This chapter deals with mathematical fundamentals of curves and surfaces, and more generally manifolds and varieties.1 For that, we will pay particular attention to their smoothness or, putting it differently, to their singularities (i.e. lack of smoothness). As will be seen later on, these shape particularities are important in the design and implementation of rendering algorithms for implicit curves and surfaces. Therefore, although the context is the differential topology and geometry, we are interested in their applications in geometric modelling and computer graphics.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Mathematical Fundamentals. In: Gomes, A.J.P., Voiculescu, I., Jorge, J., Wyvill, B., Galbraith, C. (eds) Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms. Springer, London. https://doi.org/10.1007/978-1-84882-406-5_1
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DOI: https://doi.org/10.1007/978-1-84882-406-5_1
Publisher Name: Springer, London
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