src/java.desktop/share/classes/sun/java2d/pisces/Helpers.java - platform/libcore - Gitiles

 /*
  * Copyright (c) 2007, 2011, 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 sun.java2d.pisces;

 import java.util.Arrays;
 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 {
     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 > 0) {
                 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 >= 0) {
                     zeroes[ret++] = (2 * c) / (-b - sqrtDis);
                     zeroes[ret++] = (-b - sqrtDis) / (2 * a);
                 } else {
                     zeroes[ret++] = (-b + sqrtDis) / (2 * a);
                     zeroes[ret++] = (2 * c) / (-b + sqrtDis);
                 }
             } else if (dis == 0f) {
                 t = (-b) / (2 * 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 == 0) {
             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 * (-1.0/3 * sq_A + b);
         double q = 1.0/2 * (2.0/27 * a * sq_A - 1.0/3 * a * b + c);

         /* use Cardano's formula */

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

         int num;
         if (D < 0) {
             // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
             final double phi = 1.0/3 * acos(-q / sqrt(-cb_p));
             final double t = 2 * sqrt(-p);

             pts[ off+0 ] =  (float)( t * cos(phi));
             pts[ off+1 ] =  (float)(-t * cos(phi + PI / 3));
             pts[ off+2 ] =  (float)(-t * cos(phi - PI / 3));
             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, 1e-8)) {
                 pts[off+1] = -(pts[off] / 2);
                 num = 2;
             }
         }

         final float sub = 1.0f/3 * a;

         for (int i = 0; i < num; ++i) {
             pts[ off+i ] -= sub;
         }

         return filterOutNotInAB(pts, off, num, A, B) - off;
     }

     // These use a hardcoded factor of 2 for increasing sizes. Perhaps this
     // should be provided as an argument.
     static float[] widenArray(float[] in, final int cursize, final int numToAdd) {
         if (in.length >= cursize + numToAdd) {
             return in;
         }
         return Arrays.copyOf(in, 2 * (cursize + numToAdd));
     }

     static int[] widenArray(int[] in, final int cursize, final int numToAdd) {
         if (in.length >= cursize + numToAdd) {
             return in;
         }
         return Arrays.copyOf(in, 2 * (cursize + numToAdd));
     }

     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; i < off + len; 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);
             break;
         case 8:
             Helpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
             break;
         default:
             throw new InternalError("Unsupported curve type");
         }
     }

     static void isort(float[] a, int off, int len) {
         for (int i = off + 1; i < off + len; 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 {@code src} array at indices {@code srcoff}
      * through ({@code srcoff}&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} and {@code right}
      * arrays may be {@code null} or a reference to the same array
      * as the {@code 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 {@code left}
      * and {@code right} and to use offsets, such as {@code rightoff}
      * equals ({@code leftoff} + 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) / 2.0f;
         y1 = (y1 + ctrly1) / 2.0f;
         x2 = (x2 + ctrlx2) / 2.0f;
         y2 = (y2 + ctrly2) / 2.0f;
         float centerx = (ctrlx1 + ctrlx2) / 2.0f;
         float centery = (ctrly1 + ctrly2) / 2.0f;
         ctrlx1 = (x1 + centerx) / 2.0f;
         ctrly1 = (y1 + centery) / 2.0f;
         ctrlx2 = (x2 + centerx) / 2.0f;
         ctrly2 = (y2 + centery) / 2.0f;
         centerx = (ctrlx1 + ctrlx2) / 2.0f;
         centery = (ctrly1 + ctrly2) / 2.0f;
         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) / 2.0f;
         y1 = (y1 + ctrly) / 2.0f;
         x2 = (x2 + ctrlx) / 2.0f;
         y2 = (y2 + ctrly) / 2.0f;
         ctrlx = (x1 + x2) / 2.0f;
         ctrly = (y1 + y2) / 2.0f;
         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);
             break;
         case 6:
             subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
             break;
         }
     }
 }
	/*
	* Copyright (c) 2007, 2011, 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 sun.java2d.pisces;

