/*
* @(#)QuadCurve2D.java 1.29 03/12/19
*
* Copyright 2004 Sun Microsystems, Inc. All rights reserved.
* SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
*/
package java.awt.geom;
import java.awt.Shape;
import java.awt.Rectangle;
/**
* The <code>QuadCurve2D</code> class defines a quadratic parametric curve
* segment in (x, y) coordinate space.
* <p>
* This class is only the abstract superclass for all objects that
* store a 2D quadratic curve segment.
* The actual storage representation of the coordinates is left to
* the subclass.
*
* @version 1.29, 12/19/03
* @author Jim Graham
*/
public abstract class QuadCurve2D implements Shape, Cloneable {
/**
* A quadratic parametric curve segment specified with
* <code>float</code> coordinates.
*/
public static class Float extends QuadCurve2D {
/**
* The x coordinate of the start point of the quadratic curve
* segment.
*/
public float x1;
/**
* The y coordinate of the start point of the quadratic curve
* segment.
*/
public float y1;
/**
* The x coordinate of the control point of the quadratic curve
* segment.
*/
public float ctrlx;
/**
* The y coordinate of the control point of the quadratic curve
* segment.
*/
public float ctrly;
/**
* The x coordinate of the end point of the quadratic curve
* segment.
*/
public float x2;
/**
* The y coordinate of the end point of the quadratic curve
* segment.
*/
public float y2;
/**
* Constructs and initializes a <code>QuadCurve2D</code> with
* coordinates (0, 0, 0, 0, 0, 0).
*/
public Float() {
}
/**
* Constructs and initializes a <code>QuadCurve2D</code> from the
* specified coordinates.
* @param x1, y1 the starting point coordinates
* @param ctrlx, ctrly the coordinates of the control point
* @param x2, y2 the ending point coordinates
*/
public Float(float x1, float y1,
float ctrlx, float ctrly,
float x2, float y2) {
setCurve(x1, y1, ctrlx, ctrly, x2, y2);
}
/**
* Returns the x coordinate of the start point in
* <code>double</code> precision.
* @return the x coordinate of the starting point.
*/
public double getX1() {
return (double) x1;
}
/**
* Returns the y coordinate of the start point in
* <code>double</code> precision.
* @return the y coordinate of the starting point.
*/
public double getY1() {
return (double) y1;
}
/**
* Returns the start point.
* @return a {@link Point2D} object that is the starting point
* of this <code>QuadCurve2D</code>.
*/
public Point2D getP1() {
return new Point2D.Float(x1, y1);
}
/**
* Returns the x coordinate of the control point in
* <code>double</code> precision.
* @return the x coordinate of the control point.
*/
public double getCtrlX() {
return (double) ctrlx;
}
/**
* Returns the y coordinate of the control point in
* <code>double</code> precision.
* @return the y coordiante of the control point.
*/
public double getCtrlY() {
return (double) ctrly;
}
/**
* Returns the control point.
* @return a <code>Point2D</code> that is the control point of
* this <code>QuadCurve2D</code>.
*/
public Point2D getCtrlPt() {
return new Point2D.Float(ctrlx, ctrly);
}
/**
* Returns the x coordinate of the end point in
* <code>double</code> precision.
* @return the x coordinate of the end point.
*/
public double getX2() {
return (double) x2;
}
/**
* Returns the y coordinate of the end point in
* <code>double</code> precision.
* @return the y coordiante of the end point.
*/
public double getY2() {
return (double) y2;
}
/**
* Returns the end point.
* @return a <code>Point2D</code> that is the end point of this
* <code>QuadCurve2D</code>.
*/
public Point2D getP2() {
return new Point2D.Float(x2, y2);
}
/**
* Sets the location of the endpoints and controlpoint of this
* <code>QuadCurve2D</code> to the specified <code>double</code>
* coordinates.
* @param x1, y1 the coordinates of the starting point
* @param ctrlx, ctrly the coordinates of the control point
* @param x2, y2 the coordinates of the ending point
*/
public void setCurve(double x1, double y1,
double ctrlx, double ctrly,
double x2, double y2) {
this.x1 = (float) x1;
this.y1 = (float) y1;
this.ctrlx = (float) ctrlx;
this.ctrly = (float) ctrly;
this.x2 = (float) x2;
this.y2 = (float) y2;
}
/**
* Sets the location of the endpoints and controlpoint of this curve
* to the specified <code>float</code> coordinates.
* @param x1, y1 the coordinates of the starting point
* @param ctrlx, ctrly the coordinates of the control point
* @param x2, y2 the coordinates of the ending point
*/
public void setCurve(float x1, float y1,
float ctrlx, float ctrly,
float x2, float y2) {
this.x1 = x1;
this.y1 = y1;
this.ctrlx = ctrlx;
this.ctrly = ctrly;
this.x2 = x2;
this.y2 = y2;
}
/**
* Returns the bounding box of this <code>QuadCurve2D</code>.
