外文翻译--字符的计算机处理与显示(编辑修改稿)

外文翻译--字符的计算机处理与显示(编辑修改稿)内容摘要：

its construction. Various cubic forms exist, though through the popularity of the Postscript language, the Bezier spline has gained emphasis and is regarded as one of the primary descriptive types for modelling font outlines. A Bezier cubic curve segment consists of four points: two endpoints (often called anchor or knot points) and two control points. The knot points lie on the original outline and are interpolated。 whilst the positioning of the two control points determines the overall shape of the segment. In the rational parametric form, each point also has a tension parameter (sometimes referred to as the weight) associated with it. Weights at the knot points are called “point tensions” and are used to smooth out a curve shape. The weights at the control points are usually labelled as “interval tensions” and are available to the user to either pull outwards or push inwards the respective curve shape. Taking the nonrational parametric form for the Bezier cubic as an example, the 外 文翻译 第 5 页 modelling of outlines is realised through three phases: The first phase attempts to find a suitable relationship between the parametric variable used in the description and the given outline. The second phase calculates respective values for the control points, whilst the third stage evaluates both the goodnessoffit and also updates the relationship approximated in phase one. The way these phases are connected to form a modellingalgorithm is shown in Fig 4. Although the above described approach yields the desired model, it does so at a price. hoking at Fig 4, it can 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 文翻译 第 6 页 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 triang。