java.awt.geom
public abstract class CubicCurve2D extends Object implements Shape, Cloneable
Modifier and Type | Class and Description |
---|---|
static class |
CubicCurve2D.Double
A two-dimensional curve that is parameterized with a cubic
function and stores coordinate values in double-precision
floating-point format.
|
static class |
CubicCurve2D.Float
A two-dimensional curve that is parameterized with a cubic
function and stores coordinate values in single-precision
floating-point format.
|
Modifier | Constructor and Description |
---|---|
protected |
CubicCurve2D()
Constructs a new CubicCurve2D.
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Modifier and Type | Method and Description |
---|---|
Object |
clone()
Create a new curve with the same contents as this one.
|
boolean |
contains(double x,
double y)
Determines whether a position lies inside the area bounded
by the curve and the straight line connecting its end points.
|
boolean |
contains(double x,
double y,
double w,
double h)
Determine whether a rectangle is entirely inside the area that is bounded
by the curve and the straight line connecting its end points.
|
boolean |
contains(Point2D p)
Determines whether a point lies inside the area bounded
by the curve and the straight line connecting its end points.
|
boolean |
contains(Rectangle2D r)
Determine whether a Rectangle2D is entirely inside the area that is
bounded by the curve and the straight line connecting its end points.
|
Rectangle |
getBounds()
Determines the smallest rectangle that encloses the
curve’s start, end and control points.
|
abstract Point2D |
getCtrlP1()
Returns the curve’s first control point.
|
abstract Point2D |
getCtrlP2()
Returns the curve’s second control point.
|
abstract double |
getCtrlX1()
Returns the x coordinate of the curve’s first
control point.
|
abstract double |
getCtrlX2()
Returns the x coordinate of the curve’s second
control point.
|
abstract double |
getCtrlY1()
Returns the y coordinate of the curve’s first
control point.
|
abstract double |
getCtrlY2()
Returns the y coordinate of the curve’s second
control point.
|
double |
getFlatness()
Calculates the flatness of this curve.
|
static double |
getFlatness(double[] coords,
int offset)
Calculates the flatness of a cubic curve, specifying the
coordinate values in an array.
|
static double |
getFlatness(double x1,
double y1,
double cx1,
double cy1,
double cx2,
double cy2,
double x2,
double y2)
Calculates the flatness of a cubic curve, directly specifying
each coordinate value.
|
double |
getFlatnessSq()
Calculates the squared flatness of this curve.
|
static double |
getFlatnessSq(double[] coords,
int offset)
Calculates the squared flatness of a cubic curve, specifying the
coordinate values in an array.
|
static double |
getFlatnessSq(double x1,
double y1,
double cx1,
double cy1,
double cx2,
double cy2,
double x2,
double y2)
Calculates the squared flatness of a cubic curve, directly
specifying each coordinate value.
|
abstract Point2D |
getP1()
Returns the curve’s start point.
|
abstract Point2D |
getP2()
Returns the curve’s end point.
|
PathIterator |
getPathIterator(AffineTransform at)
Return an iterator along the shape boundary.
|
PathIterator |
getPathIterator(AffineTransform at,
double flatness)
Return an iterator along the flattened version of the shape boundary.
|
abstract double |
getX1()
Returns the x coordinate of the curve’s start
point.
|
abstract double |
getX2()
Returns the x coordinate of the curve’s end
point.
|
abstract double |
getY1()
Returns the y coordinate of the curve’s start
point.
|
abstract double |
getY2()
Returns the y coordinate of the curve’s end
point.
|
boolean |
intersects(double x,
double y,
double w,
double h)
Determines whether any part of a rectangle is inside the area bounded
by the curve and the straight line connecting its end points.
|
boolean |
intersects(Rectangle2D r)
Determines whether any part of a Rectangle2D is inside the area bounded
by the curve and the straight line connecting its end points.
|
void |
setCurve(CubicCurve2D c)
Changes the curve geometry to that of another curve.
|
void |
setCurve(double[] coords,
int offset)
Changes the curve geometry, specifying coordinate values in an
array.
|
abstract void |
setCurve(double x1,
double y1,
double cx1,
double cy1,
double cx2,
double cy2,
double x2,
double y2)
Changes the curve geometry, separately specifying each coordinate
value.
|
void |
setCurve(Point2D[] pts,
int offset)
Changes the curve geometry, specifying coordinate values in an
array of Point objects.
|
void |
setCurve(Point2D p1,
Point2D c1,
Point2D c2,
Point2D p2)
Changes the curve geometry, specifying coordinate values in
separate Point objects.
|
static int |
solveCubic(double[] eqn)
Finds the non-complex roots of a cubic equation, placing the
results into the same array as the equation coefficients.
|
static int |
solveCubic(double[] eqn,
double[] res)
Finds the non-complex roots of a cubic equation.
