vmm.planecurve.parametric
Class PlaneCurveParametric

java.lang.Object
  vmm.core.Exhibit
      vmm.planecurve.PlaneCurve
          vmm.planecurve.parametric.PlaneCurveParametric

All Implemented Interfaces:

java.util.EventListener, javax.swing.event.ChangeListener, Decorateable, Parameterizable

Direct Known Subclasses:

ArchimedeanSpiral, Catenary, ConicSection, DecoratedCurve, Folium, Limacon, Lissajous, Logarithmicspiral, Nephroid, NephroidOfFreeth, UserPlaneCurveParametric, UserPlaneCurveParametricKappa, UserPlaneCurveParametricPolar

public abstract class PlaneCurveParametric
extends PlaneCurve

A curve in the plane that is defined by differentiable functions x(t) and y(t).

Nested Class Summary

static class

PlaneCurveParametric.PlaneCurveParametricView Defines the default View of a PlaneCurveParametric.

Field Summary

protected RealParam	tmax The maximum value of t for points on the curve.
protected RealParam	tmin The minimum valur of t for points on the curve.
protected IntegerParam	tResolution The number of t-values for points on the curve.
protected double[]	tVals The t-values used to compute the points (x(t),y(t)) on the curve.

Fields inherited from class vmm.planecurve.PlaneCurve

movingSquare, points, randomSquare

Fields inherited from class vmm.core.Exhibit

decorations, exhibitNeedsRedraw, isMorphing, morphingView, parameters, previousTransform

Constructor Summary

PlaneCurveParametric()
Construct a plane curve with Parameters tmin, tmax, and tResolution.

Method Summary

void	doDraw(java.awt.Graphics2D g, View view, Transform transform) Draw the curve in a specified View.
ActionList	getActionsForView(View view) Returns a list of actions that can be applied to a PlaneCurveParametric.
Animation	getCreateAnimation(View view) Returns an animation that shows the curve being drawn bit-by-bit.
View	getDefaultView() Returns a new instance of the nested class PlaneCurveParametric.PlaneCurveParametricView.
double	getT(int index) Return the t-value for one of the points on the curve.
int	getTResolution() Returns the number of intervals into which the curve is divided.
protected void	makePoints() Calcululates the array of points for this curve using the functions xValue(double) and yValue(double) to compute the points at equally spaced t-values between tmin and tmax.
java.awt.geom.Point2D[]	myCircle(double mx, double my, double rad, int numPoints) parametrized circle to draw circle arcs in different colors.
double	x2ndDerivativeValue(double t) Computes x''(t) for a given value of t.
double	xDerivativeValue(double t) Computes x'(t) for a given value of t.
abstract double	xValue(double t) Computes x(t) for a given value of t.
double	y2ndDerivativeValue(double t) Computes y''(t) for a given value of t.
double	yDerivativeValue(double t) Computes y'(t) for a given value of t.
abstract double	yValue(double t) Computes y(t) for a given value of t.

Methods inherited from class vmm.planecurve.PlaneCurve

computeDrawData, fillRandomSquare, getPoint, getPointCount, initializeMovingSquare, moveSquare

Methods inherited from class vmm.core.Exhibit

addChangeListener, addDecoration, addExtraXML, addParameter, addView, clearDecorations, computeDrawDataHook, doDrawHook, fireExhibitChangeEvent, forceRedraw, getAdditionalAnimationsForView, getAlternativeViews, getBuildAnimation, getDecorations, getDefaultBackground, getDefaultForeground, getDefaultTransform, getDefaultWindow, getFramesForMorphing, getMorphingAnimation, getName, getParameterByName, getParameters, getSettingsCommandsForView, getTitle, getUseFilmstripForMorphing, getViews, parameterChanged, readExtraXML, removeChangeListener, removeDecoration, removeParameter, removeView, render, setDefaultBackground, setDefaultForeground, setDefaultWindow, setDefaultWindow, setFramesForMorphing, setName, setUseFilmstripForMorphing, stateChanged

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

tResolution

protected IntegerParam tResolution

The number of t-values for points on the curve. Points of the form (x(t),y(t)) are computed for 1 plus this many values of t, and these points are joined by line segments to draw the curve. Note that the starting and ending values of t are given by the values of tmin and tmax. This interval is divided into tResolution sub-intervals, giving tResolution+1 points.

tmin

protected RealParam tmin

The minimum valur of t for points on the curve.

tmax

protected RealParam tmax

The maximum value of t for points on the curve.

tVals

protected double[] tVals

The t-values used to compute the points (x(t),y(t)) on the curve. These are evenly spaced between the minimum and maximum t-values.

