![]() ![]() The reason I wanted to do things in an automated manner was for the most part because the project is more high-concept than based on typographically sound principals. Thanks there is no problem with doing it in that manner and in fact I am aware that this is certainly possible, more supportive and much simpler to do! Project is for BA Hons Graphic Design at the University of the West of England I think that old style Postscript MM fonts should be supported at least back to CS5 I understand I may have been a little overambitious in what I aim to do especially for my first type design project but as it currently stands I have a set of compatible master outlines for linear interpolation and so feel as though I’ve already surmounted the hardest part! I may be wrong in that assumption you mentioned on Twitter that there was a way to ‘add the optical size feature manually’ is this still the case? I know that it is possible using the OpenType ‘size’ tag but also that this is currently unsupported in all desktop publishing If my research is correct then the ‘automatically use correct optical size’ preference in Adobe InDesign actually extends much farther back than just in CC. These may be defined as indeed higher-dimensional piecewise linear function (see second figure below).I have a copy of Fontographer 5.0 so should be able to import my Glyphs masters as Opentype files and then create PST1 MM in Fontographer. Other extensions of linear interpolation can be applied to other kinds of mesh such as triangular and tetrahedral meshes, including Bézier surfaces. Notice, though, that these interpolants are no longer linear functions of the spatial coordinates, rather products of linear functions this is illustrated by the clearly non-linear example of bilinear interpolation in the figure below. For two spatial dimensions, the extension of linear interpolation is called bilinear interpolation, and in three dimensions, trilinear interpolation. Linear interpolation as described here is for data points in one spatial dimension. If a C 0 function is insufficient, for example if the process that has produced the data points is known to be smoother than C 0, it is common to replace linear interpolation with spline interpolation or, in some cases, polynomial interpolation. Their heights above the ground correspond to their values. Because this operation is cheap, it's also a good way to implement accurate lookup tables with quick lookup for smooth functions without having too many table entries.Ĭomparison of linear and bilinear interpolation some 1- and 2-dimensional interpolations.īlack and red/ yellow/ green/ blue dots correspond to the interpolated point and neighbouring samples, respectively. They are often used as building blocks for more complex operations: for example, a bilinear interpolation can be accomplished in three lerps. Lerp operations are built into the hardware of all modern computer graphics processors. " Bresenham's algorithm lerps incrementally between the two endpoints of the line." The term can be used as a verb or noun for the operation. In that field's jargon it is sometimes called a lerp (from linear int erpolation). ![]() The basic operation of linear interpolation between two values is commonly used in computer graphics. A description of linear interpolation can be found in the ancient Chinese mathematical text called The Nine Chapters on the Mathematical Art (九章算術), dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. It is believed that it was used in the Seleucid Empire (last three centuries BC) and by the Greek astronomer and mathematician Hipparchus (second century BC). Linear interpolation is an easy way to do this. Suppose that one has a table listing the population of some country in 1970, 1980, 19, and that one wanted to estimate the population in 1994. Linear interpolation has been used since antiquity for filling the gaps in tables. This is intuitively correct as well: the "curvier" the function is, the worse the approximations made with simple linear interpolation become. That is, the approximation between two points on a given function gets worse with the second derivative of the function that is approximated. ![]()
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