Mathematical Tools in Computer Graphics with C# Implementations
Mathematics is vital for an understanding of computer graphics. This volume helps the reader gain such an understanding by presenting all introductory and most advanced topics in the field of computer graphics with mathematical descriptions and derivations. Offering a balance of theory, applications, and code, the underlying numerical methods and algorithms are derived and a large number of examples are given. The book begins with a discussion of basic graphics tools such as vectors, matrices, and quaternions, and then builds up to more advanced topics such as the intersection of three-dimensional objects. Both classical and newer topics, such as parameterization, wavelets, fractals, and geometry images, are covered. In particular, the book contains all of the classes in C# necessary for computer graphics, providing a full explanation of the C# code and C# implementations for almost all algorithms.
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algorithm ambient occlusion angles applied approximate B-spline B´ezier curves B´ezier patches B´ezier surfaces barycentric coordinates basis functions BBox boundary edges calculate Catmull-Clark CloneO coeﬃcients color compute Console Write control points convex hull created curvature plot deﬁned determine diﬀerent diﬀuse EdgeSet eﬀect f Write faces fc=o ﬁeld ﬁgure ﬁnd ﬁrst ﬂuid for(i=0;i<vertices.getCount();i++ for(int fractal Gaussian curvature geometry image given Haar wavelet harmonic interpolation harmonic surface illustrated in ﬁgure interpolation points intersection interval iteration Kronecker product light source lighting model matrix Mean curvature mesh METAPOST non-uniform normal object obtain parameter values parametric surfaces photon mapping pixel polygon polynomials produced public bool public class public double public int public static public Vector public void Quaternion radiosity raytracing reﬂection return false return null return true rotation segment speciﬁed specular sphere subdivision scheme subdivision surfaces supersampling techniques tensor product tensor product surface theorem torus triangle valence velocity vertex VertexSet vertices