* @return a {@link Rectangle2D} that is the bounding box
* of the shape of this <code>QuadCurve2D</code>.
*/
public Rectangle2D getBounds2D() {
float left = Math.min(Math.min(x1, x2), ctrlx);
float top = Math.min(Math.min(y1, y2), ctrly);
float right = Math.max(Math.max(x1, x2), ctrlx);
float bottom = Math.max(Math.max(y1, y2), ctrly);
return new Rectangle2D.Float(left, top,
right - left, bottom - top);
}
}
/**
* A quadratic parametric curve segment specified with
* <code>double</code> coordinates.
*/
public static class Double extends QuadCurve2D {
/**
* The x coordinate of the start point of the quadratic curve
* segment.
*/
public double x1;
/**
* The x coordinate of the start point of the quadratic curve
* segment.
*/
public double y1;
/**
* The x coordinate of the control point of the quadratic curve
* segment.
*/
public double ctrlx;
/**
* The y coordinate of the control point of the quadratic curve
* segment.
*/
public double ctrly;
/**
* The x coordinate of the end point of the quadratic curve
* segment.
*/
public double x2;
/**
* The y coordinate of the end point of the quadratic curve
* segment.
*/
public double y2;
/**
* Constructs and initializes a <code>QuadCurve2D</code> with
* coordinates (0, 0, 0, 0, 0, 0).
*/
public Double() {
}
/**
* Constructs and initializes a <code>QuadCurve2D</code> from the
* specified coordinates.
* @param x1, y1 the coordinates of the starting point
* @param ctrlx, ctrly the coordinates of the control point
* @param x2, y2 the coordinates of the ending point
*/
public Double(double x1, double y1,
double ctrlx, double ctrly,
double x2, double y2) {
setCurve(x1, y1, ctrlx, ctrly, x2, y2);
}
/**
* Returns the x coordinate of the start point in
* <code>double</code> precision.
* @return the x coordinate of the starting point.
*/
public double getX1() {
return x1;
}
/**
* Returns the y coordinate of the start point in
* <code>double</code> precision.
* @return the y coordiante of the starting point.
*/
public double getY1() {
return y1;
}
/**
* Returns the start point.
* @return a <code>Point2D</code> that is the starting point
* of this <code>QuadCurve2D</code>.
*/
public Point2D getP1() {
return new Point2D.Double(x1, y1);
}
/**
* Returns the x coordinate of the control point in
* <code>double</code> precision.
* @return the x coordinate of the control point.
*/
public double getCtrlX() {
return ctrlx;
}
/**
* Returns the y coordinate of the control point in
* <code>double</code> precision.
* @return the y coordiante of the control point.
*/
public double getCtrlY() {
return ctrly;
}
/**
* Returns the control point.
* @return a <code>Point2D</code> object that is the control
* point of this <code>QuadCurve2D</code>.
*/
public Point2D getCtrlPt() {
return new Point2D.Double(ctrlx, ctrly);
}
/**
* Returns the x coordinate of the end point in
* <code>double</code> precision.
* @return the x coordiante of the end point.
*/
public double getX2() {
return x2;
}
/**
* Returns the y coordinate of the end point in
* <code>double</code> precision.
* @return the y coordiante of the end point.
*/
public double getY2() {
return y2;
}
/**
* Returns the end point.
* @return a <code>Point2D</code> that is the end point
* of this <code>QuadCurve2D</code>.
*/
public Point2D getP2() {
return new Point2D.Double(x2, y2);
}
/**
* Sets the location of the endpoints and controlpoint of this curve
* to the specified <code>double</code> coordinates.
* @param x1, y1 the coordinates of the starting point
* @param ctrlx, ctrly the coordinates of the control point
* @param x2, y2 the coordinates of the ending point
*/
public void setCurve(double x1, double y1,
double ctrlx, double ctrly,
double x2, double y2) {
this.x1 = x1;
this.y1 = y1;
this.ctrlx = ctrlx;
this.ctrly = ctrly;
this.x2 = x2;
this.y2 = y2;
}
/**
* Returns the bounding box of this <code>QuadCurve2D</code>.
* @return a <code>Rectangle2D</code> that is the bounding
* box of the shape of this <code>QuadCurve2D</code>.
*/
public Rectangle2D getBounds2D() {
double left = Math.min(Math.min(x1, x2), ctrlx);
double top = Math.min(Math.min(y1, y2), ctrly);
double right = Math.max(Math.max(x1, x2), ctrlx);
double bottom = Math.max(Math.max(y1, y2), ctrly);
return new Rectangle2D.Double(left, top,
right - left, bottom - top);
}
}
/**
* This is an abstract class that cannot be instantiated directly.
