * @see #SEG_QUADTO

  191.      * @see #SEG_CUBICTO

  192.      * @see #SEG_CLOSE

  193.      */

  194.     public int currentSegment(float[] coords) {

  195. 	if (isDone()) {

  196. 	    throw new NoSuchElementException("arc iterator out of bounds");

  197. 	}

  198. 	double angle = angStRad;

  199. 	if (index == 0) {

  200. 	    coords[0] = (float) (x + Math.cos(angle) * w);

  201. 	    coords[1] = (float) (y + Math.sin(angle) * h);

  202. 	    if (affine != null) {

  203. 		affine.transform(coords, 0, coords, 0, 1);

  204. 	    }

  205. 	    return SEG_MOVETO;

  206. 	}

  207. 	if (index > arcSegs) {

  208. 	    if (index == arcSegs + lineSegs) {

  209. 		return SEG_CLOSE;

  210. 	    }

  211. 	    coords[0] = (float) x;

  212. 	    coords[1] = (float) y;

  213. 	    if (affine != null) {

  214. 		affine.transform(coords, 0, coords, 0, 1);

  215. 	    }

  216. 	    return SEG_LINETO;

  217. 	}

  218. 	angle += increment * (index - 1);

  219. 	double relx = Math.cos(angle);

  220. 	double rely = Math.sin(angle);

  221. 	coords[0] = (float) (x + (relx - cv * rely) * w);

  222. 	coords[1] = (float) (y + (rely + cv * relx) * h);

  223. 	angle += increment;

  224. 	relx = Math.cos(angle);

  225. 	rely = Math.sin(angle);

  226. 	coords[2] = (float) (x + (relx + cv * rely) * w);

  227. 	coords[3] = (float) (y + (rely - cv * relx) * h);

  228. 	coords[4] = (float) (x + relx * w);

  229. 	coords[5] = (float) (y + rely * h);

  230. 	if (affine != null) {

  231. 	    affine.transform(coords, 0, coords, 0, 3);

  232. 	}

  233. 	return SEG_CUBICTO;

  234.     }

  235. 

  236.     /**

  237.      * Returns the coordinates and type of the current path segment in

  238.      * the iteration.

  239.      * The return value is the path segment type:

  240.      * SEG_MOVETO, SEG_LINETO, SEG_QUADTO, SEG_CUBICTO, or SEG_CLOSE.

  241.      * A double array of length 6 must be passed in and may be used to

  242.      * store the coordinates of the point(s).

  243.      * Each point is stored as a pair of double x,y coordinates.

  244.      * SEG_MOVETO and SEG_LINETO types will return one point,

  245.      * SEG_QUADTO will return two points,

  246.      * SEG_CUBICTO will return 3 points

  247.      * and SEG_CLOSE will not return any points.

  248.      * @see #SEG_MOVETO

  249.      * @see #SEG_LINETO

  250.      * @see #SEG_QUADTO

  251.      * @see #SEG_CUBICTO

  252.      * @see #SEG_CLOSE

  253.      */

  254.     public int currentSegment(double[] coords) {

  255. 	if (isDone()) {

  256. 	    throw new NoSuchElementException("arc iterator out of bounds");

  257. 	}

  258. 	double angle = angStRad;

  259. 	if (index == 0) {

  260. 	    coords[0] = x + Math.cos(angle) * w;

  261. 	    coords[1] = y + Math.sin(angle) * h;

  262. 	    if (affine != null) {

  263. 		affine.transform(coords, 0, coords, 0, 1);

  264. 	    }

  265. 	    return SEG_MOVETO;

  266. 	}

  267. 	if (index > arcSegs) {

  268. 	    if (index == arcSegs + lineSegs) {

  269. 		return SEG_CLOSE;

  270. 	    }

  271. 	    coords[0] = x;

  272. 	    coords[1] = y;

  273. 	    if (affine != null) {

  274. 		affine.transform(coords, 0, coords, 0, 1);

  275. 	    }

  276. 	    return SEG_LINETO;

  277. 	}

  278. 	angle += increment * (index - 1);

  279. 	double relx = Math.cos(angle);

  280. 	double rely = Math.sin(angle);

  281. 	coords[0] = x + (relx - cv * rely) * w;

  282. 	coords[1] = y + (rely + cv * relx) * h;

  283. 	angle += increment;

  284. 	relx = Math.cos(angle);

  285. 	rely = Math.sin(angle);

  286. 	coords[2] = x + (relx + cv * rely) * w;

  287. 	coords[3] = y + (rely - cv * relx) * h;

  288. 	coords[4] = x + relx * w;

  289. 	coords[5] = y + rely * h;

  290. 	if (affine != null) {

  291. 	    affine.transform(coords, 0, coords, 0, 3);

  292. 	}

  293. 	return SEG_CUBICTO;

  294.     }

  295. }