1725 lines
52 KiB
Java
1725 lines
52 KiB
Java
/* CubicCurve2D.java -- represents a parameterized cubic curve in 2-D space
|
|
Copyright (C) 2002, 2003, 2004 Free Software Foundation
|
|
|
|
This file is part of GNU Classpath.
|
|
|
|
GNU Classpath is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2, or (at your option)
|
|
any later version.
|
|
|
|
GNU Classpath 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 for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with GNU Classpath; see the file COPYING. If not, write to the
|
|
Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
|
|
02110-1301 USA.
|
|
|
|
Linking this library statically or dynamically with other modules is
|
|
making a combined work based on this library. Thus, the terms and
|
|
conditions of the GNU General Public License cover the whole
|
|
combination.
|
|
|
|
As a special exception, the copyright holders of this library give you
|
|
permission to link this library with independent modules to produce an
|
|
executable, regardless of the license terms of these independent
|
|
modules, and to copy and distribute the resulting executable under
|
|
terms of your choice, provided that you also meet, for each linked
|
|
independent module, the terms and conditions of the license of that
|
|
module. An independent module is a module which is not derived from
|
|
or based on this library. If you modify this library, you may extend
|
|
this exception to your version of the library, but you are not
|
|
obligated to do so. If you do not wish to do so, delete this
|
|
exception statement from your version. */
|
|
|
|
package java.awt.geom;
|
|
|
|
import java.awt.Rectangle;
|
|
import java.awt.Shape;
|
|
import java.util.NoSuchElementException;
|
|
|
|
|
|
/**
|
|
* A two-dimensional curve that is parameterized with a cubic
|
|
* function.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* @author Eric Blake (ebb9@email.byu.edu)
|
|
* @author Graydon Hoare (graydon@redhat.com)
|
|
* @author Sascha Brawer (brawer@dandelis.ch)
|
|
* @author Sven de Marothy (sven@physto.se)
|
|
*
|
|
* @since 1.2
|
|
*/
|
|
public abstract class CubicCurve2D implements Shape, Cloneable
|
|
{
|
|
private static final double BIG_VALUE = java.lang.Double.MAX_VALUE / 10.0;
|
|
private static final double EPSILON = 1E-10;
|
|
|
|
/**
|
|
* Constructs a new CubicCurve2D. Typical users will want to
|
|
* construct instances of a subclass, such as {@link
|
|
* CubicCurve2D.Float} or {@link CubicCurve2D.Double}.
|
|
*/
|
|
protected CubicCurve2D()
|
|
{
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s start
|
|
* point.
|
|
*/
|
|
public abstract double getX1();
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s start
|
|
* point.
|
|
*/
|
|
public abstract double getY1();
|
|
|
|
/**
|
|
* Returns the curve’s start point.
|
|
*/
|
|
public abstract Point2D getP1();
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s first
|
|
* control point.
|
|
*/
|
|
public abstract double getCtrlX1();
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s first
|
|
* control point.
|
|
*/
|
|
public abstract double getCtrlY1();
|
|
|
|
/**
|
|
* Returns the curve’s first control point.
|
|
*/
|
|
public abstract Point2D getCtrlP1();
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s second
|
|
* control point.
|
|
*/
|
|
public abstract double getCtrlX2();
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s second
|
|
* control point.
|
|
*/
|
|
public abstract double getCtrlY2();
|
|
|
|
/**
|
|
* Returns the curve’s second control point.
|
|
*/
|
|
public abstract Point2D getCtrlP2();
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s end
|
|
* point.
|
|
*/
|
|
public abstract double getX2();
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s end
|
|
* point.
|
|
*/
|
|
public abstract double getY2();
|
|
|
|
/**
|
|
* Returns the curve’s end point.
|
|
*/
|
|
public abstract Point2D getP2();
|
|
|
|
/**
|
|
* Changes the curve geometry, separately specifying each coordinate
|
|
* value.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* @param x1 the <i>x</i> coordinate of the curve’s new start
|
|
* point.
|
|
*
|
|
* @param y1 the <i>y</i> coordinate of the curve’s new start
|
|
* point.
|
|
*
|
|
* @param cx1 the <i>x</i> coordinate of the curve’s new
|
|
* first control point.
|
|
*
|
|
* @param cy1 the <i>y</i> coordinate of the curve’s new
|
|
* first control point.
|
|
*
|
|
* @param cx2 the <i>x</i> coordinate of the curve’s new
|
|
* second control point.
|
|
*
|
|
* @param cy2 the <i>y</i> coordinate of the curve’s new
|
|
* second control point.
|
|
*
|
|
* @param x2 the <i>x</i> coordinate of the curve’s new end
|
|
* point.
|
|
*
|
|
* @param y2 the <i>y</i> coordinate of the curve’s new end
|
|
* point.
|
|
*/
|
|
public abstract void setCurve(double x1, double y1, double cx1, double cy1,
|
|
double cx2, double cy2, double x2, double y2);
|
|
|
|
/**
|
|
* Changes the curve geometry, specifying coordinate values in an
|
|
* array.
|
|
*
|
|
* @param coords an array containing the new coordinate values. The
|
|
* <i>x</i> coordinate of the new start point is located at
|
|
* <code>coords[offset]</code>, its <i>y</i> coordinate at
|
|
* <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the
|
|
* new first control point is located at <code>coords[offset +
|
|
* 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
|
|
* 3]</code>. The <i>x</i> coordinate of the new second control
|
|
* point is located at <code>coords[offset + 4]</code>, its <i>y</i>
|
|
* coordinate at <code>coords[offset + 5]</code>. The <i>x</i>
|
|
* coordinate of the new end point is located at <code>coords[offset
|
|
* + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
|
|
* 7]</code>.
|
|
*
|
|
* @param offset the offset of the first coordinate value in
|
|
* <code>coords</code>.
|
|
*/
|
|
public void setCurve(double[] coords, int offset)
|
|
{
|
|
setCurve(coords[offset++], coords[offset++], coords[offset++],
|
|
coords[offset++], coords[offset++], coords[offset++],
|
|
coords[offset++], coords[offset++]);
|
|
}
|
|
|
|
/**
|
|
* Changes the curve geometry, specifying coordinate values in
|
|
* separate Point objects.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* <p>The curve does not keep any reference to the passed point
|
|
* objects. Therefore, a later change to <code>p1</code>,
|
|
* <code>c1</code>, <code>c2</code> or <code>p2</code> will not
|
|
* affect the curve geometry.
|
|
*
|
|
* @param p1 the new start point.
|
|
* @param c1 the new first control point.
|
|
* @param c2 the new second control point.
|
|
* @param p2 the new end point.
|
|
*/
|
|
public void setCurve(Point2D p1, Point2D c1, Point2D c2, Point2D p2)
|
|
{
|
|
setCurve(p1.getX(), p1.getY(), c1.getX(), c1.getY(), c2.getX(), c2.getY(),
|
|
p2.getX(), p2.getY());
|
|
}
|
|
|
|
/**
|
|
* Changes the curve geometry, specifying coordinate values in an
|
|
* array of Point objects.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* <p>The curve does not keep references to the passed point
|
|
* objects. Therefore, a later change to the <code>pts</code> array
|
|
* or any of its elements will not affect the curve geometry.
|
|
*
|
|
* @param pts an array containing the points. The new start point
|
|
* is located at <code>pts[offset]</code>, the new first control
|
|
* point at <code>pts[offset + 1]</code>, the new second control
|
|
* point at <code>pts[offset + 2]</code>, and the new end point
|
|
* at <code>pts[offset + 3]</code>.
