\page a1d_meshing_hypo_page 1D Meshing Hypotheses
-<br>
+Basic 1D hypothesis specifies:
+<ul>
+<li>how \ref a1d_algos_anchor "Wire Discretization" should divide the edge;</li>
+<li>how \ref a1d_algos_anchor "Composite Side Discretization" should divide the group of C1-continues edges.</li>
+</ul>
+
+By type of nodes distribution the 1D hypotheses can be categorized as follows:
<ul>
-<li>\ref adaptive_1d_anchor "Adaptive"</li>
-<li>\ref arithmetic_1d_anchor "Arithmetic 1D"</li>
-<li>\ref geometric_1d_anchor "Geometric Progression"</li>
-<li>\ref average_length_anchor "Local Length"</li>
-<li>\ref max_length_anchor "Max Size"</li>
-<li>\ref deflection_1d_anchor "Deflection 1D"</li>
-<li>\ref number_of_segments_anchor "Number of segments"</li>
-<li>\ref start_and_end_length_anchor "Start and end length"</li>
-<li>\ref automatic_length_anchor "Automatic Length"</li>
-<li>\ref fixed_points_1d_anchor "Fixed points 1D"</li>
+<li>Uniform distribution
+ <ul>
+ <li>\ref average_length_anchor "Local Length"</li>
+ <li>\ref max_length_anchor "Max Size"</li>
+ <li>\ref number_of_segments_anchor "Number of segments" with Equidistant distribution</li>
+ <li>\ref automatic_length_anchor "Automatic Length"</li>
+</ul></li>
+<li>Constantly increasing or decreasing length of segments
+ <ul>
+ <li>\ref arithmetic_1d_anchor "Arithmetic 1D"</li>
+ <li>\ref geometric_1d_anchor "Geometric Progression"</li>
+ <li>\ref start_and_end_length_anchor "Start and end length"</li>
+ <li>\ref number_of_segments_anchor "Number of segments" with Scale distribution</li>
+</ul></li>
+<li>Distribution depending on curvature
+ <ul>
+ <li>\ref adaptive_1d_anchor "Adaptive"</li>
+ <li>\ref deflection_1d_anchor "Deflection 1D"</li>
+</ul></li>
+<li>Arbitrary distribution
+ <ul>
+ <li>\ref fixed_points_1d_anchor "Fixed points 1D"</li>
+ <li>\ref number_of_segments_anchor "Number of segments" with
+ \ref analyticdensity_anchor "Analytic Density Distribution" or Table Density Distribution</li>
+</ul></li>
</ul>
<br>
<h2>Deflection 1D hypothesis</h2>
<b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
-composing your geometrical object. It uses only one parameter: the
-value of deflection.
-\n A geometrical edge is divided into equal segments. The maximum
-distance between a point on the edge within a segment and the line
-connecting the ends of the segment should not exceed the specified
-value of deflection . Then mesh nodes are constructed at end segment
-locations and 1D mesh elements are constructed on segments.
+composing your geometrical object. It defines only one parameter: the
+value of deflection (or chord error).
+
+A geometrical edge is divided into segments of length depending on
+edge curvature. The more curved the edge, the shorter the
+segment. Nodes on the edge are placed so that the maximum distance
+between the edge and a segment approximating a part of edge between
+two nodes should not exceed the value of deflection.
\image html a-deflection1d.png
<b>Local Length</b> hypothesis can be applied for meshing of edges
composing your geometrical object. Definition of this hypothesis
-consists of setting the \b length of segments, which will split these
-edges, and the \b precision of rounding. The points on the edges
-generated by these segments will represent nodes of your mesh.
-Later these nodes will be used for meshing of the faces abutting to
-these edges.
-
-The \b precision parameter is used to allow rounding a number of
-segments, calculated from the edge length and average length of
-segment, to the lower integer, if this value outstands from it in
-bounds of the precision. Otherwise, the number of segments is rounded
-to the higher integer. Use value 0.5 to provide rounding to the
-nearest integer, 1.0 for the lower integer, 0.0 for the higher
+consists of setting the \b length of segments, which will approximate these
+edges, and the \b precision of rounding.
