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In this module, I presented and explained four programs that use the game-math library named GM2D04 . The purpose of the program named VectorAdd05 is to use the addVectorToPoint method of the GM2D04.Point class to translate a geometric object from one location in space to a different location in space.
The purpose of the program named VectorAdd05a is to accomplish the same translation operation, but to do so in a possibly moreefficient manner.
The purpose of the program named VectorAdd06 is to teach you how to do rudimentary animation using the game-math library.
The purpose of the program named StringArt01 is to teach you how to use methods of the game-math library to produce relatively complexdrawings.
All of the programs are interactive in that they provide a GUI that allows the user to modify certain aspects of the behavior of the program.
In the next module, you will learn how to update the game-math library to support 3D math, how to program the equations for projecting a 3D world onto a2D plane, and how to add vectors in 3D.
You will also learn about scaling, translation, and rotation of a point in both 2D and 3D, about the rotation equations and how to implement them in both2D and 3D, and much more.
This section contains a variety of miscellaneous information.
Financial : Although the Connexions site makes it possible for you to download a PDF file for thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.
I also want you to know that, I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.
In the past, unknown individuals have copied my modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing me as the author. Ineither receive compensation for those sales nor do I know who does receive compensation. If you purchase such a book, please beaware that it is a copy of a module that is freely available on cnx.org and that it was made and published withoutmy prior knowledge.
Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.
Complete listings of the programs discussed in this module are shown in Listing 17 through Listing 21 below.
Listing 17 . Source code for the game-math library named GM2D04.
/*GM2D04.java
Copyright 2008, R.G.BaldwinRevised 02/08/08
The name GM2Dnn is an abbreviation for GameMath2Dnn.See the file named GM2D01.java for a general description
of this game-math library file. This file is an update ofGM2D03.
This update added the following new capabilities:Vector addition - Adds this Vector object to a Vector
object received as an incoming parameter and returns thesum as a resultant Vector object.
Added a method named getLength that returns the lengthof a vector as type double.
Added a method named addVectorToPoint to add a Vector toa Point producing a new Point.
Tested using JDK 1.6 under WinXP.*********************************************************/
import java.awt.geom.*;import java.awt.*;
public class GM2D04{//An object of this class represents a 2D column matrix.
// An object of this class is the fundamental building// block for several of the other classes in the
// library.public static class ColMatrix{
double[]data = new double[2];public ColMatrix(double data0,double data1){data[0] = data0;data[1] = data1;}//end constructor
//--------------------------------------------------//public String toString(){return data[0] + "," + data[1];
}//end overridden toString method//--------------------------------------------------//public double getData(int index){
if((index<0) || (index>1)){
throw new IndexOutOfBoundsException();}else{
return data[index];
}//end else}//end getData method
//--------------------------------------------------//public void setData(int index,double data){if((index<0) || (index>1)){
throw new IndexOutOfBoundsException();}else{
this.data[index]= data;
}//end else}//end setData method
//--------------------------------------------------////This method overrides the equals method inherited// from the class named Object. It compares the values
// stored in two matrices and returns true if the// values are equal or almost equal and returns false
// otherwise.public boolean equals(Object obj){
if(obj instanceof GM2D04.ColMatrix&&Math.abs(((GM2D04.ColMatrix)obj).getData(0) -
getData(0))<= 0.00001&&Math.abs(((GM2D04.ColMatrix)obj).getData(1) -
getData(1))<= 0.00001){
return true;}else{
return false;}//end else}//end overridden equals method
//--------------------------------------------------////Adds one ColMatrix object to another ColMatrix
// object, returning a ColMatrix object.public GM2D04.ColMatrix add(GM2D04.ColMatrix matrix){
return new GM2D04.ColMatrix(getData(0)+matrix.getData(0),
getData(1)+matrix.getData(1));}//end subtract
//--------------------------------------------------////Subtracts one ColMatrix object from another
// ColMatrix object, returning a ColMatrix object. The// object that is received as an incoming parameter
// is subtracted from the object on which the method// is called.
public GM2D04.ColMatrix subtract(GM2D04.ColMatrix matrix){
return new GM2D04.ColMatrix(getData(0)-matrix.getData(0),
getData(1)-matrix.getData(1));}//end subtract
//--------------------------------------------------//}//end class ColMatrix
//====================================================//public static class Point{GM2D04.ColMatrix point;public Point(GM2D04.ColMatrix point){//constructor
//Create and save a clone of the ColMatrix object// used to define the point to prevent the point
// from being corrupted by a later change in the// values stored in the original ColMatrix object
// through use of its set method.this.point =
new ColMatrix(point.getData(0),point.getData(1));}//end constructor
//--------------------------------------------------//public String toString(){
return point.getData(0) + "," + point.getData(1);}//end toString
//--------------------------------------------------//public double getData(int index){if((index<0) || (index>1)){
throw new IndexOutOfBoundsException();}else{
return point.getData(index);}//end else
}//end getData//--------------------------------------------------//public void setData(int index,double data){
if((index<0) || (index>1)){
throw new IndexOutOfBoundsException();}else{
point.setData(index,data);}//end else
}//end setData//--------------------------------------------------////This method draws a small circle around the location
// of the point on the specified graphics context.public void draw(Graphics2D g2D){
Ellipse2D.Double circle =new Ellipse2D.Double(getData(0)-3,
getData(1)-3,6,
6);g2D.draw(circle);
}//end draw//--------------------------------------------------////Returns a reference to the ColMatrix object that
// defines this Point object.public GM2D04.ColMatrix getColMatrix(){
return point;}//end getColMatrix
//--------------------------------------------------////This method overrides the equals method inherited
// from the class named Object. It compares the values// stored in the ColMatrix objects that define two
// Point objects and returns true if they are equal// and false otherwise.
