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Class figPac.fBezier
java.lang.Object

+figPac.fBezier
 public class fBezier
 extends Object
 implements fElement, S2V, fInteractive, MouseListener, MouseMotionListener, ItemListener, ActionListener
The class fBezier plots a smooth, Bezier curve through a sequence of points.
A Bezier curve is a union of Bezier intervals, with each Bezier interval connecting
two successive points in the specified sequence. A Bezier interval is determined
by two twodimensional position vectors x1[], x2[] and two twodimensional
velocity vectors v1[], v2[]. The Bezier interval is the parameterized curve x[](t)
that is given by the unique cubic polynomial
x[](t) = a0[] + a1[]*t + a2[]*t**2 + a3[]*t**3
obeying the conditions
x[](0) = x1[]
x'[](0) = v1[]
x[](1) = x2[]
x'[](1) = v2[]
Here, x'[](t) is the derivative (i.e. velocity vector) for the curve x[](t) at time t.
The simplest way to specify a Bezier curve to the class fBezier is to just
pass it a sequence of position vectors. Then fBezier automatically builds
a corresponding sequence of velocity vectors by the following algorithm.
Consider the Bezier interval joining x1[] and x2[] and denote by x0[] and
x3[] the points in the sequence immediately preceeding and following x1[] and x2[].
Also denote by d0, d1 and d2 the distances from x0[] to x1[], from x1[] to x2[]
and from x2[] to x3[] respectively. Then, if none of d0, d1 and d2 are zero,
v1[] = (d1/2)*( (x1[]x0[])/d0 + (x2[]x1[])/d1 )
v2[] = (d1/2)*( (x2[]x1[])/d1 + (x3[]x2[])/d2 )
If d1=0
v1[] = 0
v2[] = 0
If d1!=0 but d0=0 replace v1[] by
v1[] = x2[]x1[]
If d1!=0 but d2=0 replace v2[] by
v2[] = x2[]x1[]
You can modify this choice of velocity vectors by assigning nondefault values,
for example using the configure() methods, to one or more of
scale[i], relScale[i], angle[i], relAngle[i]. Here i is the index (starting at i=0)
of a point of the sequence. Call the point x[]. Denote by v_in[] the velocity
with which the Bezier curve enters x[] (that is, the second velocity vector
for the Bezier interval whose second point is x[]) and by v_out[] the velocity
with which the Bezier curve leaves x[] (that is, the first velocity vector
for the Bezier interval whose first point is x[]). The computeCoeff() method
first uses the above algorithm to assign preliminary values to v_in[] and v_out
and then
 multiplies the lengths of both v_in[] and v_out[] by scale[i] and then
 multiplies the ratio v_out[]/v_in[] of the lengths by relScale[i] and then
 rotates both v_in[] and v_out[] by angle[i] degrees and then
 increases the angle between v_in[] and v_out[] by relAngle[i] degrees
One may also choose explicit directions for v_in[] and v_out[]. To do so
just change the value, for example using the configure() methods, of
inAngle[i] or outAngle[i] from NaN to an angle in degrees.

angle


CLOSED


curve
 The parametrized curve whose graph is the Bezier curve.

defaultFillColor
 The default color used to fill the curve on the screen.

defaultPsFillColor
 The default PostScript command used to color in the curve in PostScript when the fEnv variable useColorPs is "true".

defaultPsFillGray
 Controls the default density used to fill the curve in postscript.

DOT


fillColor
 The color used to fill the curve on the screen.

FILLED


inAngle


OPEN


outAngle


psDotFont
 In the postcsript image, when fBezier.DOT is included in the type of
the fPolygon, character number psDotSymbol of the font psDotFont is printed at each vertex.

psDotSymbol
 In the postcsript image, when fBezier.DOT is included in the type of
the fPolygon, character number psDotSymbol of the font psDotFont is printed at each vertex.

psFillColor
 The PostScript command used to color in the curve in PostScript when the fEnv variable useColorPs is "true".

psFillGray
 Controls the density used to fill the curve in postscript.

relAngle


relScale


scale


tmax
 The parameter limits for curve.

tmin
 The parameter limits for curve.

type
 The type determines whether the curve is plotted as an open or closed path,
whether or not it is filled and so on.

x


y


fBezier()


fBezier(double[], double[], double[], double[], double[], double[], double[], double[], int, long)


fBezier(double[], double[], double[], double[], double[], double[], int, long)


fBezier(double[], double[], int)


fBezier(double[], double[], int, long)


fBezier(double[], double[], int, long, Color)


fBezier(double[][])
 Creates the fBezier whose vertices are taken from the array list.

fBezier(double[][], int)
 Creates the fBezier whose vertices are the first nopoints of the array list.

fBezier(double[][], int, long)


fBezier(double[][], int, long, Color)


fBezier(double[][], long)
 Creates the fBezier whose vertices are taken from the array list and also
sets its type.