|
|
*
|
|
* @param offset the offset of the start point in <code>pts</code>.
|
|
*/
|
|
public void setCurve(Point2D[] pts, int offset)
|
|
{
|
|
setCurve(pts[offset].getX(), pts[offset++].getY(), pts[offset].getX(),
|
|
pts[offset++].getY(), pts[offset].getX(), pts[offset++].getY(),
|
|
pts[offset].getX(), pts[offset++].getY());
|
|
}
|
|
|
|
/**
|
|
* Changes the curve geometry to that of another curve.
|
|
*
|
|
* @param c the curve whose coordinates will be copied.
|
|
*/
|
|
public void setCurve(CubicCurve2D c)
|
|
{
|
|
setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
|
|
c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
|
|
}
|
|
|
|
/**
|
|
* Calculates the squared flatness of a cubic curve, directly
|
|
* specifying each coordinate value. The flatness is the maximal
|
|
* distance of a control point to the line between start and end
|
|
* point.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
|
|
* alt="A drawing that illustrates the flatness" />
|
|
*
|
|
* <p>In the above drawing, the straight line connecting start point
|
|
* P1 and end point P2 is depicted in gray. In comparison to C1,
|
|
* control point C2 is father away from the gray line. Therefore,
|
|
* the result will be the square of the distance between C2 and the
|
|
* gray line, i.e. the squared length of the red line.
|
|
*
|
|
* @param x1 the <i>x</i> coordinate of the start point P1.
|
|
* @param y1 the <i>y</i> coordinate of the start point P1.
|
|
* @param cx1 the <i>x</i> coordinate of the first control point C1.
|
|
* @param cy1 the <i>y</i> coordinate of the first control point C1.
|
|
* @param cx2 the <i>x</i> coordinate of the second control point C2.
|
|
* @param cy2 the <i>y</i> coordinate of the second control point C2.
|
|
* @param x2 the <i>x</i> coordinate of the end point P2.
|
|
* @param y2 the <i>y</i> coordinate of the end point P2.
|
|
*/
|
|
public static double getFlatnessSq(double x1, double y1, double cx1,
|
|
double cy1, double cx2, double cy2,
|
|
double x2, double y2)
|
|
{
|
|
return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, cx1, cy1),
|
|
Line2D.ptSegDistSq(x1, y1, x2, y2, cx2, cy2));
|
|
}
|
|
|
|
/**
|
|
* Calculates the flatness of a cubic curve, directly specifying
|
|
* each coordinate value. The flatness is the maximal distance of a
|
|
* control point to the line between start and end point.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
|
|
* alt="A drawing that illustrates the flatness" />
|
|
*
|
|
* <p>In the above drawing, the straight line connecting start point
|
|
* P1 and end point P2 is depicted in gray. In comparison to C1,
|
|
* control point C2 is father away from the gray line. Therefore,
|
|
* the result will be the distance between C2 and the gray line,
|
|
* i.e. the length of the red line.
|
|
*
|
|
* @param x1 the <i>x</i> coordinate of the start point P1.
|
|
* @param y1 the <i>y</i> coordinate of the start point P1.
|
|
* @param cx1 the <i>x</i> coordinate of the first control point C1.
|
|
* @param cy1 the <i>y</i> coordinate of the first control point C1.
|
|
* @param cx2 the <i>x</i> coordinate of the second control point C2.
|
|
* @param cy2 the <i>y</i> coordinate of the second control point C2.
|
|
* @param x2 the <i>x</i> coordinate of the end point P2.
|
|
* @param y2 the <i>y</i> coordinate of the end point P2.
|
|
*/
|
|
public static double getFlatness(double x1, double y1, double cx1,
|
|
double cy1, double cx2, double cy2,
|
|
double x2, double y2)
|
|
{
|
|
return Math.sqrt(getFlatnessSq(x1, y1, cx1, cy1, cx2, cy2, x2, y2));
|
|
}
|
|
|
|
/**
|
|
* Calculates the squared flatness of a cubic curve, specifying the
|
|
* coordinate values in an array. The flatness is the maximal
|
|
* distance of a control point to the line between start and end
|
|
* point.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
|
|
* alt="A drawing that illustrates the flatness" />
|
|
*
|
|
* <p>In the above drawing, the straight line connecting start point
|
|
* P1 and end point P2 is depicted in gray. In comparison to C1,
|
|
* control point C2 is father away from the gray line. Therefore,
|
|
* the result will be the square of the distance between C2 and the
|
|
* gray line, i.e. the squared length of the red line.
|
|
*
|
|
* @param coords an array containing the coordinate values. The
|
|
* <i>x</i> coordinate of the start point P1 is located at
|
|
* <code>coords[offset]</code>, its <i>y</i> coordinate at
|
|
* <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the
|
|
* first control point C1 is located at <code>coords[offset +
|
|
* 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
|
|
* 3]</code>. The <i>x</i> coordinate of the second control point C2
|
|
* is located at <code>coords[offset + 4]</code>, its <i>y</i>
|
|
* coordinate at <code>coords[offset + 5]</code>. The <i>x</i>
|
|
* coordinate of the end point P2 is located at <code>coords[offset
|
|
* + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
|
|
* 7]</code>.
|
|
*
|
|
* @param offset the offset of the first coordinate value in
|
|
* <code>coords</code>.
|
|
*/
|
|
public static double getFlatnessSq(double[] coords, int offset)
|
|
{
|
|
return getFlatnessSq(coords[offset++], coords[offset++], coords[offset++],
|
|
coords[offset++], coords[offset++], coords[offset++],
|
|
coords[offset++], coords[offset++]);
|
|
}
|
|
|
|
/**
|
|
* Calculates the flatness of a cubic curve, specifying the
|
|
* coordinate values in an array. The flatness is the maximal
|
|
* distance of a control point to the line between start and end
|
|
* point.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
|
|
* alt="A drawing that illustrates the flatness" />
|
|
*
|
|
* <p>In the above drawing, the straight line connecting start point
|
|
* P1 and end point P2 is depicted in gray. In comparison to C1,
|
|
* control point C2 is father away from the gray line. Therefore,
|
|
* the result will be the distance between C2 and the gray line,
|
|
* i.e. the length of the red line.
|
|
*
|
|
* @param coords an array containing the coordinate values. The
|
|
* <i>x</i> coordinate of the start point P1 is located at
|
|
* <code>coords[offset]</code>, its <i>y</i> coordinate at
|
|
* <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the
|
|
* first control point C1 is located at <code>coords[offset +
|
|
* 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
|
|
* 3]</code>. The <i>x</i> coordinate of the second control point C2
|
|
* is located at <code>coords[offset + 4]</code>, its <i>y</i>
|
|
* coordinate at <code>coords[offset + 5]</code>. The <i>x</i>
|
|
* coordinate of the end point P2 is located at <code>coords[offset
|
|
* + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
|
|
* 7]</code>.
|
|
*
|
|
* @param offset the offset of the first coordinate value in
|
|
* <code>coords</code>.