public boolean equals(Object obj){if(point.equals(((GM2D04.Point)obj).
getColMatrix())){return true;
}else{return false;
}//end else}//end overridden equals method//--------------------------------------------------//
//Gets a displacement vector from one Point object to// a second Point object. The vector points from the
// object on which the method is called to the object// passed as a parameter to the method. Kjell
// describes this as the distance you would have to// walk along the x and then the y axes to get from
// the first point to the second point.public GM2D04.Vector getDisplacementVector(
GM2D04.Point point){return new GM2D04.Vector(new GM2D04.ColMatrix(
point.getData(0)-getData(0),point.getData(1)-getData(1)));
}//end getDisplacementVector//--------------------------------------------------////Adds a Vector to a Point producing a new Point.
public GM2D04.Point addVectorToPoint(GM2D04.Vector vec){
return new GM2D04.Point(new GM2D04.ColMatrix(getData(0) + vec.getData(0),
getData(1) + vec.getData(1)));}//end addVectorToPoint
//--------------------------------------------------//}//end class Point
//====================================================//public static class Vector{GM2D04.ColMatrix vector;public Vector(GM2D04.ColMatrix vector){//constructor
//Create and save a clone of the ColMatrix object// used to define the vector to prevent the vector
// from being corrupted by a later change in the// values stored in the original ColVector object.
this.vector = new ColMatrix(vector.getData(0),vector.getData(1));
}//end constructor//--------------------------------------------------//
public String toString(){return vector.getData(0) + "," + vector.getData(1);
}//end toString//--------------------------------------------------//public double getData(int index){
if((index<0) || (index>1)){
throw new IndexOutOfBoundsException();}else{
return vector.getData(index);}//end else
}//end getData//--------------------------------------------------//public void setData(int index,double data){
if((index<0) || (index>1)){
throw new IndexOutOfBoundsException();}else{
vector.setData(index,data);}//end else
}//end setData//--------------------------------------------------////This method draws a vector on the specified graphics
// context, with the tail of the vector located at a// specified point, and with a small circle at the
// head.public void draw(Graphics2D g2D,GM2D04.Point tail){
Line2D.Double line = new Line2D.Double(tail.getData(0),
tail.getData(1),tail.getData(0)+vector.getData(0),
tail.getData(1)+vector.getData(1));//Draw a small circle to identify the head.
Ellipse2D.Double circle = new Ellipse2D.Double(tail.getData(0)+vector.getData(0)-2,
tail.getData(1)+vector.getData(1)-2,4,
4);g2D.draw(circle);
g2D.draw(line);}//end draw
//--------------------------------------------------////Returns a reference to the ColMatrix object that// defines this Vector object.
public GM2D04.ColMatrix getColMatrix(){return vector;
}//end getColMatrix//--------------------------------------------------//
//This method overrides the equals method inherited// from the class named Object. It compares the values
// stored in the ColMatrix objects that define two// Vector objects and returns true if they are equal
// and false otherwise.public boolean equals(Object obj){
if(vector.equals(((GM2D04.Vector)obj).getColMatrix())){
return true;}else{
return false;}//end else}//end overridden equals method
//--------------------------------------------------////Adds this vector to a vector received as an incoming// parameter and returns the sum as a vector.
public GM2D04.Vector add(GM2D04.Vector vec){return new GM2D04.Vector(new ColMatrix(
vec.getData(0)+vector.getData(0),vec.getData(1)+vector.getData(1)));
}//end add//--------------------------------------------------////Returns the length of a Vector object.
public double getLength(){return Math.sqrt(
getData(0)*getData(0) + getData(1)*getData(1));}//end getLength
//--------------------------------------------------//}//end class Vector
//====================================================////A line is defined by two points. One is called the// tail and the other is called the head.
public static class Line{GM2D04.Point[] line = new GM2D04.Point[2];public Line(GM2D04.Point tail,GM2D04.Point head){
//Create and save clones of the points used to// define the line to prevent the line from being
// corrupted by a later change in the coordinate// values of the points.
this.line[0]= new Point(new GM2D04.ColMatrix(
tail.getData(0),tail.getData(1)));this.line[1] = new Point(new GM2D04.ColMatrix(head.getData(0),head.getData(1)));
}//end constructor//--------------------------------------------------//
public String toString(){return "Tail = " + line[0].getData(0) + ","+ line[0].getData(1) + "\nHead = "+ line[1].getData(0) + ","+ line[1].getData(1);}//end toString
//--------------------------------------------------//public GM2D04.Point getTail(){
return line[0];
}//end getTail//--------------------------------------------------//public GM2D04.Point getHead(){
return line[1];
}//end getHead//--------------------------------------------------//public void setTail(GM2D04.Point newPoint){
//Create and save a clone of the new point to// prevent the line from being corrupted by a
// later change in the coordinate values of the// point.
this.line[0]= new Point(new GM2D04.ColMatrix(
newPoint.getData(0),newPoint.getData(1)));}//end setTail
//--------------------------------------------------//public void setHead(GM2D04.Point newPoint){//Create and save a clone of the new point to
// prevent the line from being corrupted by a// later change in the coordinate values of the
// point.this.line[1] = new Point(new GM2D04.ColMatrix(newPoint.getData(0),newPoint.getData(1)));
}//end setHead//--------------------------------------------------//public void draw(Graphics2D g2D){
Line2D.Double line = new Line2D.Double(getTail().getData(0),
getTail().getData(1),getHead().getData(0),
getHead().getData(1));g2D.draw(line);
}//end draw//--------------------------------------------------//
}//end class Line//====================================================//
}//end class GM2D04//======================================================//
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