Representing implicit curves of procedural geometric surfaces

摘要

Compact and accurate piecewise parametric representations of implicit curves may be achieved by iteratively selecting ranges of parameterizing regions and testing each for satisfying an intervalized super convergence test. In one aspect, the implicit curves is represented as a compact form of one or more representations of such convergence regions. For memory and bandwidth constrained applications, starting points of convergence regions may not be stored but instead calculated at runtime prior to rendering a point on the implicit curve. Furthermore, not all endpoints relevant convergence regions of a selected implicit curve need be stored. Instead, based on at least one endpoint, the other endpoints can be derived via Newton iterations. To further reduce memory and bandwidth costs, coordinates can be stored in a quantized format and the points reflecting floating point accuracy can be derived at runtime again by Newton iteration.