|
|
*/
|
|
public static double getFlatness(double[] coords, int offset)
|
|
{
|
|
return Math.sqrt(getFlatnessSq(coords[offset++], coords[offset++],
|
|
coords[offset++], coords[offset++],
|
|
coords[offset++], coords[offset++],
|
|
coords[offset++], coords[offset++]));
|
|
}
|
|
|
|
/**
|
|
* Calculates the squared flatness of this curve. The flatness is
|
|
* the maximal distance of a control point to the line between start
|
|
* and end point.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
|
|
* alt="A drawing that illustrates the flatness" />
|
|
*
|
|
* <p>In the above drawing, the straight line connecting start point
|
|
* P1 and end point P2 is depicted in gray. In comparison to C1,
|
|
* control point C2 is father away from the gray line. Therefore,
|
|
* the result will be the square of the distance between C2 and the
|
|
* gray line, i.e. the squared length of the red line.
|
|
*/
|
|
public double getFlatnessSq()
|
|
{
|
|
return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
|
|
getCtrlX2(), getCtrlY2(), getX2(), getY2());
|
|
}
|
|
|
|
/**
|
|
* Calculates the flatness of this curve. The flatness is the
|
|
* maximal distance of a control point to the line between start and
|
|
* end point.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
|
|
* alt="A drawing that illustrates the flatness" />
|
|
*
|
|
* <p>In the above drawing, the straight line connecting start point
|
|
* P1 and end point P2 is depicted in gray. In comparison to C1,
|
|
* control point C2 is father away from the gray line. Therefore,
|
|
* the result will be the distance between C2 and the gray line,
|
|
* i.e. the length of the red line.
|
|
*/
|
|
public double getFlatness()
|
|
{
|
|
return Math.sqrt(getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
|
|
getCtrlX2(), getCtrlY2(), getX2(), getY2()));
|
|
}
|
|
|
|
/**
|
|
* Subdivides this curve into two halves.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-3.png" width="700"
|
|
* height="180" alt="A drawing that illustrates the effects of
|
|
* subdividing a CubicCurve2D" />
|
|
*
|
|
* @param left a curve whose geometry will be set to the left half
|
|
* of this curve, or <code>null</code> if the caller is not
|
|
* interested in the left half.
|
|
*
|
|
* @param right a curve whose geometry will be set to the right half
|
|
* of this curve, or <code>null</code> if the caller is not
|
|
* interested in the right half.
|
|
*/
|
|
public void subdivide(CubicCurve2D left, CubicCurve2D right)
|
|
{
|
|
// Use empty slots at end to share single array.
|
|
double[] d = new double[]
|
|
{
|
|
getX1(), getY1(), getCtrlX1(), getCtrlY1(), getCtrlX2(),
|
|
getCtrlY2(), getX2(), getY2(), 0, 0, 0, 0, 0, 0
|
|
};
|
|
subdivide(d, 0, d, 0, d, 6);
|
|
if (left != null)
|
|
left.setCurve(d, 0);
|
|
if (right != null)
|
|
right.setCurve(d, 6);
|
|
}
|
|
|
|
/**
|
|
* Subdivides a cubic curve into two halves.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-3.png" width="700"
|
|
* height="180" alt="A drawing that illustrates the effects of
|
|
* subdividing a CubicCurve2D" />
|
|
*
|
|
* @param src the curve to be subdivided.
|
|
*
|
|
* @param left a curve whose geometry will be set to the left half
|
|
* of <code>src</code>, or <code>null</code> if the caller is not
|
|
* interested in the left half.
|
|
*
|
|
* @param right a curve whose geometry will be set to the right half
|
|
* of <code>src</code>, or <code>null</code> if the caller is not
|
|
* interested in the right half.
|
|
*/
|
|
public static void subdivide(CubicCurve2D src, CubicCurve2D left,
|
|
CubicCurve2D right)
|
|
{
|
|
src.subdivide(left, right);
|
|
}
|
|
|
|
/**
|
|
* Subdivides a cubic curve into two halves, passing all coordinates
|
|
* in an array.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-3.png" width="700"
|
|
* height="180" alt="A drawing that illustrates the effects of
|
|
* subdividing a CubicCurve2D" />
|
|
*
|
|
* <p>The left end point and the right start point will always be
|
|
* identical. Memory-concious programmers thus may want to pass the
|
|
* same array for both <code>left</code> and <code>right</code>, and
|
|
* set <code>rightOff</code> to <code>leftOff + 6</code>.
|
|
*
|
|
* @param src an array containing the coordinates of the curve to be
|
|
* subdivided. The <i>x</i> coordinate of the start point P1 is
|
|
* located at <code>src[srcOff]</code>, its <i>y</i> at
|
|
* <code>src[srcOff + 1]</code>. The <i>x</i> coordinate of the
|
|
* first control point C1 is located at <code>src[srcOff +
|
|
* 2]</code>, its <i>y</i> at <code>src[srcOff + 3]</code>. The
|
|
* <i>x</i> coordinate of the second control point C2 is located at
|
|
* <code>src[srcOff + 4]</code>, its <i>y</i> at <code>src[srcOff +
|
|
* 5]</code>. The <i>x</i> coordinate of the end point is located at
|
|
* <code>src[srcOff + 6]</code>, its <i>y</i> at <code>src[srcOff +
|
|
* 7]</code>.
|
|
*
|
|
* @param srcOff an offset into <code>src</code>, specifying
|
|
* the index of the start point’s <i>x</i> coordinate.
|
|
*
|
|
* @param left an array that will receive the coordinates of the
|
|
* left half of <code>src</code>. It is acceptable to pass
|
|
* <code>src</code>. A caller who is not interested in the left half
|
|
* can pass <code>null</code>.
|
|
*
|
|
* @param leftOff an offset into <code>left</code>, specifying the
|
|
* index where the start point’s <i>x</i> coordinate will be
|
|
* stored.
|
|
*
|
|
* @param right an array that will receive the coordinates of the
|
|
* right half of <code>src</code>. It is acceptable to pass
|
|
* <code>src</code> or <code>left</code>. A caller who is not
|
|
* interested in the right half can pass <code>null</code>.
|
|
*
|
|
* @param rightOff an offset into <code>right</code>, specifying the
|
|
* index where the start point’s <i>x</i> coordinate will be
|
|
* stored.
|
|
*/
|
|
public static void subdivide(double[] src, int srcOff, double[] left,
|
|
int leftOff, double[] right, int rightOff)
|
|
{
|
|
// To understand this code, please have a look at the image
|
|
// "CubicCurve2D-3.png" in the sub-directory "doc-files".
