Minimum sized text containment shapes

Abstract

In many text-processing applications, we would like shapes that expand (or shrink) in size to fit their textual content. We address how to efficiently compute the minimum size for such text shapes. A variant of this problem is to take a fixed shape and determine the maximal size font that will still allow the content to fit into it. Our approach is to model the problem as a constrained optimisation problem with a single variable that controls the geometry of the text shape. We use a variant of secant search to determine the minimum area for the shape, guided by the area of the text. We represent the shape by regions that are composed of trapezoids whose coordinates are a linear function of the unknown variable. This allows us to use a novel linear time algorithm (based on computing Minkowski difference) that takes a trapezoid list and text height and determines the region in which a line of text of that height and some minimum width can start and still remain inside the shape.

Review of automatic document formatting

“…Column balancing was provided in Type & Set [2] using a dynamic programming approach. Another approach is to use one-dimensional optimization techniques [39] -these can also be used for vertical centering. Type & Set also provided a dynamic programming algorithm to fine-tune allocation of text to pages to globally minimize the number of widows and orphans.…”

“…This works for smaller documents but probably does not scale up to larger documents. As suggested in [39] one-dimensional optimization techniques seem like a more scalable approach.…”

“…This gives rise to a O(W log N ) time algorithm where W is the number of words and N the length of the total text. This approach was suggested in Anderson and Sobti and some improvements are described in [39].…”

“…However the Anderson and Sobti algorithm requires a significant once-off pre-computation that takes, as best we understand, O(N 3/2 log N ) time. Hurst et al [39] generalized the problem of finding a minimal width or height rectangle that is large enough to contain its content to more complex shapes. They modelled the shape using a trapezoid list where the vertices of the trapezoids are a linear function of a single variable α and the area of the shape increases monotonically in α.…”

Approximating text by its area

“…The obvious choice is to approximate the text by its area. This has proven useful for page layout [2], for table layout [4,3], finding a minimal containing shape for some fixed [5], and for float placement in multi-column documents [6].…”