* Type-specific implementation subclasses are available for
* instantiation and provide a number of formats for storing
* the information necessary to satisfy the various accessor
* methods below.
*
* @see java.awt.geom.QuadCurve2D.Float
* @see java.awt.geom.QuadCurve2D.Double
*/
protected QuadCurve2D() {
}
/**
* Returns the x coordinate of the start point in
* <code>double</code> in precision.
* @return the x coordinate of the start point.
*/
public abstract double getX1();
/**
* Returns the y coordinate of the start point in
* <code>double</code> precision.
* @return the y coordinate of the start point.
*/
public abstract double getY1();
/**
* Returns the start point.
* @return a <code>Point2D</code> that is the start point of this
* <code>QuadCurve2D</code>.
*/
public abstract Point2D getP1();
/**
* Returns the x coordinate of the control point in
* <code>double</code> precision.
* @return x coordinate the control point
*/
public abstract double getCtrlX();
/**
* Returns the y coordinate of the control point in
* <code>double</code> precision.
* @return the y coordinate of the control point.
*/
public abstract double getCtrlY();
/**
* Returns the control point.
* @return a <code>Point2D</code> that is the control point of this
* <code>Point2D</code>.
*/
public abstract Point2D getCtrlPt();
/**
* Returns the x coordinate of the end point in
* <code>double</code> precision.
* @return the x coordiante of the end point.
*/
public abstract double getX2();
/**
* Returns the y coordinate of the end point in
* <code>double</code> precision.
* @return the y coordinate of the end point.
*/
public abstract double getY2();
/**
* Returns the end point.
* @return a <code>Point</code> object that is the end point
* of this <code>Point2D</code>.
*/
public abstract Point2D getP2();
/**
* Sets the location of the endpoints and controlpoint of this curve
* to the specified <code>double</code> coordinates.
* @param x1, y1 the coordinates of the starting point
* @param ctrlx, ctrly the coordinates of the control point
* @param x2, y2 the coordinates of the ending point
*/
public abstract void setCurve(double x1, double y1,
double ctrlx, double ctrly,
double x2, double y2);
/**
* Sets the location of the endpoints and controlpoints of this
* <code>QuadCurve2D</code> to the <code>double</code> coordinates at
* the specified offset in the specified array.
* @param coords the array containing coordinate values
* @param offset the index into the array from which to start
* getting the coordinate values and assigning them to this
* <code>QuadCurve2D</code>
*/
public void setCurve(double[] coords, int offset) {
setCurve(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5]);
}
/**
* Sets the location of the endpoints and controlpoint of this
* <code>QuadCurve2D</code> to the specified <code>Point2D</code>
* coordinates.
* @param p1 the starting point
* @param cp the control point
* @param p2 the ending point
*/
public void setCurve(Point2D p1, Point2D cp, Point2D p2) {
setCurve(p1.getX(), p1.getY(),
cp.getX(), cp.getY(),
p2.getX(), p2.getY());
}
/**
* Sets the location of the endpoints and controlpoints of this
* <code>QuadCurve2D</code> to the coordinates of the
* <code>Point2D</code> objects at the specified offset in
* the specified array.
* @param pts an array containing <code>Point2D</code> that define
* coordinate values
* @param offset the index into <code>pts</code> at which to start
* getting the coordinate values and assigning them to this
* <code>QuadCurve2D</code>
*/
public void setCurve(Point2D[] pts, int offset) {
setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
pts[offset + 1].getX(), pts[offset + 1].getY(),
pts[offset + 2].getX(), pts[offset + 2].getY());
}
/**
* Sets the location of the endpoints and controlpoint of this
* <code>QuadCurve2D</code> to the same as those in the specified
* <code>QuadCurve2D</code>.
* @param c the specified <code>QuadCurve2D</code>
*/
public void setCurve(QuadCurve2D c) {
setCurve(c.getX1(), c.getY1(),
c.getCtrlX(), c.getCtrlY(),
c.getX2(), c.getY2());
}
/**
* Returns the square of the flatness, or maximum distance of a
* controlpoint from the line connecting the endpoints, of the
* quadratic curve specified by the indicated controlpoints.
* @param x1, y1 the coordinates of the starting point
* @param ctrlx, ctrly the coordinates of the control point
* @param x2, y2 the coordinates of the ending point
* @return the square of the flatness of the quadratic curve
* defined by the specified coordinates.
*/
public static double getFlatnessSq(double x1, double y1,
double ctrlx, double ctrly,
double x2, double y2) {
return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
}
/**
* Returns the flatness, or maximum distance of a
* controlpoint from the line connecting the endpoints, of the
* quadratic curve specified by the indicated controlpoints.
