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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 two-dimensional position vectors x1[], x2[] and two two-dimensional 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] (t-i) + a2x[i+1] (t-i)^2 + a3x[i+1] (t-i)^3, a0y[i+1] + a1y[i+1] (t-i) + a2y[i+1] (t-i)^2 + a3y[i+1] (t-i)^3 )
mouseClicked(MouseEvent)
mouseDragged(MouseEvent)
mouseEntered(MouseEvent)
mouseExited(MouseEvent)
mouseMoved(MouseEvent)
mousePressed(MouseEvent)
mouseReleased(MouseEvent)
startEdit(figEdit)
toString()

 public double x[]

 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] (t-i) + a2x[i+1] (t-i)^2 + a3x[i+1] (t-i)^3, a0y[i+1] + a1y[i+1] (t-i) + a2y[i+1] (t-i)^2 + a3y[i+1] (t-i)^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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