• View
• Edit
• History
• Print

2DTransformations

In the properties of a 2D view element, when you hover over the word 'Transform' the tooltip shows the kinds of input that the view property accepts. The listing states: AffineTransform, int, double, double[], double[][], Object.

Int and Double shortcuts The inputs 'int' and 'double' provide the shortest way to specify a rotation. (Of course, the input can be either a simple number, or a variable that has been declared on the variables panel.) EJS takes an int to specify degrees, and a double to specify an angle in radians.

Dialog box

The image to the right shows the dialog box that accompanies the cell 'Transform'. This dialog box will generate strings that specify various transformations.

For example: enter the number "45" in the cell next to the button "Rotation", and press the button. The line on the bottom will then read: ro:45d That is entirely a string. To create the specified transform EJS processes that string.

A subsequent transformation can be added by adding another number and pressing the adjacent button. For example 1 and 1 the cells next to "Translation" and pressing the button. The line on the bottom will then read ro:45d & tr:1,1

Advanced options

A transformation for a 2D element is an object of the AffineTransform Java class. You can find some nice references if you google for AffineTransform, such as http://www.glyphic.com/transform/.

• If you link a double[] array (with at least 6 numbers in it) to the property transformation EJS set the transformation to new AffineTransform(array). See the Javadoc page for AffineTransform to learn what this means.
• If you link a double[][] array to the property transformation EJS set the transformation to:
  • if (array[0].length==2): new AffineTransform(array[0][0],array[1][0],array[0][1],array[1][1],0,0));
  • if (array[0].length>=3): new AffineTransform(array[0][0],array[1][0],array[0][1],array[1][1],array[0][2],array[1][2]));

• Finally, if you link an object of the org.opensourcephysics.numerics.Matrix2DTransformation class, EJS will use the AffineTransform returned by its getTotalTransform() for the element. The Matrix2DTransformation includes the constructors:
  • public static Matrix2DTransformation rotation(double theta): Creates a 2D transformation representing a rotation about the origin by the given angle.
  • public static Matrix2DTransformation rotation(double theta, double anchorx, double anchory) : Creates a 2D transformation representing a rotation about the origin by the given angle around the given axis.
  • public static Matrix2DTransformation createAlignmentTransformation(double[] v1, double v2[]) : Instantiates a rotation that aligns the first vector with the second vector.