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void |
subdivide(CubicCurve2D left,
CubicCurve2D right)
Subdivides this curve into two halves.
|
static void |
subdivide(CubicCurve2D src,
CubicCurve2D left,
CubicCurve2D right)
Subdivides a cubic curve into two halves.
|
static void |
subdivide(double[] src,
int srcOff,
double[] left,
int leftOff,
double[] right,
int rightOff)
Subdivides a cubic curve into two halves, passing all coordinates
in an array.
|
equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
getBounds2D
protected CubicCurve2D()
CubicCurve2D.Float
or CubicCurve2D.Double
.public abstract double getX1()
public abstract double getY1()
public abstract double getCtrlX1()
public abstract double getCtrlY1()
public abstract double getCtrlX2()
public abstract double getCtrlY2()
public abstract double getX2()
public abstract double getY2()
public abstract void setCurve(double x1, double y1, double cx1, double cy1, double cx2, double cy2, double x2, double y2)
x1
- the x coordinate of the curve’s new start
point.y1
- the y coordinate of the curve’s new start
point.cx1
- the x coordinate of the curve’s new
first control point.cy1
- the y coordinate of the curve’s new
first control point.cx2
- the x coordinate of the curve’s new
second control point.cy2
- the y coordinate of the curve’s new
second control point.x2
- the x coordinate of the curve’s new end
point.y2
- the y coordinate of the curve’s new end
point.public void setCurve(double[] coords, int offset)
coords
- an array containing the new coordinate values. The
x coordinate of the new start point is located at
coords[offset]
, its y coordinate at
coords[offset + 1]
. The x coordinate of the
new first control point is located at coords[offset +
2]
, its y coordinate at coords[offset +
3]
. The x coordinate of the new second control
point is located at coords[offset + 4]
, its y
coordinate at coords[offset + 5]
. The x
coordinate of the new end point is located at coords[offset
+ 6]
, its y coordinate at coords[offset +
7]
.offset
- the offset of the first coordinate value in
coords
.public void setCurve(Point2D p1, Point2D c1, Point2D c2, Point2D p2)
The curve does not keep any reference to the passed point
objects. Therefore, a later change to p1
,
c1
, c2
or p2
will not
affect the curve geometry.
p1
- the new start point.c1
- the new first control point.c2
- the new second control point.p2
- the new end point.public void setCurve(Point2D[] pts, int offset)
The curve does not keep references to the passed point
objects. Therefore, a later change to the pts
array
or any of its elements will not affect the curve geometry.
pts
- an array containing the points. The new start point
is located at pts[offset]
, the new first control
point at pts[offset + 1]
, the new second control
point at pts[offset + 2]
, and the new end point
at pts[offset + 3]
.offset
- the offset of the start point in pts
.public void setCurve(CubicCurve2D c)
c
- the curve whose coordinates will be copied.public static double getFlatnessSq(double x1, double y1, double cx1, double cy1, double cx2, double cy2, double x2, double y2)
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.
x1
- the x coordinate of the start point P1.y1
- the y coordinate of the start point P1.cx1
- the x coordinate of the first control point C1.cy1
- the y coordinate of the first control point C1.cx2
- the x coordinate of the second control point C2.cy2
- the y coordinate of the second control point C2.x2
- the x coordinate of the end point P2.y2
- the y 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)
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.
x1
- the x coordinate of the start point P1.y1
- the y coordinate of the start point P1.cx1
- the x coordinate of the first control point C1.cy1
- the y coordinate of the first control point C1.cx2
- the x coordinate of the second control point C2.cy2
- the y coordinate of the second control point C2.x2
- the x coordinate of the end point P2.y2
- the y coordinate of the end point P2.public static double getFlatnessSq(double[] coords, int offset)
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.
coords
- an array containing the coordinate values. The
x coordinate of the start point P1 is located at
coords[offset]
, its y coordinate at
coords[offset + 1]
. The x coordinate of the
first control point C1 is located at coords[offset +
2]
, its y coordinate at coords[offset +
3]
. The x coordinate of the second control point C2
is located at coords[offset + 4]
, its y
coordinate at coords[offset + 5]
. The x
coordinate of the end point P2 is located at coords[offset
+ 6]
, its y coordinate at coords[offset +
7]
.offset
- the offset of the first coordinate value in
coords
.public static double getFlatness(double[] coords, int offset)
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.