|
|
double src_C1_x;
|
|
double src_C1_y;
|
|
double src_C2_x;
|
|
double src_C2_y;
|
|
double left_P1_x;
|
|
double left_P1_y;
|
|
double left_C1_x;
|
|
double left_C1_y;
|
|
double left_C2_x;
|
|
double left_C2_y;
|
|
double right_C1_x;
|
|
double right_C1_y;
|
|
double right_C2_x;
|
|
double right_C2_y;
|
|
double right_P2_x;
|
|
double right_P2_y;
|
|
double Mid_x; // Mid = left.P2 = right.P1
|
|
double Mid_y; // Mid = left.P2 = right.P1
|
|
|
|
left_P1_x = src[srcOff];
|
|
left_P1_y = src[srcOff + 1];
|
|
src_C1_x = src[srcOff + 2];
|
|
src_C1_y = src[srcOff + 3];
|
|
src_C2_x = src[srcOff + 4];
|
|
src_C2_y = src[srcOff + 5];
|
|
right_P2_x = src[srcOff + 6];
|
|
right_P2_y = src[srcOff + 7];
|
|
|
|
left_C1_x = (left_P1_x + src_C1_x) / 2;
|
|
left_C1_y = (left_P1_y + src_C1_y) / 2;
|
|
right_C2_x = (right_P2_x + src_C2_x) / 2;
|
|
right_C2_y = (right_P2_y + src_C2_y) / 2;
|
|
Mid_x = (src_C1_x + src_C2_x) / 2;
|
|
Mid_y = (src_C1_y + src_C2_y) / 2;
|
|
left_C2_x = (left_C1_x + Mid_x) / 2;
|
|
left_C2_y = (left_C1_y + Mid_y) / 2;
|
|
right_C1_x = (Mid_x + right_C2_x) / 2;
|
|
right_C1_y = (Mid_y + right_C2_y) / 2;
|
|
Mid_x = (left_C2_x + right_C1_x) / 2;
|
|
Mid_y = (left_C2_y + right_C1_y) / 2;
|
|
|
|
if (left != null)
|
|
{
|
|
left[leftOff] = left_P1_x;
|
|
left[leftOff + 1] = left_P1_y;
|
|
left[leftOff + 2] = left_C1_x;
|
|
left[leftOff + 3] = left_C1_y;
|
|
left[leftOff + 4] = left_C2_x;
|
|
left[leftOff + 5] = left_C2_y;
|
|
left[leftOff + 6] = Mid_x;
|
|
left[leftOff + 7] = Mid_y;
|
|
}
|
|
|
|
if (right != null)
|
|
{
|
|
right[rightOff] = Mid_x;
|
|
right[rightOff + 1] = Mid_y;
|
|
right[rightOff + 2] = right_C1_x;
|
|
right[rightOff + 3] = right_C1_y;
|
|
right[rightOff + 4] = right_C2_x;
|
|
right[rightOff + 5] = right_C2_y;
|
|
right[rightOff + 6] = right_P2_x;
|
|
right[rightOff + 7] = right_P2_y;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Finds the non-complex roots of a cubic equation, placing the
|
|
* results into the same array as the equation coefficients. The
|
|
* following equation is being solved:
|
|
*
|
|
* <blockquote><code>eqn[3]</code> · <i>x</i><sup>3</sup>
|
|
* + <code>eqn[2]</code> · <i>x</i><sup>2</sup>
|
|
* + <code>eqn[1]</code> · <i>x</i>
|
|
* + <code>eqn[0]</code>
|
|
* = 0
|
|
* </blockquote>
|
|
*
|
|
* <p>For some background about solving cubic equations, see the
|
|
* article <a
|
|
* href="http://planetmath.org/encyclopedia/CubicFormula.html"
|
|
* >“Cubic Formula”</a> in <a
|
|
* href="http://planetmath.org/" >PlanetMath</a>. For an extensive
|
|
* library of numerical algorithms written in the C programming
|
|
* language, see the <a href= "http://www.gnu.org/software/gsl/">GNU
|
|
* Scientific Library</a>, from which this implementation was
|
|
* adapted.
|
|
*
|
|
* @param eqn an array with the coefficients of the equation. When
|
|
* this procedure has returned, <code>eqn</code> will contain the
|
|
* non-complex solutions of the equation, in no particular order.
|
|
*
|
|
* @return the number of non-complex solutions. A result of 0
|
|
* indicates that the equation has no non-complex solutions. A
|
|
* result of -1 indicates that the equation is constant (i.e.,
|
|
* always or never zero).
|
|
*
|
|
* @see #solveCubic(double[], double[])
|
|
* @see QuadCurve2D#solveQuadratic(double[],double[])
|
|
*
|
|
* @author Brian Gough (bjg@network-theory.com)
|
|
* (original C implementation in the <a href=
|
|
* "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
|
|
*
|
|
* @author Sascha Brawer (brawer@dandelis.ch)
|
|
* (adaptation to Java)
|
|
*/
|
|
public static int solveCubic(double[] eqn)
|
|
{
|
|
return solveCubic(eqn, eqn);
|
|
}
|
|
|
|
/**
|
|
* Finds the non-complex roots of a cubic equation. The following
|
|
* equation is being solved:
|
|
*
|
|
* <blockquote><code>eqn[3]</code> · <i>x</i><sup>3</sup>
|
|
* + <code>eqn[2]</code> · <i>x</i><sup>2</sup>
|
|
* + <code>eqn[1]</code> · <i>x</i>
|
|
* + <code>eqn[0]</code>
|
|
* = 0
|
|
* </blockquote>
|
|
*
|
|
* <p>For some background about solving cubic equations, see the
|
|
* article <a
|
|
* href="http://planetmath.org/encyclopedia/CubicFormula.html"
|
|
* >“Cubic Formula”</a> in <a
|
|
* href="http://planetmath.org/" >PlanetMath</a>. For an extensive
|
|
* library of numerical algorithms written in the C programming
|
|
* language, see the <a href= "http://www.gnu.org/software/gsl/">GNU
|
|
* Scientific Library</a>, from which this implementation was
|
|
* adapted.
|
|
*
|
|
* @see QuadCurve2D#solveQuadratic(double[],double[])
|
|
*
|
|
* @param eqn an array with the coefficients of the equation.
|
|
*
|
|
* @param res an array into which the non-complex roots will be
|
|
* stored. The results may be in an arbitrary order. It is safe to
|
|
* pass the same array object reference for both <code>eqn</code>
|
|
* and <code>res</code>.
|
|
*
|
|
* @return the number of non-complex solutions. A result of 0
|
|
* indicates that the equation has no non-complex solutions. A
|
|
* result of -1 indicates that the equation is constant (i.e.,
|
|
* always or never zero).
|
|
*
|
|
* @author Brian Gough (bjg@network-theory.com)
|
|
* (original C implementation in the <a href=
|
|
* "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
|
|
*
|
|
* @author Sascha Brawer (brawer@dandelis.ch)
|
|
* (adaptation to Java)
|
|
*/
|
|
public static int solveCubic(double[] eqn, double[] res)
|
|
{
|
|
// Adapted from poly/solve_cubic.c in the GNU Scientific Library
|
|
// (GSL), revision 1.7 of 2003-07-26. For the original source, see
|
|
// http://www.gnu.org/software/gsl/
|
|
//
|
|
// Brian Gough, the author of that code, has granted the
|
|
// permission to use it in GNU Classpath under the GNU Classpath
|
|
// license, and has assigned the copyright to the Free Software
|
|
// Foundation.
|
|
//
|
|
// The Java implementation is very similar to the GSL code, but
|
|
// not a strict one-to-one copy. For example, GSL would sort the
|
|
// result.
|
|
|
|
double a;
|
|
double b;
|
|
double c;
|
|
double q;
|
|
double r;
|
|
double Q;
|
|
double R;
|
|
double c3;
|
|
double Q3;
|
|
double R2;
|
|
double CR2;
|
|
double CQ3;
|
|
|
|
// If the cubic coefficient is zero, we have a quadratic equation.
|
|
c3 = eqn[3];
|
|
if (c3 == 0)
|
|
return QuadCurve2D.solveQuadratic(eqn, res);
|
|
|
|
// Divide the equation by the cubic coefficient.
|
|
c = eqn[0] / c3;
|
|
b = eqn[1] / c3;
|
|
a = eqn[2] / c3;
|
|
|
|
// We now need to solve x^3 + ax^2 + bx + c = 0.
|
|
q = a * a - 3 * b;
|
|
r = 2 * a * a * a - 9 * a * b + 27 * c;
|
|
|
|
Q = q / 9;
|
|
R = r / 54;
|
|
|
|
Q3 = Q * Q * Q;
|
|
R2 = R * R;
|
|
|
|
CR2 = 729 * r * r;
|
|
CQ3 = 2916 * q * q * q;
|
|
|
|
if (R == 0 && Q == 0)
|
|
{
|
|
// The GNU Scientific Library would return three identical
|
|
// solutions in this case.
