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The Java 2D API and its documentation are available for download as a part of JDK 6. Java 2D API classes are organised into the following packages in JDK 6: java.awt The main package for the Java Abstract Window Toolkit. java.awt.geom The Java standard library of two dimensional geometric shapes such as lines, ellipses, and quadrilaterals.
The problem of writing a computer program to produce this triangle has been frequently used as an exercise or example for beginning computer programmers, covering the concepts of text formatting and simple loop constructs. [1] [2] [3] [4]
Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:
Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing over elements collapses the input array by 1 dimension.
A rotation of the vector through an angle θ in counterclockwise direction is given by the rotation matrix: = ( ), which can be viewed either as an active transformation or a passive transformation (where the above matrix will be inverted), as described below.
A rotation can be represented by a unit-length quaternion q = (w, r →) with scalar (real) part w and vector (imaginary) part r →. The rotation can be applied to a 3D vector v → via the formula = + (+). This requires only 15 multiplications and 15 additions to evaluate (or 18 multiplications and 12 additions if the factor of 2 is done via ...
In contrast, two-dimensional arrays are always rectangular [4] so jagged arrays should not be confused with multidimensional arrays, but the former is often used to emulate the latter. Arrays of arrays in languages such as Java, PHP, Python (multidimensional lists), Ruby, C#.NET, Visual Basic.NET , Perl, JavaScript, Objective-C, Swift, and ...
For example, in 2-space n = 2, a rotation by angle θ has eigenvalues λ = e iθ and λ = e −iθ, so there is no axis of rotation except when θ = 0, the case of the null rotation. In 3-space n = 3 , the axis of a non-null proper rotation is always a unique line, and a rotation around this axis by angle θ has eigenvalues λ = 1, e iθ , e ...