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Chris Solarski. The Functional Art. Alberto Cairo. InDesign in Easy Steps. Robert Shufflebotham. The Photoshop Workbook. Glyn Dewis. Points cannot be drawn directly. If one wants to draw a point, i. Objects of the class Point2D are mainly used to specify coordinates for other geometric objects.

Therefore, the class Point2D will not occur very often in the example programs. The abstract class Point2D is extended by the two classes Point2D. Float and Point2D. When using the abstract class Point2D it is not necessary to specify whether coordinates are given as float- or double-values. The same concept is also used for most of the other geometric objects. Basic principles of two-dimensional graphics The elementary geometric objects in Java 2D introduced in the following extend the class Shape, so that they can be drawn by applying one of the methods draw or fill. Double x1,y1,x2,y2 ; The parameters x1, y1, x2 and y2 are of type double.

Similarly, Line2D. Float requires the same parameters, but of type float. Only when the method g2d. Analogously to lines, quadratic curves are modelled by the abstract class QuadCurve2D. Java 2D provides the abstract class CubicCurve2D for modelling cubic curves. Analogously to the cases of lines and quadratic curves, CubicCurve2D.

## Introduction to Computer Graphics - Using Java 2D and 3D

Double x1,y1, ctrlx1,ctrly1, ctrlx2,ctrly2, x2,y2 ; The program CurveDemo. Double, QuadCurve2D.

Double and CubicCurve2D. The class GeneralPath allows the construction not only of polylines, i. A GeneralPath starts in the origin of the coordinate system, i. Each method will append a corresponding line or curve to the endpoint of the last element in the sequence of the GeneralPath. The methods lineTo, quadTo and curveTo append a line, 2.

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In addition to these three methods for curves and lines, the class GeneralPath also contains the method moveTo that allows to jump from the endpoint of the previous curve to another point without connecting the points by a line or curve. Basic principles of two-dimensional graphics g2d. The complete class for drawing the car can be found in the example program GeneralPathCar. In addition to the class GeneralPath Java 2D also provides classes for axes-parallel rectangles and ellipses as basic geometric objects.

By the class Rectangle2D. It is still necessary to call the method g2d. A circle is a special case of an ellipse, where the bounding rectangle is a square. A circle with centre point x, y and radius r can be generated by Ellipse2D. The angle is given as a float-value in terms of degrees. Otherwise, the angle is determined relative to the rectangle. Analogously to the start angle, extend corresponds to the true angle of the arc only in the case of a circular arc.

### Introduction to Computer Graphics - Using Java 2D and 3D | Frank Klawonn | Springer

PIE and Arc2D. CHORD, specifying whether only the arc itself, the corresponding segment or the arc with the chord of the ellipse, respectively, should be constructed.

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Basic principles of two-dimensional graphics Figure 2. The same applies to the opening angle. At the end of section 2. Given two Area objects areaA and areaB, the following methods are available, implementing the corresponding set-theoretic operations. The Area object areaA contains the result of the application of the corresponding set-theoretic operation. Geometric transformations can be used to position objects, i.

Before discussing geometric transformations in more detail, it is necessary to explain some general conventions. In computer graphics, points as well as vectors are used.

From a purely mathematical point of view, both can be represented as elements of the space Rn , i. Especially in physics, it is very important to distinguish clearly between these two concepts of points and vectors. A tuple x1 ,. Hopefully, physicists will tolerate the abuse of notation in the context of this book. For equations within this book, column vectors will be used consistently. Within the text, points are sometimes written as row vectors in order to avoid stretching of text lines.

In those cases where a point is explicitly understood as a column vector, the symbol for transposing vectors will be used, i. The dot product of two vectors u and v will be denoted in the following 24 2. A scaling leads to stretching or shrinking of objects in the direction of the x- and the y-axis. For sx Figure 2. The same holds for all other geometric transformations. They carry out pointwise transformations of objects.

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## Introduction to Computer Graphics : Frank Klawonn :

The 2. But in addition, the centre of the rectangle is also transformed so that the transformed rectangle is shifted to the lower right compared to the original rectangle. A scaling is always carried out with respect to the origin of the coordinate system. Applying a scaling to an object that is not centred around the origin of the coordinate system will lead to a translation of the centre of the object in addition to the scaling.

Another important group of geometric transformations are rotations that are determined by a single parameter, the rotation angle.