|
|
res[0] = -a / 3;
|
|
return 1;
|
|
}
|
|
|
|
if (CR2 == CQ3)
|
|
{
|
|
/* this test is actually R2 == Q3, written in a form suitable
|
|
for exact computation with integers */
|
|
/* Due to finite precision some double roots may be missed, and
|
|
considered to be a pair of complex roots z = x +/- epsilon i
|
|
close to the real axis. */
|
|
double sqrtQ = Math.sqrt(Q);
|
|
|
|
if (R > 0)
|
|
{
|
|
res[0] = -2 * sqrtQ - a / 3;
|
|
res[1] = sqrtQ - a / 3;
|
|
}
|
|
else
|
|
{
|
|
res[0] = -sqrtQ - a / 3;
|
|
res[1] = 2 * sqrtQ - a / 3;
|
|
}
|
|
return 2;
|
|
}
|
|
|
|
if (CR2 < CQ3) /* equivalent to R2 < Q3 */
|
|
{
|
|
double sqrtQ = Math.sqrt(Q);
|
|
double sqrtQ3 = sqrtQ * sqrtQ * sqrtQ;
|
|
double theta = Math.acos(R / sqrtQ3);
|
|
double norm = -2 * sqrtQ;
|
|
res[0] = norm * Math.cos(theta / 3) - a / 3;
|
|
res[1] = norm * Math.cos((theta + 2.0 * Math.PI) / 3) - a / 3;
|
|
res[2] = norm * Math.cos((theta - 2.0 * Math.PI) / 3) - a / 3;
|
|
|
|
// The GNU Scientific Library sorts the results. We don't.
|
|
return 3;
|
|
}
|
|
|
|
double sgnR = (R >= 0 ? 1 : -1);
|
|
double A = -sgnR * Math.pow(Math.abs(R) + Math.sqrt(R2 - Q3), 1.0 / 3.0);
|
|
double B = Q / A;
|
|
res[0] = A + B - a / 3;
|
|
return 1;
|
|
}
|
|
|
|
/**
|
|
* Determines whether a position lies inside the area bounded
|
|
* by the curve and the straight line connecting its end points.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
|
|
* alt="A drawing of the area spanned by the curve" />
|
|
*
|
|
* <p>The above drawing illustrates in which area points are
|
|
* considered “inside” a CubicCurve2D.
|
|
*/
|
|
public boolean contains(double x, double y)
|
|
{
|
|
if (! getBounds2D().contains(x, y))
|
|
return false;
|
|
|
|
return ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0);
|
|
}
|
|
|
|
/**
|
|
* Determines whether a point lies inside the area bounded
|
|
* by the curve and the straight line connecting its end points.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
|
|
* alt="A drawing of the area spanned by the curve" />
|
|
*
|
|
* <p>The above drawing illustrates in which area points are
|
|
* considered “inside” a CubicCurve2D.
|
|
*/
|
|
public boolean contains(Point2D p)
|
|
{
|
|
return contains(p.getX(), p.getY());
|
|
}
|
|
|
|
/**
|
|
* Determines whether any part of a rectangle is inside the area bounded
|
|
* by the curve and the straight line connecting its end points.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
|
|
* alt="A drawing of the area spanned by the curve" />
|
|
*
|
|
* <p>The above drawing illustrates in which area points are
|
|
* considered “inside” in a CubicCurve2D.
|
|
* @see #contains(double, double)
|
|
*/
|
|
public boolean intersects(double x, double y, double w, double h)
|
|
{
|
|
if (! getBounds2D().contains(x, y, w, h))
|
|
return false;
|
|
|
|
/* Does any edge intersect? */
|
|
if (getAxisIntersections(x, y, true, w) != 0 /* top */
|
|
|| getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
|
|
|| getAxisIntersections(x + w, y, false, h) != 0 /* right */
|
|
|| getAxisIntersections(x, y, false, h) != 0) /* left */
|
|
return true;
|
|
|
|
/* No intersections, is any point inside? */
|
|
if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
|
|
return true;
|
|
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
* Determines whether any part of a Rectangle2D is inside the area bounded
|
|
* by the curve and the straight line connecting its end points.
|
|
* @see #intersects(double, double, double, double)
|
|
*/
|
|
public boolean intersects(Rectangle2D r)
|
|
{
|
|
return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
|
|
}
|
|
|
|
/**
|
|
* Determine whether a rectangle is entirely inside the area that is bounded
|
|
* by the curve and the straight line connecting its end points.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
|
|
* alt="A drawing of the area spanned by the curve" />
|
|
*
|
|
* <p>The above drawing illustrates in which area points are
|
|
* considered “inside” a CubicCurve2D.
|
|
* @see #contains(double, double)
|
|
*/
|
|
public boolean contains(double x, double y, double w, double h)
|
|
{
|
|
if (! getBounds2D().intersects(x, y, w, h))
|
|
return false;
|
|
|
|
/* Does any edge intersect? */
|
|
if (getAxisIntersections(x, y, true, w) != 0 /* top */
|
|
|| getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
|
|
|| getAxisIntersections(x + w, y, false, h) != 0 /* right */
|
|
|| getAxisIntersections(x, y, false, h) != 0) /* left */
|
|
return false;
|
|
|
|
/* No intersections, is any point inside? */
|
|
if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
|
|
return true;
|
|
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
* Determine whether a Rectangle2D is entirely inside the area that is
|
|
* bounded by the curve and the straight line connecting its end points.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
|
|
* alt="A drawing of the area spanned by the curve" />
|
|
*
|
|
* <p>The above drawing illustrates in which area points are
|
|
* considered “inside” a CubicCurve2D.
|
|
* @see #contains(double, double)
|
|
*/
|
|
public boolean contains(Rectangle2D r)
|
|
{
|
|
return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
|
|
}
|
|
|
|
/**
|
|
* Determines the smallest rectangle that encloses the
|
|
* curve’s start, end and control points.
