By C. H. Edwards

Smooth conceptual therapy of multivariable calculus, emphasizing the interaction of geometry and research through linear algebra and the approximation of nonlinear mappings by way of linear ones. while, abundant recognition is paid to the classical purposes and computational tools. hundreds of thousands of examples, difficulties and figures. 1973 edition.

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Extra info for Advanced Calculus of Several Variables (Dover Books on Mathematics)

Example text

The texture function has the usual 2D texture space with the texture image in the unit square. The built-in variables s and t are the standard RenderMan texture coordinates, which by default range over the unit interval [0, 1] for any type of surface. The shading language also provides an environment function whose 2D texture space is accessed using a 3D direction vector that is converted internally into 2D form to access a latitude-longitude or cube-face environment map (Greene 1986). When the texture image is suitable, there is no easier or more realistic way to generate texture patterns.

Team LRN 10 CHAPTER 2 Building Procedural Textures Peachey (1985) and Perlin (1985) described space-filling textures called solid textures as an alternative to the 2D texture images that had traditionally been used. Gardner (1984, 1985) used solid textures generated by sums of sinusoidal functions to add texture to models of trees, terrains, and clouds. Solid textures are evaluated based on the 3D coordinates of the point being textured, rather than the 2D surface parameters of the point. Consequently, solid textures are unaffected by distortions of the surface parameter space, such as you might see near the poles of a sphere.

The first step is to go out and examine Team LRN 24 CHAPTER 2 Building Procedural Textures the real material: its color and color variations, its reflection properties, and its surface characteristics (smooth or rough, bumpy or pitted). Photographs that you can take back to your desk are very valuable. Architectural and design magazines and books are a good source of pictures of materials. Texture Spaces The RenderMan shading language provides many different built-in coordinate systems (also called spaces).