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By Patria Dobbins

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The case of piercing polygons arises when one polygon intersects another. As with cyclic overlap, this problem may be resolved by cutting the offending polygons. In basic implementations, the painter's algorithm can be inefficient. It forces the system to render each point on every polygon in the visible set, even if that polygon is occluded in the finished scene. This means that, for detailed scenes, the painter's algorithm can overly tax the computer hardware. A reverse painter's algorithm is sometimes used, in which objects nearest to the viewer are painted first — with the rule that paint must never be applied to parts of the image that are already painted.

Curves with such knot vectors start and end in a control point. The individual knot values are not meaningful by themselves; only the ratios of the difference between the knot values matter. Hence, the knot vectors (0, 0, 1, 2, 3, 3) and (0, 0, 2, 4, 6, 6) produce the same curve. The positions of the knot values influences the mapping of parameter space to curve space. Rendering a NURBS curve is usually done by stepping with a fixed stride through the parameter range. By changing the knot span lengths, more sample points can be used in regions where the curvature is high.

These spatial dimensions are relative to a constant coordinate system for object-space normal maps, or to a smoothly varying coordinate system (based on the derivatives of position with respect to texture coordinates) in the case of tangent-space normal maps. This adds much more detail to the surface of a model, especially in conjunction with advanced lighting techniques. Calculating Tangent Space In order to find the perturbation in the normal the tangent space must be correctly calculated. Most often the normal is perturbed in a fragment shader after applying the model and view matrices.

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3D Rendering In Computer Graphics by Patria Dobbins

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