Download PDF by Lars-Erik Andersson: Introduction to the mathematics of subdivision surfaces

By Lars-Erik Andersson

ISBN-10: 0898716977

ISBN-13: 9780898716979

This can be an advent to the mathematical concept which underlies subdivision surfaces, because it is utilized in special effects and animation. Subdivision surfaces permit a clothier to specify the approximate kind of a floor that defines an item after which to refine it to get a extra worthy or beautiful model. a large amount of mathematical idea is required to appreciate the features of the resulting Read more...

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Extra info for Introduction to the mathematics of subdivision surfaces

Sample text

We give the definition5 first for a locally planar mesh without boundary and then extend the definition to the case of a locally planar mesh with boundary. Let M be a locally planar mesh without boundary. 7/11 (left). 7/11 . 9/13 , and throughout the book, vertices of the dual mesh are shown as black squares. There is an edge connecting two vertices in the dual of M if the corresponding faces in M are separated by an edge; the edges in the dual are shown in the figure by dashed lines. Finally, there is a face in the dual of M for each vertex in M .

Plan of the book Many subdivision surfaces can be viewed as generalizations of B-spline surfaces in the sense that, instead of being limited to surfaces defined in terms of a planar parametric domain, we can represent directly surfaces of more general form, such as an elastic deformation of a sphere, or of a torus (the surface of a doughnut) with several holes. Other subdivision surfaces are generalizations of box splines, which themselves are generalizations (in a different sense) of B-splines. A natural order of mathematical presentation is, therefore, to begin with B-spline surfaces, and later to proceed to the more general cases.

20]: the strong interest in subdivision surfaces that appeared in the 1990s arose out of a desire to circumvent the problem of topology limitations involved with the use of ordinary B-spline surfaces. Choice of method, including data structures and implementation We can describe in very general terms some typical criteria that might be used to guide our choice of method. Some of these criteria, such as mesh type, the level and nature of continuity, and whether the surface interpolates given data, have ✐ ✐ ✐ ✐ ✐ ✐ ✐ 6 book 2010/3/3 page 6 ✐ Chapter 1.

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Introduction to the mathematics of subdivision surfaces by Lars-Erik Andersson


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