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/*
* Copyright (c) 2007, 2013, 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 com.sun.openpisces;
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 src array at indices srcoff
* through (srcoff + 7) and stores the
* resulting two subdivided curves into the two result arrays at the
* corresponding indices.
* Either or both of the left and right
* arrays may be null or a reference to the same array
* as the 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 left
* and right and to use offsets, such as rightoff
* equals (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
*/
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;
}
}
}