|
|
*/
|
|
public Rectangle getBounds()
|
|
{
|
|
return getBounds2D().getBounds();
|
|
}
|
|
|
|
public PathIterator getPathIterator(final AffineTransform at)
|
|
{
|
|
return new PathIterator()
|
|
{
|
|
/** Current coordinate. */
|
|
private int current = 0;
|
|
|
|
public int getWindingRule()
|
|
{
|
|
return WIND_NON_ZERO;
|
|
}
|
|
|
|
public boolean isDone()
|
|
{
|
|
return current >= 2;
|
|
}
|
|
|
|
public void next()
|
|
{
|
|
current++;
|
|
}
|
|
|
|
public int currentSegment(float[] coords)
|
|
{
|
|
int result;
|
|
switch (current)
|
|
{
|
|
case 0:
|
|
coords[0] = (float) getX1();
|
|
coords[1] = (float) getY1();
|
|
result = SEG_MOVETO;
|
|
break;
|
|
case 1:
|
|
coords[0] = (float) getCtrlX1();
|
|
coords[1] = (float) getCtrlY1();
|
|
coords[2] = (float) getCtrlX2();
|
|
coords[3] = (float) getCtrlY2();
|
|
coords[4] = (float) getX2();
|
|
coords[5] = (float) getY2();
|
|
result = SEG_CUBICTO;
|
|
break;
|
|
default:
|
|
throw new NoSuchElementException("cubic iterator out of bounds");
|
|
}
|
|
if (at != null)
|
|
at.transform(coords, 0, coords, 0, 3);
|
|
return result;
|
|
}
|
|
|
|
public int currentSegment(double[] coords)
|
|
{
|
|
int result;
|
|
switch (current)
|
|
{
|
|
case 0:
|
|
coords[0] = getX1();
|
|
coords[1] = getY1();
|
|
result = SEG_MOVETO;
|
|
break;
|
|
case 1:
|
|
coords[0] = getCtrlX1();
|
|
coords[1] = getCtrlY1();
|
|
coords[2] = getCtrlX2();
|
|
coords[3] = getCtrlY2();
|
|
coords[4] = getX2();
|
|
coords[5] = getY2();
|
|
result = SEG_CUBICTO;
|
|
break;
|
|
default:
|
|
throw new NoSuchElementException("cubic iterator out of bounds");
|
|
}
|
|
if (at != null)
|
|
at.transform(coords, 0, coords, 0, 3);
|
|
return result;
|
|
}
|
|
};
|
|
}
|
|
|
|
public PathIterator getPathIterator(AffineTransform at, double flatness)
|
|
{
|
|
return new FlatteningPathIterator(getPathIterator(at), flatness);
|
|
}
|
|
|
|
/**
|
|
* Create a new curve with the same contents as this one.
|
|
*
|
|
* @return the clone.
|
|
*/
|
|
public Object clone()
|
|
{
|
|
try
|
|
{
|
|
return super.clone();
|
|
}
|
|
catch (CloneNotSupportedException e)
|
|
{
|
|
throw (Error) new InternalError().initCause(e); // Impossible
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Helper method used by contains() and intersects() methods, that
|
|
* returns the number of curve/line intersections on a given axis
|
|
* extending from a certain point.
|
|
*
|
|
* @param x x coordinate of the origin point
|
|
* @param y y coordinate of the origin point
|
|
* @param useYaxis axis used, if true the positive Y axis is used,
|
|
* false uses the positive X axis.
|
|
*
|
|
* This is an implementation of the line-crossings algorithm,
|
|
* Detailed in an article on Eric Haines' page:
|
|
* http://www.acm.org/tog/editors/erich/ptinpoly/
|
|
*
|
|
* A special-case not adressed in this code is self-intersections
|
|
* of the curve, e.g. if the axis intersects the self-itersection,
|
|
* the degenerate roots of the polynomial will erroneously count as
|
|
* a single intersection of the curve, and not two.
|
|
*/
|
|
private int getAxisIntersections(double x, double y, boolean useYaxis,
|
|
double distance)
|
|
{
|
|
int nCrossings = 0;
|
|
double a0;
|
|
double a1;
|
|
double a2;
|
|
double a3;
|
|
double b0;
|
|
double b1;
|
|
double b2;
|
|
double b3;
|
|
double[] r = new double[4];
|
|
int nRoots;
|
|
|
|
a0 = a3 = 0.0;
|
|
|
|
if (useYaxis)
|
|
{
|
|
a0 = getY1() - y;
|
|
a1 = getCtrlY1() - y;
|
|
a2 = getCtrlY2() - y;
|
|
a3 = getY2() - y;
|
|
b0 = getX1() - x;
|
|
b1 = getCtrlX1() - x;
|
|
b2 = getCtrlX2() - x;
|
|
b3 = getX2() - x;
|
|
}
|
|
else
|
|
{
|
|
a0 = getX1() - x;
|
|
a1 = getCtrlX1() - x;
|
|
a2 = getCtrlX2() - x;
|
|
a3 = getX2() - x;
|
|
b0 = getY1() - y;
|
|
b1 = getCtrlY1() - y;
|
|
b2 = getCtrlY2() - y;
|
|
b3 = getY2() - y;
|
|
}
|
|
|
|
/* If the axis intersects a start/endpoint, shift it up by some small
|
|
amount to guarantee the line is 'inside'
|
|
If this is not done, bad behaviour may result for points on that axis.*/
|
|
if (a0 == 0.0 || a3 == 0.0)
|
|
{
|
|
double small = getFlatness() * EPSILON;
|
|
if (a0 == 0.0)
|
|
a0 -= small;
|
|
if (a3 == 0.0)
|
|
a3 -= small;
|
|
}
|
|
|
|
if (useYaxis)
|
|
{
|
|
if (Line2D.linesIntersect(b0, a0, b3, a3, EPSILON, 0.0, distance, 0.0))
|
|
nCrossings++;
|
|
}
|
|
else
|
|
{
|
|
if (Line2D.linesIntersect(a0, b0, a3, b3, 0.0, EPSILON, 0.0, distance))
|
|
nCrossings++;
|
|
}
|
|
|
|
r[0] = a0;
|
|
r[1] = 3 * (a1 - a0);
|
|
r[2] = 3 * (a2 + a0 - 2 * a1);
|
|
r[3] = a3 - 3 * a2 + 3 * a1 - a0;
|
|
|
|
if ((nRoots = solveCubic(r)) != 0)
|
|
for (int i = 0; i < nRoots; i++)
|
|
{
|
|
double t = r[i];
|
|
if (t >= 0.0 && t <= 1.0)
|
|
{
|
|
double crossing = -(t * t * t) * (b0 - 3 * b1 + 3 * b2 - b3)
|
|
+ 3 * t * t * (b0 - 2 * b1 + b2)
|
|
+ 3 * t * (b1 - b0) + b0;
|
|
if (crossing > 0.0 && crossing <= distance)
|
|
nCrossings++;
|
|
}
|
|
}
|
|
|
|
return (nCrossings);
|
|
}
|
|
|
|
/**
|
|
* A two-dimensional curve that is parameterized with a cubic
|
|
* function and stores coordinate values in double-precision
|
|
* floating-point format.
|
|
*
|
|
* @see CubicCurve2D.Float
|
|
*
|
|
* @author Eric Blake (ebb9@email.byu.edu)
|
|
* @author Sascha Brawer (brawer@dandelis.ch)
|
|
*/
|
|
public static class Double extends CubicCurve2D
|
|
{
|
|
/**
|
|
* The <i>x</i> coordinate of the curve’s start point.
|
|
*/
|
|
public double x1;
|
|
|
|
/**
|
|
* The <i>y</i> coordinate of the curve’s start point.
|
|
*/
|
|
public double y1;
|
|
|
|
/**
|
|
* The <i>x</i> coordinate of the curve’s first control point.
|
|
*/
|
|
public double ctrlx1;
|
|
|
|
/**
|
|
* The <i>y</i> coordinate of the curve’s first control point.
|
|
*/
|
|
public double ctrly1;
|
|
|
|
/**
|
|
* The <i>x</i> coordinate of the curve’s second control point.
|
|
*/
|
|
public double ctrlx2;
|
|
|
|
/**
|
|
* The <i>y</i> coordinate of the curve’s second control point.
|
|
*/
|
|
public double ctrly2;
|
|
|
|
/**
|
|
* The <i>x</i> coordinate of the curve’s end point.
|
|
*/
|
|
public double x2;
|
|
|
|
/**
|
|
* The <i>y</i> coordinate of the curve’s end point.
|
|
*/
|
|
public double y2;
|
|
|
|
/**
|
|
* Constructs a new CubicCurve2D that stores its coordinate values
|
|
* in double-precision floating-point format. All points are
|
|
* initially at position (0, 0).