* @param x1, y1 the coordinates of the starting point
* @param ctrlx, ctrly the coordinates of the control point
* @param x2, y2 the coordinates of the ending point
* @return the flatness of the quadratic curve defined by the
* specified coordinates.
*/
public static double getFlatness(double x1, double y1,
double ctrlx, double ctrly,
double x2, double y2) {
return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
}
/**
* Returns the square of the flatness, or maximum distance of a
* controlpoint from the line connecting the endpoints, of the
* quadratic curve specified by the controlpoints stored in the
* indicated array at the indicated index.
* @param coords an array containing coordinate values
* @param offset the index into <code>coords</code> at which to
* to start getting the values from the array and
* assigning them to a quadratic curve
* @return the flatness of the quadratic curve that is defined by the
* values in the specified array at the specified index.
*/
public static double getFlatnessSq(double coords[], int offset) {
return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1],
coords[offset + 4], coords[offset + 5],
coords[offset + 2], coords[offset + 3]);
}
/**
* Returns the flatness, or maximum distance of a
* controlpoint from the line connecting the endpoints, of the
* quadratic curve specified by the controlpoints stored in the
* indicated array at the indicated index.
* @param coords an array containing coordinate values
* @param offset the index into <code>coords</code> at which to
* start getting the coordinate values and assigning
* them to a quadratic curve
* @return the flatness of a quadratic curve defined by the
* specified array at the specified offset.
*/
public static double getFlatness(double coords[], int offset) {
return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1],
coords[offset + 4], coords[offset + 5],
coords[offset + 2], coords[offset + 3]);
}
/**
* Returns the square of the flatness, or maximum distance of a
* controlpoint from the line connecting the endpoints, of this
* <code>QuadCurve2D</code>.
* @return the square of the flatness of this
* <code>QuadCurve2D</code>.
*/
public double getFlatnessSq() {
return Line2D.ptSegDistSq(getX1(), getY1(),
getX2(), getY2(),
getCtrlX(), getCtrlY());
}
/**
* Returns the flatness, or maximum distance of a
* controlpoint from the line connecting the endpoints, of this
* <code>QuadCurve2D</code>.
* @return the flatness of this <code>QuadCurve2D</code>.
*/
public double getFlatness() {
return Line2D.ptSegDist(getX1(), getY1(),
getX2(), getY2(),
getCtrlX(), getCtrlY());
}
/**
* Subdivides this <code>QuadCurve2D</code> and stores the resulting
* two subdivided curves into the <code>left</code> and
* <code>right</code> curve parameters.
* Either or both of the <code>left</code> and <code>right</code>
* objects can be the same as this <code>QuadCurve2D</code> or
* <code>null</code>.
* @param left the <code>QuadCurve2D</code> object for storing the
* left or first half of the subdivided curve
* @param right the <code>QuadCurve2D</code> object for storing the
* right or second half of the subdivided curve
*/
public void subdivide(QuadCurve2D left, QuadCurve2D right) {
subdivide(this, left, right);
}
/**
* Subdivides the quadratic curve specified by the <code>src</code>
* parameter and stores the resulting two subdivided curves into the
* <code>left</code> and <code>right</code> curve parameters.
* Either or both of the <code>left</code> and <code>right</code>
* objects can be the same as the <code>src</code> object or
* <code>null</code>.
* @param src the quadratic curve to be subdivided
* @param left the <code>QuadCurve2D</code> object for storing the
* left or first half of the subdivided curve
* @param right the <code>QuadCurve2D</code> object for storing the
* right or second half of the subdivided curve
*/
public static void subdivide(QuadCurve2D src,
QuadCurve2D left,
QuadCurve2D right) {
double x1 = src.getX1();
double y1 = src.getY1();
double ctrlx = src.getCtrlX();
double ctrly = src.getCtrlY();
double x2 = src.getX2();
double y2 = src.getY2();
double ctrlx1 = (x1 + ctrlx) / 2.0;
double ctrly1 = (y1 + ctrly) / 2.0;
double ctrlx2 = (x2 + ctrlx) / 2.0;
double ctrly2 = (y2 + ctrly) / 2.0;
ctrlx = (ctrlx1 + ctrlx2) / 2.0;
ctrly = (ctrly1 + ctrly2) / 2.0;
if (left != null) {
left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly);
}
if (right != null) {
right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2);
}
}
/**
* Subdivides the quadratic curve specified by the coordinates
* stored in the <code>src</code> array at indices
* <code>srcoff</code> through <code>srcoff</code> + 5
* and stores the resulting two subdivided curves into the two
* result arrays at the corresponding indices.