+
+The \b precision parameter is used to round a number of segments,
+calculated by dividing the edge length by the specified \b length of
+segment, to the higher integer if the remainder exceeds the precision
+and to the lower integer otherwise. Use value 0.5 to provide rounding
+to the nearest integer, 1.0 for the lower integer, 0.0 for the higher
integer. Default value is 1e-07.
\image html image41.gif
\image html a-averagelength.png
-\image html b-erage_length.png "Local Length hypothesis - all 1D mesh elements are roughly equal"
+\image html b-erage_length.png "Local Length hypothesis - all 1D mesh segments are equal"
<b>See Also</b> a sample TUI Script of a
\ref tui_average_length "Defining Local Length" hypothesis
<b>Max Size</b> hypothesis allows splitting geometrical edges into
segments not longer than the given length. Definition of this hypothesis
consists of setting the maximal allowed \b length of segments.
-<b>Use preestimated length</b> check box lets you specify \b length
+<b>Use preestimated length</b> check box lets you use \b length
automatically calculated basing on size of your geometrical object,
namely as diagonal of bounding box divided by ten. The divider can be
changed via "Ratio Bounding Box Diagonal / Max Size"
\anchor number_of_segments_anchor
<h2>Number of segments hypothesis</h2>
-<b>Number of segments</b> hypothesis can be applied for meshing of edges
-composing your geometrical object. Definition of this hypothesis
-consists of setting the number of segments, which will split these
-edges. In other words your edges will be split into a definite number
-of segments with approximately the same length. The points on the
-edges generated by these segments will represent nodes of your
-mesh. Later these nodes will be used for meshing of the faces abutting
-to these edges.
+<b>Number of segments</b> hypothesis can be applied for approximating
+edges by a definite number of mesh segments with length depending on
+the selected type of distribution of nodes.
The direction of the splitting is defined by the orientation of the
underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
\image html image46.gif
-You can set the type of distribution for this hypothesis in the
+You can set the type of node distribution for this hypothesis in the
<b>Hypothesis Construction</b> dialog bog :
\image html a-nbsegments1.png
<b>Start and End Length</b> hypothesis allows to divide a geometrical edge
into segments so that the first and the last segments have a specified
length. The length of medium segments changes with automatically chosen
-geometric progression. Then mesh nodes are
-constructed at segment ends location and 1D mesh elements are
-constructed on them.
+geometric progression.
The direction of the splitting is defined by the orientation of the
underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
The dialog box prompts you to define the quality of the future mesh by
only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
-low number of elements) to 1 (extremely fine mesh, great number of
-elements).
+low number of segments) to 1 (extremely fine mesh, great number of
+segments).
\image html automaticlength.png
Compare one and the same object (sphere) meshed with
minimum and maximum value of this parameter.
-\image html image147.gif "Example of a very rough mesh. Automatic Length works for 0."
+\image html image147.gif "Example of a rough mesh at Automatic Length Fineness of 0."
-\image html image148.gif "Example of a very fine mesh. Automatic Length works for 1."
+\image html image148.gif "Example of a fine mesh at Automatic Length Fineness of 1."
<br>
\anchor fixed_points_1d_anchor
<h2>Fixed points 1D hypothesis</h2>
<b>Fixed points 1D</b> hypothesis allows splitting edges through a
-set of points parameterized on the edge (from 1 to 0) and a number of segments for each
-interval limited by the points.
+set of points parametrized on the edge (from 1 to 0) and a number of
+segments for each interval limited by the points.
\image html hypo_fixedpnt_dlg.png
the 3D viewer or selecting the edges or groups of edges in the
Object Browser.
-\image html mesh_fixedpnt.png "Example of a submesh on the edge built using Fixed points 1D hypothesis"
+\image html mesh_fixedpnt.png "Example of a sub-mesh on the edge built using Fixed points 1D hypothesis"
<b>See Also</b> a sample TUI Script of a
\ref tui_fixed_points "Defining Fixed Points" hypothesis operation.
