Introduction to Computer Graphics: Using Java 2D and 3D by Frank Klawonn

By Frank Klawonn

This publication is an important instrument for second-year undergraduate scholars and above, supplying transparent and concise causes of the fundamental ideas of special effects, and allowing the reader to right away enforce those thoughts in Java second and/or 3D with merely effortless wisdom of the programming language. beneficial properties: offers an incredible, self-contained advent to special effects, with thought and perform provided in built-in mix; offers a pragmatic consultant to simple special effects programming utilizing Java second and 3D; contains new and multiplied content material at the integration of textual content in 3D, particle structures, billboard behaviours, dynamic surfaces, the concept that of point of aspect, and using features of 2 variables for floor modelling; comprises many pedagogical instruments, together with a variety of easy-to-understand instance courses and end-of-chapter workouts; provides priceless supplementary fabric, together with extra routines, suggestions, and software examples, at an linked website.

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The point will be written as (x, y) ∈ R2 and (x, y, z) ∈ R3 , respectively. 5 Geometric Transformations 21 ⎞ v1 ⎜ ⎟ u · v = (u1 , . . , un ) · ⎝ ... ⎠ = ⎛ n ui · vi . i=1 vn The most important geometric transformations are scaling, rotation, shearing and translation. A scaling leads to stretching or shrinking of objects in the direction of the x- and the y-axis. A scaling S(sx , sy ) maps the point (x, y) to the point (x , y ) given by x y = sx · x sy · y = 0 sy sx 0 · x . y sx is the scaling factor in the direction of the x-axis.

It points downwards instead of upwards. When the specification in standard Cartesian coordinates is preferred, one can simply apply suitable geometric transformations, before drawing objects in the window coordinate system. In order to reverse the direction of the y-axis, a reflection with respect to the x-axis has to be carried out. After this reflection, the y-axis points upwards, but the origin of the coordinate system of the window still remains in the upper left corner, so that only objects with negative y-components would be visible.

In the beginning, the corresponding scaling had to be a scaling along the y-axis. But once the hand starts to rotate, the axis of scaling must also be rotated. Otherwise the hand would not only become longer or shorter, but also thicker or thinner. Although this strategy for modelling continuous movements of objects is applicable, the following second strategy seems to be more convenient and simpler to implement. The principle of this second strategy is to leave the objects in their initial positions and to compute accumulated geometric transformations which are applied to the objects before they are drawn.

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