fBezier(PointList)
 Creates the fBezier whose vertices are listed in the PointList.

fBezier(PointList, int)
 Creates the fBezier whose vertices are the first nopoints of the PointList.

fBezier(PointList, int, long)


fBezier(PointList, int, long, Color)


fBezier(PointList, long)
 Creates the fBezier whose vertices are listed in the PointList and also
sets its type.

fBezier(PointList, long, Color)
 Creates the fBezier whose vertices are listed in the PointList and also
sets its type and fillColor.

actionPerformed(ActionEvent)


append(double, double)
 Appends the vertex with coordinates (x,y) to the Bezier sequence.

configure(String, double)
 Sets the value of the property specified by the first argument to
the second argument.

configure(String, double[])
 Sets the value of the property specified by the first argument to
the second argument.

configure(String, String)


delete(int)
 Removes vertex number vertexNo from the Bezier sequence.

drawgfx(Figure, Hashtable, V2V)


drawps(Figure, Hashtable, V2V)


endEdit()


endEditAndDelete()


insert(double, double, int)
 Inserts a vertex with coordinates (x,y) at position number vertexNo in
Bezier sequence.

itemStateChanged(ItemEvent)


map(double)
 On the interval [i, i+1) returns the cubic polynomial
( a0x[i+1] + a1x[i+1] (ti) + a2x[i+1] (ti)^2 + a3x[i+1] (ti)^3,
a0y[i+1] + a1y[i+1] (ti) + a2y[i+1] (ti)^2 + a3y[i+1] (ti)^3 )

mouseClicked(MouseEvent)


mouseDragged(MouseEvent)


mouseEntered(MouseEvent)


mouseExited(MouseEvent)


mouseMoved(MouseEvent)


mousePressed(MouseEvent)


mouseReleased(MouseEvent)


startEdit(figEdit)


toString()