* Either or both of the <code>left</code> and <code>right</code>
* arrays can be <code>null</code> or a reference to the same array
* and offset as the <code>src</code> 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</code> and
* <code>right</code> and to use offsets such that
* <code>rightoff</code> equals <code>leftoff</code> + 4 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
*/
public static void subdivide(double src[], int srcoff,
double left[], int leftoff,
double right[], int rightoff) {
double x1 = src[srcoff + 0];
double y1 = src[srcoff + 1];
double ctrlx = src[srcoff + 2];
double ctrly = src[srcoff + 3];
double x2 = src[srcoff + 4];
double 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) / 2.0;
y1 = (y1 + ctrly) / 2.0;
x2 = (x2 + ctrlx) / 2.0;
y2 = (y2 + ctrly) / 2.0;
ctrlx = (x1 + x2) / 2.0;
ctrly = (y1 + y2) / 2.0;
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;
}
}
/**
* Solves the quadratic whose coefficients are in the <code>eqn</code>
* array and places the non-complex roots back into the same array,
* returning the number of roots. The quadratic solved is represented
* by the equation:
* <pre>
* eqn = {C, B, A};
* ax^2 + bx + c = 0
* </pre>
* A return value of <code>-1</code> is used to distinguish a constant
* equation, which might be always 0 or never 0, from an equation that
* has no zeroes.
* @param eqn the array that contains the quadratic coefficients
* @return the number of roots, or <code>-1</code> if the equation is
* a constant
*/
public static int solveQuadratic(double eqn[]) {
return solveQuadratic(eqn, eqn);
}
/**
* Solves the quadratic whose coefficients are in the <code>eqn</code>
* array and places the non-complex roots into the <code>res</code>
* array, returning the number of roots.
* The quadratic solved is represented by the equation:
* <pre>
* eqn = {C, B, A};
* ax^2 + bx + c = 0
* </pre>
* A return value of <code>-1</code> is used to distinguish a constant
* equation, which might be always 0 or never 0, from an equation that
* has no zeroes.
* @param eqn the specified array of coefficients to use to solve
* the quadratic equation
* @param res the array that contains the non-complex roots
* resulting from the solution of the quadratic equation
* @return the number of roots, or <code>-1</code> if the equation is
* a constant.
*/
public static int solveQuadratic(double eqn[], double res[]) {
double a = eqn[2];
double b = eqn[1];
double c = eqn[0];
int roots = 0;
if (a == 0.0) {
// The quadratic parabola has degenerated to a line.
if (b == 0.0) {
// The line has degenerated to a constant.
return -1;
}
res[roots++] = -c / b;
} else {
// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
double d = b * b - 4.0 * a * c;
if (d < 0.0) {
// If d < 0.0, then there are no roots
return 0;
}
d = Math.sqrt(d);
// For accuracy, calculate one root using:
// (-b +/- d) / 2a
// and the other using:
// 2c / (-b +/- d)
// Choose the sign of the +/- so that b+d gets larger in magnitude
if (b < 0.0) {
d = -d;
}
double q = (b + d) / -2.0;
// We already tested a for being 0 above
res[roots++] = q / a;
if (q != 0.0) {
res[roots++] = c / q;
}
}
return roots;
}
/**
* Tests if a specified coordinate is inside the boundary of the
* shape of this <code>QuadCurve2D</code>.
* @param x, y the specified coordinates
* @return <code>true</code> if the specified coordinate is inside
* the boundary of the shape of this
* <code>QuadCurve2D</code>; <code>false</code> otherwise.
*/
public boolean contains(double x, double y) {
double x1 = getX1();
double y1 = getY1();
double xc = getCtrlX();
double yc = getCtrlY();
double x2 = getX2();
double y2 = getY2();
/*
* We have a convex shape bounded by quad curve Pc(t)
* and ine Pl(t).
*
* P1 = (x1, y1) - start point of curve
* P2 = (x2, y2) - end point of curve
* Pc = (xc, yc) - control point
*
* Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 =
* = (P1 - 2*Pc + P2)*t^2 + 2*(Pc - P1)*t + P1
* Pl(t) = P1*(1 - t) + P2*t
* t = [0:1]
*
* P = (x, y) - point of interest
*
* Let's look at second derivative of quad curve equation:
*
* Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq''
* It's constant vector.
*
* Let's draw a line through P to be parallel to this
* vector and find the intersection of the quad curve
* and the line.
*
* Pq(t) is point of intersection if system of equations
* below has the solution.
*
* L(s) = P + Pq''*s == Pq(t)
* Pq''*s + (P - Pq(t)) == 0
*
* | xq''*s + (x - xq(t)) == 0
* | yq''*s + (y - yq(t)) == 0
*
* This system has the solution if rank of its matrix equals to 1.
* That is, determinant of the matrix should be zero.
*
* (y - yq(t))*xq'' == (x - xq(t))*yq''
*
* Let's solve this equation with 't' variable.