|
|
*/
|
|
public Double()
|
|
{
|
|
}
|
|
|
|
/**
|
|
* Constructs a new CubicCurve2D that stores its coordinate values
|
|
* in double-precision floating-point format, specifying the
|
|
* initial position of each point.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* @param x1 the <i>x</i> coordinate of the curve’s start
|
|
* point.
|
|
*
|
|
* @param y1 the <i>y</i> coordinate of the curve’s start
|
|
* point.
|
|
*
|
|
* @param cx1 the <i>x</i> coordinate of the curve’s first
|
|
* control point.
|
|
*
|
|
* @param cy1 the <i>y</i> coordinate of the curve’s first
|
|
* control point.
|
|
*
|
|
* @param cx2 the <i>x</i> coordinate of the curve’s second
|
|
* control point.
|
|
*
|
|
* @param cy2 the <i>y</i> coordinate of the curve’s second
|
|
* control point.
|
|
*
|
|
* @param x2 the <i>x</i> coordinate of the curve’s end
|
|
* point.
|
|
*
|
|
* @param y2 the <i>y</i> coordinate of the curve’s end
|
|
* point.
|
|
*/
|
|
public Double(double x1, double y1, double cx1, double cy1, double cx2,
|
|
double cy2, double x2, double y2)
|
|
{
|
|
this.x1 = x1;
|
|
this.y1 = y1;
|
|
ctrlx1 = cx1;
|
|
ctrly1 = cy1;
|
|
ctrlx2 = cx2;
|
|
ctrly2 = cy2;
|
|
this.x2 = x2;
|
|
this.y2 = y2;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s start
|
|
* point.
|
|
*/
|
|
public double getX1()
|
|
{
|
|
return x1;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s start
|
|
* point.
|
|
*/
|
|
public double getY1()
|
|
{
|
|
return y1;
|
|
}
|
|
|
|
/**
|
|
* Returns the curve’s start point.
|
|
*/
|
|
public Point2D getP1()
|
|
{
|
|
return new Point2D.Double(x1, y1);
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s first
|
|
* control point.
|
|
*/
|
|
public double getCtrlX1()
|
|
{
|
|
return ctrlx1;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s first
|
|
* control point.
|
|
*/
|
|
public double getCtrlY1()
|
|
{
|
|
return ctrly1;
|
|
}
|
|
|
|
/**
|
|
* Returns the curve’s first control point.
|
|
*/
|
|
public Point2D getCtrlP1()
|
|
{
|
|
return new Point2D.Double(ctrlx1, ctrly1);
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s second
|
|
* control point.
|
|
*/
|
|
public double getCtrlX2()
|
|
{
|
|
return ctrlx2;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s second
|
|
* control point.
|
|
*/
|
|
public double getCtrlY2()
|
|
{
|
|
return ctrly2;
|
|
}
|
|
|
|
/**
|
|
* Returns the curve’s second control point.
|
|
*/
|
|
public Point2D getCtrlP2()
|
|
{
|
|
return new Point2D.Double(ctrlx2, ctrly2);
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s end
|
|
* point.
|
|
*/
|
|
public double getX2()
|
|
{
|
|
return x2;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s end
|
|
* point.
|
|
*/
|
|
public double getY2()
|
|
{
|
|
return y2;
|
|
}
|
|
|
|
/**
|
|
* Returns the curve’s end point.
|
|
*/
|
|
public Point2D getP2()
|
|
{
|
|
return new Point2D.Double(x2, y2);
|
|
}
|
|
|
|
/**
|
|
* Changes the curve geometry, separately specifying each coordinate
|
|
* value.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* @param x1 the <i>x</i> coordinate of the curve’s new start
|
|
* point.
|
|
*
|
|
* @param y1 the <i>y</i> coordinate of the curve’s new start
|
|
* point.
|
|
*
|
|
* @param cx1 the <i>x</i> coordinate of the curve’s new
|
|
* first control point.
|
|
*
|
|
* @param cy1 the <i>y</i> coordinate of the curve’s new
|
|
* first control point.
|
|
*
|
|
* @param cx2 the <i>x</i> coordinate of the curve’s new
|
|
* second control point.
|
|
*
|
|
* @param cy2 the <i>y</i> coordinate of the curve’s new
|
|
* second control point.
|
|
*
|
|
* @param x2 the <i>x</i> coordinate of the curve’s new end
|
|
* point.
|
|
*
|
|
* @param y2 the <i>y</i> coordinate of the curve’s new end
|
|
* point.
|
|
*/
|
|
public void setCurve(double x1, double y1, double cx1, double cy1,
|
|
double cx2, double cy2, double x2, double y2)
|
|
{
|
|
this.x1 = x1;
|
|
this.y1 = y1;
|
|
ctrlx1 = cx1;
|
|
ctrly1 = cy1;
|
|
ctrlx2 = cx2;
|
|
ctrly2 = cy2;
|
|
this.x2 = x2;
|
|
this.y2 = y2;
|
|
}
|
|
|
|
/**
|
|
* Determines the smallest rectangle that encloses the
|
|
* curve’s start, end and control points. As the
|
|
* illustration below shows, the invisible control points may cause
|
|
* the bounds to be much larger than the area that is actually
|
|
* covered by the curve.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-2.png" width="350" height="180"
|
|
* alt="An illustration of the bounds of a CubicCurve2D" />
|
|
*/
|
|
public Rectangle2D getBounds2D()
|
|
{
|
|
double nx1 = Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2));
|
|
double ny1 = Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2));
|
|
double nx2 = Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2));
|
|
double ny2 = Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2));
|
|
return new Rectangle2D.Double(nx1, ny1, nx2 - nx1, ny2 - ny1);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* A two-dimensional curve that is parameterized with a cubic
|
|
* function and stores coordinate values in single-precision
|
|
* floating-point format.
|
|
*
|
|
* @see CubicCurve2D.Float
|
|
*
|
|
* @author Eric Blake (ebb9@email.byu.edu)
|
|
* @author Sascha Brawer (brawer@dandelis.ch)
|
|
*/
|
|
public static class Float extends CubicCurve2D
|
|
{
|
|
/**
|
|
* The <i>x</i> coordinate of the curve’s start point.
|
|
*/
|
|
public float x1;
|
|
|
|
/**
|
|
* The <i>y</i> coordinate of the curve’s start point.
|
|
*/
|
|
public float y1;
|
|
|
|
/**
|
|
* The <i>x</i> coordinate of the curve’s first control point.
|
|
*/
|
|
public float ctrlx1;
|
|
|
|
/**
|
|
* The <i>y</i> coordinate of the curve’s first control point.
|
|
*/
|
|
public float ctrly1;
|
|
|
|
/**
|
|
* The <i>x</i> coordinate of the curve’s second control point.
|
|
*/
|
|
public float ctrlx2;
|
|
|
|
/**
|
|
* The <i>y</i> coordinate of the curve’s second control point.
|
|
*/
|
|
public float ctrly2;
|
|
|
|
/**
|
|
* The <i>x</i> coordinate of the curve’s end point.
|
|
*/
|
|
public float x2;
|
|
|
|
/**
|
|
* The <i>y</i> coordinate of the curve’s end point.
|
|
*/
|
|
public float y2;
|
|
|
|
/**
|
|
* Constructs a new CubicCurve2D that stores its coordinate values
|
|
* in single-precision floating-point format. All points are
|
|
* initially at position (0, 0).
