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Titlebook: Calculus for Computer Graphics; John Vince Textbook 20192nd edition Springer Nature Switzerland AG 2019 Calculus for Computer Animation.Ca

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書目名稱Calculus for Computer Graphics
編輯John Vince
視頻videohttp://file.papertrans.cn/221/220869/220869.mp4
概述Includes applications of calculus in the areas of arc-length parameterisation of curves, geometric continuity, tangent and normal vectors, and curvature.Numerous worked examples provides the reader wi
圖書封面Titlebook: Calculus for Computer Graphics;  John Vince Textbook 20192nd edition Springer Nature Switzerland AG 2019 Calculus for Computer Animation.Ca
描述.Students studying different branches of computer graphics have to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces and as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems.?..In this 2.nd?.edition, the author extends the scope of the original book to include applications of calculus in the areas of arc-length parameterisation of curves, geometric continuity, tangent and normal vectors, and curvature. The author draws upon his experience in teaching mathematics to undergraduates to make calculus appear no more challenging than any other branch of mathematics. He introduces the subject by examining how functions depend upon their independent variables, and then derives the appropriate mathematical underpinning and definitions. This gives rise to a function’s derivative and its antiderivative, or integral. Using the idea of limits, the reader is introduced to derivatives and integrals of many common functions. Other chapters address higher-order derivatives, partial derivatives, Jacobians, vector-based functions, single, double and triple integrals, with nume
出版日期Textbook 20192nd edition
關(guān)鍵詞Calculus for Computer Animation; Calculus for Computer Games; Derivatives and Antiderivatives; Exponent
版次2
doihttps://doi.org/10.1007/978-3-030-11376-6
isbn_ebook978-3-030-11376-6
copyrightSpringer Nature Switzerland AG 2019
The information of publication is updating

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Area Under a Graph, dividing a zone into very small strips and summing the individual areas. The accuracy of the result is improved simply by making the strips smaller and smaller, taking the result towards some limiting value. In this chapter I show how integral Calculus provides a way to compute the area between a f
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Arc Length and Parameterisation of Curves,ed to compute the arc length of a continuous function. However, although the formula for the arc length results in a simple integrand, it is not always possible to integrate, and other numerical techniques have to be used.
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Surface Area, to compute surface areas and regions bounded by functions. Also in this chapter, we come across Jacobians, which are used to convert an integral from one coordinate system to another. To start, let’s examine surfaces of revolution.
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Tangent and Normal Vectors,or-valued functions and definitions for a tangent and normal vector. This includes an introduction to the grad operator, and how it is used to compute the gradient of a scalar field. I then show how these vectors are computed for a line, parabola, circle, ellipse, sine curve, cosh curve, helix, Bézi
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