* Also let kx = x1 - 2*xc + x2
* ky = y1 - 2*yc + y2
*
* t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) /
* ((xc - x1)*ky - (yc - y1)*kx)
*
* Let's do the same for our line Pl(t):
*
* t0l = ((x - x1)*ky - (y - y1)*kx) /
* ((x2 - x1)*ky - (y2 - y1)*kx)
*
* It's easy to check that t0q == t0l. This fact means
* we can compute t0 only one time.
*
* In case t0 < 0 or t0 > 1, we have an intersections outside
* of shape bounds. So, P is definitely out of shape.
*
* In case t0 is inside [0:1], we should calculate Pq(t0)
* and Pl(t0). We have three points for now, and all of them
* lie on one line. So, we just need to detect, is our point
* of interest between points of intersections or not.
*
* If the denominator in the t0q and t0l equations is
* zero, then the points must be collinear and so the
* curve is degenerate and encloses no area. Thus the
* result is false.
*/
double kx = x1 - 2 * xc + x2;
double ky = y1 - 2 * yc + y2;
double dx = x - x1;
double dy = y - y1;
double dxl = x2 - x1;
double dyl = y2 - y1;
double t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx);
if (t0 < 0 || t0 > 1 || t0 != t0) {
return false;
}
double xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1;
double yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1;
double xl = dxl * t0 + x1;
double yl = dyl * t0 + y1;
return (x >= xb && x < xl) ||
(x >= xl && x < xb) ||
(y >= yb && y < yl) ||
(y >= yl && y < yb);
}
/**
* Tests if a specified <code>Point2D</code> is inside the boundary of
* the shape of this <code>QuadCurve2D</code>.
* @param p the specified <code>Point2D</code>
* @return <code>true</code> if the specified <code>Point2D</code> is
* inside the boundary of the shape of this
* <code>QuadCurve2D</code>.
*/
public boolean contains(Point2D p) {
return contains(p.getX(), p.getY());
}
/*
* Fill an array with the coefficients of the parametric equation
* in t, ready for solving against val with solveQuadratic.
* We currently have:
* val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2
* = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2
* = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
* 0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
* 0 = C + Bt + At^2
* C = C1 - val
* B = 2*CP - 2*C1
* A = C1 - 2*CP + C2
*/
private static void fillEqn(double eqn[], double val,
double c1, double cp, double c2) {
eqn[0] = c1 - val;
eqn[1] = cp + cp - c1 - c1;
eqn[2] = c1 - cp - cp + c2;
return;
}
/*
* Evaluate the t values in the first num slots of the vals[] array
* and place the evaluated values back into the same array. Only
* evaluate t values that are within the range <0, 1>, including
* the 0 and 1 ends of the range iff the include0 or include1
* booleans are true. If an "inflection" equation is handed in,
* then any points which represent a point of inflection for that
* quadratic equation are also ignored.
*/
private static int evalQuadratic(double vals[], int num,
boolean include0,
boolean include1,
double inflect[],
double c1, double ctrl, double c2) {
int j = 0;
for (int i = 0; i < num; i++) {
double t = vals[i];
if ((include0 ? t >= 0 : t > 0) &&
(include1 ? t <= 1 : t < 1) &&
(inflect == null ||
inflect[1] + 2*inflect[2]*t != 0))
{
double u = 1 - t;
vals[j++] = c1*u*u + 2*ctrl*t*u + c2*t*t;
}
}
return j;
}
private static final int BELOW = -2;
private static final int LOWEDGE = -1;
private static final int INSIDE = 0;
private static final int HIGHEDGE = 1;
private static final int ABOVE = 2;
/*
* Determine where coord lies with respect to the range from
* low to high. It is assumed that low <= high. The return
* value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
* or ABOVE.
*/
private static int getTag(double coord, double low, double high) {
if (coord <= low) {
return (coord < low ? BELOW : LOWEDGE);
}
if (coord >= high) {
return (coord > high ? ABOVE : HIGHEDGE);
}
return INSIDE;
}
/*
* Determine if the pttag represents a coordinate that is already
* in its test range, or is on the border with either of the two
* opttags representing another coordinate that is "towards the
* inside" of that test range. In other words, are either of the
* two "opt" points "drawing the pt inward"?
*/
private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
switch (pttag) {
case BELOW:
case ABOVE:
default:
return false;
case LOWEDGE:
return (opt1tag >= INSIDE || opt2tag >= INSIDE);
case INSIDE:
return true;
case HIGHEDGE:
return (opt1tag <= INSIDE || opt2tag <= INSIDE);
}
}
/**
* Tests if the shape of this <code>QuadCurve2D</code> intersects the
* interior of a specified set of rectangular coordinates.
* @param x, y the coordinates of the upper-left corner of the
* specified rectangular area
* @param w the width of the specified rectangular area
* @param h the height of the specified rectangular area
* @return <code>true</code> if the shape of this
* <code>QuadCurve2D</code> intersects the interior of the
* specified set of rectangular coordinates;
* <code>false</code> otherwise.
