diff --git a/Set_movable_separability_2/doc/Set_movable_separability_2/Set_movable_separability_2.txt b/Set_movable_separability_2/doc/Set_movable_separability_2/Set_movable_separability_2.txt index d996c8b33a0..85dfd4fa25a 100644 --- a/Set_movable_separability_2/doc/Set_movable_separability_2/Set_movable_separability_2.txt +++ b/Set_movable_separability_2/doc/Set_movable_separability_2/Set_movable_separability_2.txt @@ -7,7 +7,7 @@ namespace CGAL { \cgalAutoToc \authors Shahar Shamai and Efi Fogel -\section sms_sec_intro Introduction +\section sms_2_sec_intro Introduction Movable Separability of Sets \cgalCite{t-mss-85} is a class of problems that deal with moving sets of objects, such as polygons in @@ -37,12 +37,12 @@ problems related to 2D castings. In particular, each of these solutions handles a single moving polygon and a single stationary polygon, and considers a single translation of the moving polygon. -\section sms_sec_casting Casting +\section sms_2_sec_casting Casting Casting is a manufacturing process where liquid material is poured into a cavity inside a mold, which has the shape of a desired -product (The mold can take any shape and form as long as it has a -cavity of the desired shape). After the material solidifies, the +product. (The mold can take any shape and form as long as it has a +cavity of the desired shape.) After the material solidifies, the product is pulled out of the mold. Typically a mold is used to manufacture numerous copies of a product. The challenge is designing a proper mold, such that the solidified product can be separated from @@ -54,7 +54,7 @@ that, given a simple closed polygon \f$P\f$, determines whether a cavity (of a mold in the plane) that has the shape of \f$P\f$ can be used so that the polygon \f$P\f$ could be pulled out of the mold without colliding into the mold (but possibly sliding along the mold -surface); see \cgalFigureRef{sms_2_fig_polygons} for an +boundary); see \cgalFigureRef{sms_2_fig_polygons} for an illustration. In reality, the mold of a castable polygon must be rotated before the polygon is casted, such that one edge becomes parallel to the \f$x\f$-axis and is located above all other edges;