New PDF release: Data Visualization : Principles and Practice

By Alexandru C. Telea

ISBN-10: 1439865930

ISBN-13: 9781439865934

"" """"An very good reference for any complex, college-level protecting powerful in special effects or information visualization techniques.""""-- The Midwest booklet evaluate , April 2008 """"For complex undergraduate or early graduate scholars of computing device technology, arithmetic, and engineering sciences, Telea introduces the rules of knowledge visualization because it is practiced in such nation-states as sign idea, imaging, computer Read more...

summary: "" """"An very good reference for any complicated, college-level preserving powerful in special effects or facts visualization techniques.""""-- The Midwest publication assessment , April 2008 """"For complex undergraduate or early graduate scholars of machine technological know-how, arithmetic, and engineering sciences, Telea introduces the foundations of knowledge visualization because it is practiced in such geographical regions as sign idea, imaging, special effects, and statistics."""" -BOOK information Inc., June 2008""

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1. Continuous Data 43 space R3 , then we have s = 1 and d = 3. You can think of the topological dimension as the number of independent variables that we need to represent our domain D. A curved surface in R3 can actually be represented by two independent variables, like latitude and longitude for the surface of the Earth. Indeed, we can describe such a surface by an implicit function f (x, y, z) = 0, which actually says that only two of the three variables x, y, and z vary independently. Similarly, a curve’s domain can be described implicitly by two equations f (x, y, z) = 0 and g(x, y, z) = 0, which means that just one of the variables x, y, and z varies independently.

B) First-order C 0 continuous function. (c) High-order C k continuous function. ✐ ✐ ✐ ✐ ✐ ✐ ✐ ✐ 42 3. Data Representation continuous of order k if the function itself and all its derivatives up to and including order k are also continuous in this sense. This is denoted as f ∈ C k . 1 illustrates the continuity concept for the case of a one-dimensional function f : R → R, whose graph is displayed in green. 1(a)) shows a function having a discontinuity at the points x0 . , how close we sample the function to the point x0 .

Moreover, they are continuous of order 1, by definition. , has piecewise constant derivatives. 10) are also sometimes called linear interpolation functions. For our height plot visualization, using these basis functions means that we approximate the function graph surface with a set of linear surface elements, that is, planes. 1 that rendered our height plot using a set of quads are nothing else but reconstructions of the function graph surface with linear basis functions. Luckily, we do not have to program this linear interpolation ourselves when doing rendering.

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Data Visualization : Principles and Practice by Alexandru C. Telea

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