Download Advanced Graphics with the Commodore 128 by M. M. Novak (auth.) PDF

Graphics Multimedia

By M. M. Novak (auth.)

ISBN-10: 1349086991

ISBN-13: 9781349086993

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2. 2 0 X Two-dimensional Transformations 51 Y1 =Y•Sy X1 =X•Sx where Sx and Sy are the scaling factors in the x- and y-directions, respectively. If Sx and Sy have the same value, then the overall shape of the transformed image is preserved, though its size is affected. If the value of the scaling factors is larger than unity then the image is expanded; if ius smaller then the image shrinks. If Sx and Sy differ, then the resultant image is distorted, because expansion (or shrinking) along different axes is not equal.

In such a case the second endpoint is assumed to be at the origin 0, having coordinates (0,0). Vectors can also be added graphically, without explicitly calculating the components of the resultant vector. To do so, place the beginning of the second vector at the end of the first one. The resultant vector is defined by the starting point of the first vector and the endpoint of the second vector. More than two vectors can be added in the same way. 5. 5 Vector subtraction As subtraction is, in fact, addition with the opposite sign, the vector addition rules just mentioned can be applied directly.

Therefore, replacing rb - ra by wu, where u is a unit vector, the alternative vector equation of a line can be written as That is, the line is defined by a single position vector ra and the direction u. Line generation Apart from points, the line segment is the most frequently used geometrical entity in computer graphics. Therefore, it is essential to develop an effective way of generating straight-line segments. In most cases we shall rely on the C-128 to ORAw lines for us. However, on occasion it may be useful to know how the software line generation method works, especially as direct recourse to the line equation proves computationally unsatisfactory.

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