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With a 16×16 base texture map, the rip-map resolutions would be 16×8, 16×4, 16×2, 16×1, 8×16, 8×8, 8×4, 8×2, 8×1, 4×16, 4×8, 4×4, 4×2, 4×1, 2×16, 2×8, 2×4, 2×2, 2×1, 1×16, 1×8, 1×4, 1×2 and 1×1. A trade off : anisotropic mip-mapping The unfortunate problem with this approach is that rip-maps require four times as much memory as the base texture map, and so rip-maps have been very unpopular. Also for 1×4 and more extreme 4 maps each rotated by 45° would be needed and the real memory requirement is growing more than linearly.

Likewise, by evaluating a NURBS surface at various values of the two parameters, the surface can be represented in cartesian space. NURBS curves and surfaces are useful for a number of reasons:      They are invariant under affine as well as perspective transformations: operations like rotations and translations can be applied to NURBS curves and surfaces by applying them to their control points. , conics) and free-form shapes. They provide the flexibility to design a large variety of shapes.

Because of the appearance of the considered objects, two main algorithm families are used. The first is based on subdividing the space in a finite amount of regions, each with a certain level of detail. The result is discrete amount of detail levels, from which the name Discrete LoD (DLOD). There's no way to support a smooth transition between LOD levels at this level, although alpha blending or morphing can be used to avoid visual popping. The latter considers the polygon mesh being rendered as a function which must be evaluated requiring to avoid excessive errors which are a function of some heuristic (usually distance) themselves.

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3D Rendering In Computer Graphics by Patria Dobbins


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