x
public double x[]
y
public double y[]
scale
public double scale[]
relScale
public double relScale[]
angle
public double angle[]
relAngle
public double relAngle[]
inAngle
public double inAngle[]
outAngle
public double outAngle[]
curve
public fCurve curve
 The parametrized curve whose graph is the Bezier curve.
tmin
public double tmin
 The parameter limits for curve. Normally tmin=0, tmax = number of Bezier
intervals.
tmax
public double tmax
 The parameter limits for curve. Normally tmin=0, tmax = number of Bezier
intervals.
OPEN
public static long OPEN
CLOSED
public static long CLOSED
FILLED
public static long FILLED
DOT
public static long DOT
type
public long type
 The type determines whether the curve is plotted as an open or closed path,
whether or not it is filled and so on. To determine the value of type, start with
type=0. If you wish to have the curve itself plotted add either fBezier.OPEN or
fBezier.CLOSED. In the latter case, a bezier segment from the last vertex to the
first vertex is plotted in addition to the curve itself. If you wish to fill the
curve add fBezier.FILLED. If you wish to plot the vertices of the curve add
fBezier.DOT. (On the screen, a small square will be centered on each vertex.
In postscript, the character number psDotSymbol of font psDotFont will be placed
as a label at each vertex.)
defaultFillColor
public Color defaultFillColor
 The default color used to fill the curve on the screen.
fillColor
public Color fillColor
 The color used to fill the curve on the screen.
defaultPsFillGray
public double defaultPsFillGray
 Controls the default density used to fill the curve in postscript. Black=0, white=1.
psFillGray
public double psFillGray
 Controls the density used to fill the curve in postscript. Black=0, white=1.
defaultPsFillColor
public String defaultPsFillColor
 The default PostScript command used to color in the curve in PostScript when the fEnv variable useColorPs is "true".
psFillColor
public String psFillColor
 The PostScript command used to color in the curve in PostScript when the fEnv variable useColorPs is "true".
psDotFont
public String psDotFont
 In the postcsript image, when fBezier.DOT is included in the type of
the fPolygon, character number psDotSymbol of the font psDotFont is printed at each vertex.
psDotSymbol
public int psDotSymbol
 In the postcsript image, when fBezier.DOT is included in the type of
the fPolygon, character number psDotSymbol of the font psDotFont is printed at each vertex.
fBezier
public fBezier(PointList p)
 Creates the fBezier whose vertices are listed in the PointList.
fBezier
public fBezier(PointList p,
long type)
 Creates the fBezier whose vertices are listed in the PointList and also
sets its type.
 Parameters:
 type  The type determines whether the curve is plotted as an open or closed path,
whether or not it is filled and so on. To determine the value of type, start with
type=0. If you wish to have the curve itself plotted add either fBezier.OPEN or
fBezier.CLOSED. In the latter case, a bezier segment from the last vertex to the first vertex
is plotted in addition to the curve itself. If you wish to fill the
curve add fBezier.FILLED. If you wish to plot the vertices of the curve add
fBezier.DOT. (On the screen, a small square will be centered on each vertex.
In postscript, the character number psDotSymbol of font psDotFont will be placed
as a label at each vertex.)
 p  The list of vertices of the curve.
fBezier
public fBezier(PointList p,
long type,
Color color)
 Creates the fBezier whose vertices are listed in the PointList and also
sets its type and fillColor.
fBezier
public fBezier(PointList p,
int nopoints)
 Creates the fBezier whose vertices are the first nopoints of the PointList.
fBezier
public fBezier(PointList p,
int nopoints,
long type)
fBezier
public fBezier(PointList p,
int nopoints,
long type,
Color color)
fBezier
public fBezier(double list[][])
 Creates the fBezier whose vertices are taken from the array list.
fBezier
public fBezier(double list[][],
long type)
 Creates the fBezier whose vertices are taken from the array list and also
sets its type.
 Parameters:
 type  The type determines whether the curve is plotted as an open or closed path,
whether or not it is filled and so on. To determine the value of type, start with
type=0. If you wish to have the curve itself plotted add either fBezier.OPEN or
fBezier.CLOSED. In the latter case, a bezier segment from the last vertex to the first vertex
is plotted in addition to the curve itself. If you wish to fill the
curve add fBezier.FILLED. If you wish to plot the vertices of the curve add
fBezier.DOT. (On the screen, a small square will be centered on each vertex.
In postscript, the character number psDotSymbol of font psDotFont will be placed
as a label at each vertex.)
 list  The list of vertices of the curve.
fBezier
public fBezier(double list[][],
int nopoints)
 Creates the fBezier whose vertices are the first nopoints of the array list.
fBezier
public fBezier(double list[][],
int nopoints,
long type)
fBezier
public fBezier(double list[][],
int nopoints,
long type,
Color color)
fBezier
public fBezier(double xlist[],
double ylist[],
int nopoints)
fBezier
public fBezier(double xlist[],
double ylist[],
int nopoints,
long type)
fBezier
public fBezier(double xlist[],
double ylist[],
double scale[],
double relScale[],
double angle[],
double relAngle[],
int nopoints,
long type)
fBezier
public fBezier(double xlist[],
double ylist[],
double scale[],
double relScale[],
double angle[],
double relAngle[],
double inAngle[],
double outAngle[],
int nopoints,
long type)
fBezier
public fBezier(double xlist[],
double ylist[],
int nopoints,
long type,
Color color)
fBezier
public fBezier()
append
public void append(double x,
double y)
 Appends the vertex with coordinates (x,y) to the Bezier sequence.
insert
public void insert(double x,
double y,
int vertexNo)
 Inserts a vertex with coordinates (x,y) at position number vertexNo in
Bezier sequence.
delete
public void delete(int vertexNo)
 Removes vertex number vertexNo from the Bezier sequence.
map
public double[] map(double t)
 On the interval [i, i+1) returns the cubic polynomial
( a0x[i+1] + a1x[i+1] (ti) + a2x[i+1] (ti)^2 + a3x[i+1] (ti)^3,
a0y[i+1] + a1y[i+1] (ti) + a2y[i+1] (ti)^2 + a3y[i+1] (ti)^3 )
drawgfx
public void drawgfx(Figure fig,
Hashtable env,
V2V usr2pxl)
drawps
public String drawps(Figure fig,
Hashtable env,
V2V usr2ps)
startEdit
public void startEdit(figEdit applet)
endEdit
public void endEdit()
endEditAndDelete
public void endEditAndDelete()
mouseClicked
public void mouseClicked(MouseEvent evt)
mousePressed
public void mousePressed(MouseEvent evt)
mouseDragged
public void mouseDragged(MouseEvent evt)
mouseReleased
public void mouseReleased(MouseEvent evt)
mouseEntered
public void mouseEntered(MouseEvent evt)
mouseExited
public void mouseExited(MouseEvent evt)
mouseMoved
public void mouseMoved(MouseEvent evt)
itemStateChanged
public void itemStateChanged(ItemEvent evt)
actionPerformed
public void actionPerformed(ActionEvent e)
configure
public void configure(String name,
String Value)
configure
public void configure(String name,
double Value)
 Sets the value of the property specified by the first argument to
the second argument. At the present time, the following properties
are supported: type, vertexIscale, vertexIrelScale, vertexIangle,
vertexIrelAngle, vertexIinAngle, vertexIoutAngle.
Here I is an integer (starting at zero) specifying the vertex number.
For example the property with name "vertex3angle" refers to angle[3].
configure
public void configure(String name,
double Value[])
 Sets the value of the property specified by the first argument to
the second argument. At the present time, the following properties
are supported: vertexI.
Here I is an integer (starting at zero) specifying the vertex number.
For example the property with name "vertex3" refers to x[3] and y[3].
toString
public String toString()
 Overrides:
 toString in class Object
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