*/
public boolean intersects(double x, double y, double w, double h) {
// Trivially reject non-existant rectangles
if (w < 0 || h < 0) {
return false;
}
// Trivially accept if either endpoint is inside the rectangle
// (not on its border since it may end there and not go inside)
// Record where they lie with respect to the rectangle.
// -1 => left, 0 => inside, 1 => right
double x1 = getX1();
double y1 = getY1();
int x1tag = getTag(x1, x, x+w);
int y1tag = getTag(y1, y, y+h);
if (x1tag == INSIDE && y1tag == INSIDE) {
return true;
}
double x2 = getX2();
double y2 = getY2();
int x2tag = getTag(x2, x, x+w);
int y2tag = getTag(y2, y, y+h);
if (x2tag == INSIDE && y2tag == INSIDE) {
return true;
}
double ctrlx = getCtrlX();
double ctrly = getCtrlY();
int ctrlxtag = getTag(ctrlx, x, x+w);
int ctrlytag = getTag(ctrly, y, y+h);
// Trivially reject if all points are entirely to one side of
// the rectangle.
if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) {
return false; // All points left
}
if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) {
return false; // All points above
}
if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) {
return false; // All points right
}
if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) {
return false; // All points below
}
// Test for endpoints on the edge where either the segment
// or the curve is headed "inwards" from them
// Note: These tests are a superset of the fast endpoint tests
// above and thus repeat those tests, but take more time
// and cover more cases
if (inwards(x1tag, x2tag, ctrlxtag) &&
inwards(y1tag, y2tag, ctrlytag))
{
// First endpoint on border with either edge moving inside
return true;
}
if (inwards(x2tag, x1tag, ctrlxtag) &&
inwards(y2tag, y1tag, ctrlytag))
{
// Second endpoint on border with either edge moving inside
return true;
}
// Trivially accept if endpoints span directly across the rectangle
boolean xoverlap = (x1tag * x2tag <= 0);
boolean yoverlap = (y1tag * y2tag <= 0);
if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
return true;
}
if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
return true;
}
// We now know that both endpoints are outside the rectangle
// but the 3 points are not all on one side of the rectangle.
// Therefore the curve cannot be contained inside the rectangle,
// but the rectangle might be contained inside the curve, or
// the curve might intersect the boundary of the rectangle.
double[] eqn = new double[3];
double[] res = new double[3];
if (!yoverlap) {
// Both y coordinates for the closing segment are above or
// below the rectangle which means that we can only intersect
// if the curve crosses the top (or bottom) of the rectangle
// in more than one place and if those crossing locations
// span the horizontal range of the rectangle.
fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly, y2);
return (solveQuadratic(eqn, res) == 2 &&
evalQuadratic(res, 2, true, true, null,
x1, ctrlx, x2) == 2 &&
getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0);
}
// Y ranges overlap. Now we examine the X ranges
if (!xoverlap) {
// Both x coordinates for the closing segment are left of
// or right of the rectangle which means that we can only
// intersect if the curve crosses the left (or right) edge
// of the rectangle in more than one place and if those
// crossing locations span the vertical range of the rectangle.
fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx, x2);
return (solveQuadratic(eqn, res) == 2 &&
evalQuadratic(res, 2, true, true, null,
y1, ctrly, y2) == 2 &&
getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0);
}
// The X and Y ranges of the endpoints overlap the X and Y
// ranges of the rectangle, now find out how the endpoint
// line segment intersects the Y range of the rectangle
double dx = x2 - x1;
double dy = y2 - y1;
double k = y2 * x1 - x2 * y1;
int c1tag, c2tag;
if (y1tag == INSIDE) {
c1tag = x1tag;
} else {
c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w);
}
if (y2tag == INSIDE) {
c2tag = x2tag;
} else {
c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w);
}
// If the part of the line segment that intersects the Y range
// of the rectangle crosses it horizontally - trivially accept
if (c1tag * c2tag <= 0) {
return true;
}
// Now we know that both the X and Y ranges intersect and that
// the endpoint line segment does not directly cross the rectangle.
//
// We can almost treat this case like one of the cases above
// where both endpoints are to one side, except that we will
// only get one intersection of the curve with the vertical
// side of the rectangle. This is because the endpoint segment
// accounts for the other intersection.
//
// (Remember there is overlap in both the X and Y ranges which
// means that the segment must cross at least one vertical edge
// of the rectangle - in particular, the "near vertical side" -
// leaving only one intersection for the curve.)
//
// Now we calculate the y tags of the two intersections on the
// "near vertical side" of the rectangle. We will have one with
// the endpoint segment, and one with the curve. If those two
// vertical intersections overlap the Y range of the rectangle,
// we have an intersection. Otherwise, we don't.
