-The mapping algorithm for 2D case is as follows:
-
-- Key-points are set in the order that they are encountered when
- walking along a pattern boundary so that elements are on the left. The
- first key-point is preserved.
-- Find geometrical vertices corresponding to key-points by vertices
- order in a face boundary; here, "Reverse order of key-points" flag is
- taken into account. \image html image95.gif
-- Boundary nodes of a pattern are mapped onto edges of a face: a
- node located between certain key-points on a pattern boundary is
- mapped on a geometrical edge limited by corresponding geometrical
- vertices. Node position on an edge reflects its distance from two
- key-points. \image html image96.gif
-- Coordinates of a non-boundary node in a parametric space of a face
- are defined as following. In a parametric space of a pattern, a node
- lays at the intersection of two iso-lines, each of which intersects a
- pattern boundary at least at two points. Knowing mapped positions of
- boundary nodes, we find where isoline-boundary intersection points are
- mapped to, and hence we can find mapped isolines direction and then,
- two node positions on two mapped isolines. The eventual mapped
- position of a node is found as an average of positions on mapped
- isolines. \image html image97.gif
-
-For 3D case the algorithm is similar.
+The mapping algorithm for a 2D case is as follows:
+
+- The key-points are set counterclockwise in the order corresponding
+ to their location on the pattern boundary. The first key-point is preserved.
+- The geometrical vertices corresponding to the key-points are found
+ on face boundary. Here, "Reverse order of key-points" flag is set.
+\image html image95.gif
+- The boundary nodes of the pattern are mapped onto the edges of the face: a
+ node located between two key-points on the pattern boundary is
+ mapped on the geometrical edge limited by the corresponding geometrical
+ vertices. The node position on the edge depends on its distance from the
+ key-points.
+\image html image96.gif
+- The cordinates of a non-boundary node in the parametric space of the face
+ are defined in the following way. In the parametric space of the
+ pattern, the node lies at the intersection of two iso-lines. Both
+ of them intersect the pattern boundary at two
+ points at least. If the mapped positions of boundary nodes are known, it is
+ possible to find, where the points at the intersection of isolines
+ and boundaries are mapped. Then it is possible to find
+ the direction of mapped isolinesection and, filally, the poitions of
+ two nodes on two mapped isolines. The eventual mapped
+ position of the node is found as an average of the positions on mapped
+ isolines.
+\image html image97.gif
+
+The 3D algorithm is similar.