coords
- an array containing the coordinate values. The
x coordinate of the start point P1 is located at
coords[offset]
, its y coordinate at
coords[offset + 1]
. The x coordinate of the
first control point C1 is located at coords[offset +
2]
, its y coordinate at coords[offset +
3]
. The x coordinate of the second control point C2
is located at coords[offset + 4]
, its y
coordinate at coords[offset + 5]
. The x
coordinate of the end point P2 is located at coords[offset
+ 6]
, its y coordinate at coords[offset +
7]
.offset
- the offset of the first coordinate value in
coords
.public double getFlatnessSq()
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 getFlatness()
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 void subdivide(CubicCurve2D left, CubicCurve2D right)
left
- a curve whose geometry will be set to the left half
of this curve, or null
if the caller is not
interested in the left half.right
- a curve whose geometry will be set to the right half
of this curve, or null
if the caller is not
interested in the right half.public static void subdivide(CubicCurve2D src, CubicCurve2D left, CubicCurve2D right)
src
- the curve to be subdivided.left
- a curve whose geometry will be set to the left half
of src
, or null
if the caller is not
interested in the left half.right
- a curve whose geometry will be set to the right half
of src
, or null
if the caller is not
interested in the right half.public static void subdivide(double[] src, int srcOff, double[] left, int leftOff, double[] right, int rightOff)
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 left
and right
, and
set rightOff
to leftOff + 6
.
src
- an array containing the coordinates of the curve to be
subdivided. The x coordinate of the start point P1 is
located at src[srcOff]
, its y at
src[srcOff + 1]
. The x coordinate of the
first control point C1 is located at src[srcOff +
2]
, its y at src[srcOff + 3]
. The
x coordinate of the second control point C2 is located at
src[srcOff + 4]
, its y at src[srcOff +
5]
. The x coordinate of the end point is located at
src[srcOff + 6]
, its y at src[srcOff +
7]
.srcOff
- an offset into src
, specifying
the index of the start point’s x coordinate.left
- an array that will receive the coordinates of the
left half of src
. It is acceptable to pass
src
. A caller who is not interested in the left half
can pass null
.leftOff
- an offset into left
, specifying the
index where the start point’s x coordinate will be
stored.right
- an array that will receive the coordinates of the
right half of src
. It is acceptable to pass
src
or left
. A caller who is not
interested in the right half can pass null
.rightOff
- an offset into right
, specifying the
index where the start point’s x coordinate will be
stored.public static int solveCubic(double[] eqn)
eqn[3]
· x3 +eqn[2]
· x2 +eqn[1]
· x +eqn[0]
= 0
For some background about solving cubic equations, see the article “Cubic Formula” in PlanetMath. For an extensive library of numerical algorithms written in the C programming language, see the GNU Scientific Library, from which this implementation was adapted.
eqn
- an array with the coefficients of the equation. When
this procedure has returned, eqn
will contain the
non-complex solutions of the equation, in no particular order.solveCubic(double[], double[])
,
QuadCurve2D.solveQuadratic(double[],double[])
public static int solveCubic(double[] eqn, double[] res)
eqn[3]
· x3 +eqn[2]
· x2 +eqn[1]
· x +eqn[0]
= 0
For some background about solving cubic equations, see the article “Cubic Formula” in PlanetMath. For an extensive library of numerical algorithms written in the C programming language, see the GNU Scientific Library, from which this implementation was adapted.
eqn
- an array with the coefficients of the equation.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 eqn
and res
.QuadCurve2D.solveQuadratic(double[],double[])
public boolean contains(double x, double y)
The above drawing illustrates in which area points are considered “inside” a CubicCurve2D.
public boolean contains(Point2D p)
The above drawing illustrates in which area points are considered “inside” a CubicCurve2D.
public boolean intersects(double x, double y, double w, double h)
The above drawing illustrates in which area points are considered “inside” in a CubicCurve2D.
intersects
in interface Shape
x
- the x coordinate of the rectangley
- the y coordinate of the rectanglew
- the width of the rectangle, undefined results if negativeh
- the height of the rectangle, undefined results if negativecontains(double, double)
public boolean intersects(Rectangle2D r)
intersects
in interface Shape
r
- the rectangleintersects(double, double, double, double)
public boolean contains(double x, double y, double w, double h)
The above drawing illustrates in which area points are considered “inside” a CubicCurve2D.
contains
in interface Shape
x
- the x coordinate of the rectangley
- the y coordinate of the rectanglew
- the width of the rectangle, undefined results if negativeh
- the height of the rectangle, undefined results if negativecontains(double, double)
public boolean contains(Rectangle2D r)
The above drawing illustrates in which area points are considered “inside” a CubicCurve2D.
contains
in interface Shape
r
- the rectanglecontains(double, double)
public Rectangle getBounds()
getBounds
in interface Shape
Shape.getBounds2D()
public PathIterator getPathIterator(AffineTransform at)
Shape
getPathIterator
in interface Shape
at
- an optional transform to apply to the
iterator (null
permitted).public PathIterator getPathIterator(AffineTransform at, double flatness)
Shape
If the optional transform is provided, the iterator is transformed accordingly. Each call returns a new object, independent from others in use. It is recommended, but not required, that the Shape isolate iterations from future changes to the boundary, and document this fact.
getPathIterator
in interface Shape
at
- an optional transform to apply to the
iterator (null
permitted).flatness
- the maximum distance for deviation from the real boundary