By Max K. Agoston

Potentially the main finished evaluate of special effects as obvious within the context of geometric modeling, this quantity paintings covers implementation and concept in an intensive and systematic style. special effects and Geometric Modeling: Implementation and Algorithms covers the pc snap shots a part of the sector of geometric modeling and contains all of the average special effects themes. the 1st half bargains with simple techniques and algorithms and the most steps serious about exhibiting photorealistic photos on a working laptop or computer. the second one half covers curves and surfaces and a few extra complicated geometric modeling themes together with intersection algorithms, distance algorithms, polygonizing curves and surfaces, trimmed surfaces, implicit curves and surfaces, offset curves and surfaces, curvature, geodesics, mixing and so on. The 3rd half touches on a few facets of computational geometry and some distinctive issues comparable to period research and finite point equipment. the quantity contains spouse courses.

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**Extra info for Computer Graphics and Geometric Modelling: Implementation & Algorithms v. 1**

**Example text**

There are some very good algorithms that solve differential equations with basically this approach by using some fancy error-correcting terms. For more information see a text on numerical analysis such as [ConD72] or [DahB74]. Discrete curve-drawing algorithms that are based on the qualitative solutions to differential equations as described above are called digital differential analyzer or DDA type algorithms. Let us see what we get in the special case of straight lines. The differential equation for the straight line that passes through the points (x0,y0) and (x1,y1) is dy Dy eDy = = , dx Dx eDx where Dy = y1 - y0, Dx = x1 - x0, and e is any positive real number.

In any case, whatever system the reader is working on, it is assumed that he/she can implement these procedures. These primitives are all that we shall need to describe all of the algorithms in this book. 5 In these programming assignments assume that the user’s world is the plane. We also assume the reader has a basic windowing program with an easily extensible menu system. The GM program is one such and the user interface in the projects below ﬁts naturally into that program. Furthermore, the term “screen” in the projects below will mean the window on the real screen in which the program is running.

1 implements the algorithm we have been describing. In our discussion above we have restricted ourselves to lines that start at the origin and end in the ﬁrst octant. Starting at another point simply amounts to adding a constant offset to all the points. Lines that end in a different octant can be handled in a similar way to the ﬁrst octant case – basically by interchanging the x and y. What this boils down to is that an algorithm which handles all lines is not much harder, involving only a case statement to separate between the case where the absolute value of the slope is either larger or less than or equal to 1.