	import java.util.Arrays;
	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 {
	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 = bb - 4a*c;
	if (dis > 0) {
	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 >= 0) {
	zeroes[ret++] = (2 * c) / (-b - sqrtDis);
	zeroes[ret++] = (-b - sqrtDis) / (2 * a);
	} else {
	zeroes[ret++] = (-b + sqrtDis) / (2 * a);
	zeroes[ret++] = (2 * c) / (-b + sqrtDis);
	}
	} else if (dis == 0f) {
	t = (-b) / (2 * a);
	zeroes[ret++] = t;
	}
	} else {
	if (b != 0f) {
	t = (-c) / b;
	zeroes[ret++] = t;
	}
	}
	return ret - off;
	}

	// find the roots of g(t) = dt^3 + at^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 == 0) {
	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 * (-1.0/3 * sq_A + b);
	double q = 1.0/2 * (2.0/27 * a * sq_A - 1.0/3 * a * b + c);

	/* use Cardano's formula */

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

	int num;
	if (D < 0) {
	// see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
	final double phi = 1.0/3 * acos(-q / sqrt(-cb_p));
	final double t = 2 * sqrt(-p);

	pts[ off+0 ] = (float)( t * cos(phi));
	pts[ off+1 ] = (float)(-t * cos(phi + PI / 3));
	pts[ off+2 ] = (float)(-t * cos(phi - PI / 3));
	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, 1e-8)) {
	pts[off+1] = -(pts[off] / 2);
	num = 2;
	}
	}

	final float sub = 1.0f/3 * a;

	for (int i = 0; i < num; ++i) {
	pts[ off+i ] -= sub;
	}

	return filterOutNotInAB(pts, off, num, A, B) - off;
	}

	// These use a hardcoded factor of 2 for increasing sizes. Perhaps this
	// should be provided as an argument.
	static float[] widenArray(float[] in, final int cursize, final int numToAdd) {
	if (in.length >= cursize + numToAdd) {
	return in;
	}
	return Arrays.copyOf(in, 2 * (cursize + numToAdd));
	}

	static int[] widenArray(int[] in, final int cursize, final int numToAdd) {
	if (in.length >= cursize + numToAdd) {
	return in;
	}
	return Arrays.copyOf(in, 2 * (cursize + numToAdd));
	}

	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; i < off + len; 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(dxdx + dydy);
	}

	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);
	break;
	case 8:
	Helpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
	break;
	default:
	throw new InternalError("Unsupported curve type");
	}
	}

	static void isort(float[] a, int off, int len) {
	for (int i = off + 1; i < off + len; 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 {@code src} array at indices {@code srcoff}
	* through ({@code srcoff} + 7) and stores the
	* resulting two subdivided curves into the two result arrays at the
	* corresponding indices.
	* Either or both of the {@code left} and {@code right}
	* arrays may be {@code null} or a reference to the same array
	* as the {@code 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 {@code left}
	* and {@code right} and to use offsets, such as {@code rightoff}
	* equals ({@code leftoff} + 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) / 2.0f;
	y1 = (y1 + ctrly1) / 2.0f;
	x2 = (x2 + ctrlx2) / 2.0f;
	y2 = (y2 + ctrly2) / 2.0f;
	float centerx = (ctrlx1 + ctrlx2) / 2.0f;
	float centery = (ctrly1 + ctrly2) / 2.0f;
	ctrlx1 = (x1 + centerx) / 2.0f;
	ctrly1 = (y1 + centery) / 2.0f;
	ctrlx2 = (x2 + centerx) / 2.0f;
	ctrly2 = (y2 + centery) / 2.0f;
	centerx = (ctrlx1 + ctrlx2) / 2.0f;
	centery = (ctrly1 + ctrly2) / 2.0f;
	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) / 2.0f;
	y1 = (y1 + ctrly) / 2.0f;
	x2 = (x2 + ctrlx) / 2.0f;
	y2 = (y2 + ctrly) / 2.0f;
	ctrlx = (x1 + x2) / 2.0f;
	ctrly = (y1 + y2) / 2.0f;
	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);
	break;
	case 6:
	subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
	break;
	}
	}
	}