|
|
*/
|
|
public Float()
|
|
{
|
|
}
|
|
|
|
/**
|
|
* Constructs a new CubicCurve2D that stores its coordinate values
|
|
* in single-precision floating-point format, specifying the
|
|
* initial position of each point.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* @param x1 the <i>x</i> coordinate of the curve’s start
|
|
* point.
|
|
*
|
|
* @param y1 the <i>y</i> coordinate of the curve’s start
|
|
* point.
|
|
*
|
|
* @param cx1 the <i>x</i> coordinate of the curve’s first
|
|
* control point.
|
|
*
|
|
* @param cy1 the <i>y</i> coordinate of the curve’s first
|
|
* control point.
|
|
*
|
|
* @param cx2 the <i>x</i> coordinate of the curve’s second
|
|
* control point.
|
|
*
|
|
* @param cy2 the <i>y</i> coordinate of the curve’s second
|
|
* control point.
|
|
*
|
|
* @param x2 the <i>x</i> coordinate of the curve’s end
|
|
* point.
|
|
*
|
|
* @param y2 the <i>y</i> coordinate of the curve’s end
|
|
* point.
|
|
*/
|
|
public Float(float x1, float y1, float cx1, float cy1, float cx2,
|
|
float cy2, float x2, float y2)
|
|
{
|
|
this.x1 = x1;
|
|
this.y1 = y1;
|
|
ctrlx1 = cx1;
|
|
ctrly1 = cy1;
|
|
ctrlx2 = cx2;
|
|
ctrly2 = cy2;
|
|
this.x2 = x2;
|
|
this.y2 = y2;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s start
|
|
* point.
|
|
*/
|
|
public double getX1()
|
|
{
|
|
return x1;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s start
|
|
* point.
|
|
*/
|
|
public double getY1()
|
|
{
|
|
return y1;
|
|
}
|
|
|
|
/**
|
|
* Returns the curve’s start point.
|
|
*/
|
|
public Point2D getP1()
|
|
{
|
|
return new Point2D.Float(x1, y1);
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s first
|
|
* control point.
|
|
*/
|
|
public double getCtrlX1()
|
|
{
|
|
return ctrlx1;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s first
|
|
* control point.
|
|
*/
|
|
public double getCtrlY1()
|
|
{
|
|
return ctrly1;
|
|
}
|
|
|
|
/**
|
|
* Returns the curve’s first control point.
|
|
*/
|
|
public Point2D getCtrlP1()
|
|
{
|
|
return new Point2D.Float(ctrlx1, ctrly1);
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>s</i> coordinate of the curve’s second
|
|
* control point.
|
|
*/
|
|
public double getCtrlX2()
|
|
{
|
|
return ctrlx2;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s second
|
|
* control point.
|
|
*/
|
|
public double getCtrlY2()
|
|
{
|
|
return ctrly2;
|
|
}
|
|
|
|
/**
|
|
* Returns the curve’s second control point.
|
|
*/
|
|
public Point2D getCtrlP2()
|
|
{
|
|
return new Point2D.Float(ctrlx2, ctrly2);
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>x</i> coordinate of the curve’s end
|
|
* point.
|
|
*/
|
|
public double getX2()
|
|
{
|
|
return x2;
|
|
}
|
|
|
|
/**
|
|
* Returns the <i>y</i> coordinate of the curve’s end
|
|
* point.
|
|
*/
|
|
public double getY2()
|
|
{
|
|
return y2;
|
|
}
|
|
|
|
/**
|
|
* Returns the curve’s end point.
|
|
*/
|
|
public Point2D getP2()
|
|
{
|
|
return new Point2D.Float(x2, y2);
|
|
}
|
|
|
|
/**
|
|
* Changes the curve geometry, separately specifying each coordinate
|
|
* value as a double-precision floating-point number.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* @param x1 the <i>x</i> coordinate of the curve’s new start
|
|
* point.
|
|
*
|
|
* @param y1 the <i>y</i> coordinate of the curve’s new start
|
|
* point.
|
|
*
|
|
* @param cx1 the <i>x</i> coordinate of the curve’s new
|
|
* first control point.
|
|
*
|
|
* @param cy1 the <i>y</i> coordinate of the curve’s new
|
|
* first control point.
|
|
*
|
|
* @param cx2 the <i>x</i> coordinate of the curve’s new
|
|
* second control point.
|
|
*
|
|
* @param cy2 the <i>y</i> coordinate of the curve’s new
|
|
* second control point.
|
|
*
|
|
* @param x2 the <i>x</i> coordinate of the curve’s new end
|
|
* point.
|
|
*
|
|
* @param y2 the <i>y</i> coordinate of the curve’s new end
|
|
* point.
|
|
*/
|
|
public void setCurve(double x1, double y1, double cx1, double cy1,
|
|
double cx2, double cy2, double x2, double y2)
|
|
{
|
|
this.x1 = (float) x1;
|
|
this.y1 = (float) y1;
|
|
ctrlx1 = (float) cx1;
|
|
ctrly1 = (float) cy1;
|
|
ctrlx2 = (float) cx2;
|
|
ctrly2 = (float) cy2;
|
|
this.x2 = (float) x2;
|
|
this.y2 = (float) y2;
|
|
}
|
|
|
|
/**
|
|
* Changes the curve geometry, separately specifying each coordinate
|
|
* value as a single-precision floating-point number.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
|
|
* alt="A drawing of a CubicCurve2D" />
|
|
*
|
|
* @param x1 the <i>x</i> coordinate of the curve’s new start
|
|
* point.
|
|
*
|
|
* @param y1 the <i>y</i> coordinate of the curve’s new start
|
|
* point.
|
|
*
|
|
* @param cx1 the <i>x</i> coordinate of the curve’s new
|
|
* first control point.
|
|
*
|
|
* @param cy1 the <i>y</i> coordinate of the curve’s new
|
|
* first control point.
|
|
*
|
|
* @param cx2 the <i>x</i> coordinate of the curve’s new
|
|
* second control point.
|
|
*
|
|
* @param cy2 the <i>y</i> coordinate of the curve’s new
|
|
* second control point.
|
|
*
|
|
* @param x2 the <i>x</i> coordinate of the curve’s new end
|
|
* point.
|
|
*
|
|
* @param y2 the <i>y</i> coordinate of the curve’s new end
|
|
* point.
|
|
*/
|
|
public void setCurve(float x1, float y1, float cx1, float cy1, float cx2,
|
|
float cy2, float x2, float y2)
|
|
{
|
|
this.x1 = x1;
|
|
this.y1 = y1;
|
|
ctrlx1 = cx1;
|
|
ctrly1 = cy1;
|
|
ctrlx2 = cx2;
|
|
ctrly2 = cy2;
|
|
this.x2 = x2;
|
|
this.y2 = y2;
|
|
}
|
|
|
|
/**
|
|
* Determines the smallest rectangle that encloses the
|
|
* curve’s start, end and control points. As the
|
|
* illustration below shows, the invisible control points may cause
|
|
* the bounds to be much larger than the area that is actually
|
|
* covered by the curve.
|
|
*
|
|
* <p><img src="doc-files/CubicCurve2D-2.png" width="350" height="180"
|
|
* alt="An illustration of the bounds of a CubicCurve2D" />
|
|
*/
|
|
public Rectangle2D getBounds2D()
|
|
{
|
|
float nx1 = (float) Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2));
|
|
float ny1 = (float) Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2));
|
|
float nx2 = (float) Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2));
|
|
float ny2 = (float) Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2));
|
|
return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1);
|
|
}
|
|
}
|
|
}
|