// c1tag = vertical intersection class of the endpoint segment
//
// Choose the y tag of the endpoint that was not on the same
// side of the rectangle as the subsegment calculated above.
// Note that we can "steal" the existing Y tag of that endpoint
// since it will be provably the same as the vertical intersection.
c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);
// c2tag = vertical intersection class of the curve
//
// We have to calculate this one the straightforward way.
// Note that the c2tag can still tell us which vertical edge
// to test against.
fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx, x2);
int num = solveQuadratic(eqn, res);
// Note: We should be able to assert(num == 2); since the
// X range "crosses" (not touches) the vertical boundary,
// but we pass num to evalQuadratic for completeness.
evalQuadratic(res, num, true, true, null, y1, ctrly, y2);
// Note: We can assert(num evals == 1); since one of the
// 2 crossings will be out of the [0,1] range.
c2tag = getTag(res[0], y, y+h);
// Finally, we have an intersection if the two crossings
// overlap the Y range of the rectangle.
return (c1tag * c2tag <= 0);
}
/**
* Tests if the shape of this <code>QuadCurve2D</code> intersects the
* interior of a specified <code>Rectangle2D</code>.
* @param r the specified <code>Rectangle2D</code>
* @return <code>true</code> if the shape of this
* <code>QuadCurve2D</code> intersects the interior of
* the specified <code>Rectangle2D</code>;
* <code>false</code> otherwise.
*/
public boolean intersects(Rectangle2D r) {
return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
}
/**
* Tests if the interior of the shape of this
* <code>QuadCurve2D</code> entirely contains the specified
* set of rectangular coordinates.
* @param x, y the coordinates of the upper-left corner of the
* specified rectangular area
* @param w the width of the specified rectangular area
* @param h the height of the specified rectangular area
* @return <code>true</code> if the interior of the shape of this
* <code>QuadCurve2D</code> entirely contains the specified
* rectangluar area; <code>false</code> otherwise.
*/
public boolean contains(double x, double y, double w, double h) {
// Assertion: Quadratic curves closed by connecting their
// endpoints are always convex.
return (contains(x, y) &&
contains(x + w, y) &&
contains(x + w, y + h) &&
contains(x, y + h));
}
/**
* Tests if the interior of the shape of this
* <code>QuadCurve2D</code> entirely contains the specified
* <code>Rectangle2D</code>.
* @param r the specified <code>Rectangle2D</code>
* @return <code>true</code> if the interior of the shape of this
* <code>QuadCurve2D</code> entirely contains the specified
* <code>Rectangle2D</code>; <code>false</code> otherwise.
*/
public boolean contains(Rectangle2D r) {
return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
}
/**
* Returns the bounding box of this <code>QuadCurve2D</code>.
* @return a {@link Rectangle} that is the bounding box of the shape
* of this <code>QuadCurve2D</code>.
*/
public Rectangle getBounds() {
return getBounds2D().getBounds();
}
/**
* Returns an iteration object that defines the boundary of the
* shape of this <code>QuadCurve2D</code>.
* The iterator for this class is not multi-threaded safe,
* which means that this <code>QuadCurve2D</code> class does not
* guarantee that modifications to the geometry of this
* <code>QuadCurve2D</code> object do not affect any iterations of
* that geometry that are already in process.
* @param at an optional {@link AffineTransform} to apply to the
* shape boundary
* @return a {@link PathIterator} object that defines the boundary
* of the shape.
*/
public PathIterator getPathIterator(AffineTransform at) {
return new QuadIterator(this, at);
}
/**
* Returns an iteration object that defines the boundary of the
* flattened shape of this <code>QuadCurve2D</code>.
* The iterator for this class is not multi-threaded safe,
* which means that this <code>QuadCurve2D</code> class does not
* guarantee that modifications to the geometry of this
* <code>QuadCurve2D</code> object do not affect any iterations of
* that geometry that are already in process.
* @param at an optional <code>AffineTransform</code> to apply
* to the boundary of the shape
* @param flatness the maximum distance that the control points for a
* subdivided curve can be with respect to a line connecting
* the endpoints of this curve before this curve is
* replaced by a straight line connecting the endpoints.
* @return a <code>PathIterator</code> object that defines the
* flattened boundary of the shape.
*/
public PathIterator getPathIterator(AffineTransform at, double flatness) {
return new FlatteningPathIterator(getPathIterator(at), flatness);
}
/**
* Creates a new object of the same class and with the same contents
* as this object.
*
* @return a clone of this instance.
* @exception OutOfMemoryError if there is not enough memory.
* @see java.lang.Cloneable
* @since 1.2
*/
public Object clone() {
try {
return super.clone();
} catch (CloneNotSupportedException e) {
// this shouldn't happen, since we are Cloneable
throw new InternalError();
}
}
}
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