外文翻譯--字符的計(jì)算機(jī)處理與顯示-全文預(yù)覽
【正文】 be seen that the algorithm uses both recursive and iterative means to provide an Output. This, in practice, means that a significant amount of time will be required to pute an output. The situation deteriorates if more than one segment will be needed to 外 文翻譯 第 6 頁 model the given outline. Optimisation of the algorithm is often addressed through improving each of the three stages mentioned. Farin discusses some of the techniques employed for gaining initial values for the parametric variable. The values for the two unknowns, the control points, can be evaluated by means of a leastsquares approach. The final section can be attained by a variety of ways, a notable contribution to this area is by Plass and Stone. Modelling by Parabolic Splines The parabolic arc belongs to the family of conics, which also includes the elliptic, hyperbolic and circular spline. Being quadratic, they model using one less parameter than the cubic case. The general conic description itself prises of two knot points, one control point and a tension (henceforth referred to as the sharpness) parameter. Variation in the sharpness value yields an appropriate conic: zero to one for an elliptic section, one for parabolic arc, and between one and infinity for a hyperbolic curve. The fact that the sharpness equals one for the parabolic case makes it attractive to use. The TrueType font, developed by Apple, employs this description for the reason given above and for the fact that there is a one to one mapping between a cubic and a quadratic model in this case. The formulation of a parabolic (and the general conic) description isvia a guiding triangle. As shown in Fig 5, this is realised through the two knot tangents which in tum intersect with each other, providing the location for the desired control point. Once the control point is known, the curve segment can be generated using the appropriate parametric equation. Although simpler in description than the general conic (sharpness equals one), the most 外 文翻譯 第 7 頁 economical way of realising a parabolic model is via its association with its conic family. In fact, as manifested in Fig 6, the approach requires that a conic model be gained first. This is then assessed to see how close it is to the parabolic case. IF tbe parison is acceptable then a solution has been found and the (conic) control point is recorded. If the quality of fit needs improving then the conic is split and modelled by two or more parabolic arcs. This may sound a lengthy process, but in reality it is much faster than the cubic case: The conic and the parabolic models are gained by means of a direct approach, without the need for iteration or recursion. This amounts to on average about five times faster conversation rates than for the cubic. Comparison of Splines When attempting to puter model a given font outline, the critical question of which mathematical description to employ often arises. Various factors such as the form of the supplied data, the level of continuity desired between joining arcs, the techniques of evaluating goodnessoffit and so forth, are mon considerations. The decision to use Bkier cubic or parabolic splines is made with similar thoughts and observations. Both descr
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