Constructor Detail

PlaneCurveParametric

public PlaneCurveParametric()

Construct a plane curve with Parameters tmin, tmax, and tResolution. The curve will be defined by the functions xValue and yValue in a concrete subclass.

Method Detail

xValue

public abstract double xValue(double t)

Computes x(t) for a given value of t.

yValue

public abstract double yValue(double t)

Computes y(t) for a given value of t.

xDerivativeValue

public double xDerivativeValue(double t)

Computes x'(t) for a given value of t. The default version defined in this class computes an approximate value numerically, using values of the function itself at points near t.

yDerivativeValue

public double yDerivativeValue(double t)

Computes y'(t) for a given value of t. The default version defined in this class computes an approximate value numerically, using values of the function itself at points near t.

x2ndDerivativeValue

public double x2ndDerivativeValue(double t)

Computes x''(t) for a given value of t. The default version defined in this class computes an approximate value numerically, using values of the function itself at points near t.

y2ndDerivativeValue

public double y2ndDerivativeValue(double t)

Computes y''(t) for a given value of t. The default version defined in this class computes an approximate value numerically, using values of the function itself at points near t.

getTResolution

public int getTResolution()

Returns the number of intervals into which the curve is divided. Note that the number of points that are drawn on the curve is one more than the tResolution.

getT

public double getT(int index)

Return the t-value for one of the points on the curve. The number of points is getTResolution() + 1, and they are numbered from 0 to getTResolution(). If this method is called before the curve has been drawn, the return value will be Double.NaN. The return value is also Double.NaN if the specified index is not in the range 0 to getTResolution(), inclusive. The corresponding point on the curve can be obtained by calling xValue() and yValue()

The value returned by this method is only valid after the curve has been drawn; if it is called before that time, the return value will be Double.NaN.

Parameters:

index - A position in the array of t-values that specifies which t-value shoud be returned.

See Also:

getTResolution(), xValue(double), yValue(double)

myCircle

public java.awt.geom.Point2D[] myCircle(double mx,
                                        double my,
                                        double rad,
                                        int numPoints)

parametrized circle to draw circle arcs in different colors.

makePoints

protected void makePoints()

Calcululates the array of points for this curve using the functions xValue(double) and yValue(double) to compute the points at equally spaced t-values between tmin and tmax. The number of points is one plus the value of tResolution.

Specified by:

makePoints in class PlaneCurve

doDraw

public void doDraw(java.awt.Graphics2D g,
                   View view,
                   Transform transform)

Draw the curve in a specified View. If the View belogs to the nested class PlaneCurveParametric.PlaneCurveParametricView (which is the default), then only a fraction of the curve might be drawn, as specified in the View; this feature is used in the creation animation for the curve.

Overrides:

doDraw in class PlaneCurve

Parameters:

g - The graphics context where the Exhibit is being drawn. It has already been cleared to the background color (assuming that drawing is being done in the usual way, as defined in the top-level View class).

view - The View that is drawing the Exhibit; this object contains other information that might be of use, such as the Display, if any, associated with the View.

transform - Contains information about the rectangular area in the xy-plane that is being drawn and about the rectangle of pixels in the graphics context where it is drawn. Note that at least for the top-level View class, transform.getX() and transform.getY() can be assumed to be zero.

See Also:

Exhibit.render(Graphics2D, View, Transform, ArrayList), Exhibit.computeDrawData(View, boolean, Transform, Transform)

getCreateAnimation

public Animation getCreateAnimation(View view)

Returns an animation that shows the curve being drawn bit-by-bit.

Overrides:

getCreateAnimation in class Exhibit

Parameters:

view - The View where the creation animation will be shown. If this is null or if it is not an instance of PlaneCurveParametric.PlaneCurveParametricView, then the return value is null.

Returns:

A creation animation for the given View of this Exhibit. The return value can be null to indicate that no creation animation is to be run.

getDefaultView

public View getDefaultView()

Returns a new instance of the nested class PlaneCurveParametric.PlaneCurveParametricView.

Overrides:

getDefaultView in class Exhibit

getActionsForView

public ActionList getActionsForView(View view)

Returns a list of actions that can be applied to a PlaneCurveParametric. This adds a separator and four actions that run various animations to the list obtained from super.getActionsForView(view).

Overrides:

getActionsForView in class Exhibit

Parameters:

view - The view for which the actions should apply. If this is null, then no new actions are added to those inherited from the superclass.