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PK_TOPOL_fctab_fin_data_t |
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struct PK_TOPOL_fctab_fin_data_s
{
int *data;
int length;
};
typedef struct PK_TOPOL_fctab_fin_data_s
PK_TOPOL_fctab_fin_data_t;
Used in:
PK_TOPOL_facet_table_t
This is a support structure for PK_TOPOL_facet_2_r_t. It is an indexed table
which maps fins into data indices. The data index is used to reference into
the 'data_point_idx', 'data_normal_idx', 'data_param_idx', 'data_deriv_idx' and
'data_curv_idx' tables. The data index is provided as a means of grouping
together the point, normal, parameter, derivative and curvature information at
a fin's head vertex (where the 'head' vertex is the vertex pointed to by the
fin).
In general, fins which share the same head vertex and for which the geometry
data (i.e. the point, normal, parameter, derivative and curvature data) is also
shared will reference the same data index. If any piece of geometry data is
not common multiple data indices will be created.
USING THE RETURNED SUBSCRIPT:
Each data index can be used as a subscript into the following tables :
data_point_idx (for the index of its point value)
data_normal_idx (for the index of its face normal vector)
data_param_idx (for the index of its surface parameter values)
data_deriv_idx (for the index of its surface derivative values)
data_curv_idx (for the index of its face curvature values)
FACET VERTICES:
Facet vertices are of three types: those at original model vertices, those
on original model edges and those representing interior points in a face.
FINS AT INTERIOR VERTICES:
With interior facet vertices, it is generally the case that all the data (i.e.
the point, normal, parameter, derivatives and curvatures) will be common to all
fins at the vertex. In this case all fins at the vertex will refer to the same
data integer value, which is the index into the 'data_point_idx',
'data_normal_idx', 'data_param_idx', 'data_deriv_idx' and 'data_curv_idx'
tables.
If the interior vertex lies at a singularity all the fins at this vertex will
reference the same point but will have different normals, parameters,
derivatives and curvatures. Thus each fin will refer to a different integer
value, but when these indices are used to reference into the 'data_point_idx'
table the same point index will be returned.
In a similar way, if the interior vertex lies on a periodic surface and
consistent parameters have been requested, all the fins at this vertex will
reference the same point, normal, derivatives and curvatures but may have
different parameters. If there are different parameters the fins cannot all
reference the same data index.
FINS AT EXTERIOR VERTICES ALONG MODEL EDGES:
With exterior facet vertices part-way along model edges, there are two cases to
consider: the facet vertex lies in only one face, the facet vertex lies in
multiple faces that meet along the model edge.
If the facet vertex lies in only one face it will behave in exactly the same
way as an internal facet vertex (as described above).
If the facet vertex lies in multiple faces, say n faces (where n will be at
most 2 for manifold parts), there will in general be n face normals and n
sets of parameter, derivative and curvature data at the vertex. All fins at
the vertex will have the same point and in many cases, the normal, parameters,
derivatives and curvatures can be shared by fins in the same face that point at
this vertex. Thus the fins at such a vertex will in general all refer to one of
n integer values.
As in the case of interior vertices, if the vertex lies on a periodic surface
and consistent parameters have been requested, it is not always the case that
all fins in a particular face will have the same parameter data so it may be
necessary to have more than n data indices, where n is the number of faces
that share the model edge.
FINS AT EXTERIOR VERTICES AT MODEL VERTICES:
Exterior vertices at original model vertices are similar to exterior vertices
at model edges only in this case we are interested in how many faces meet at
the vertex rather than how many meet along the model edge.
As in the case of interior vertices, if the vertex lies at a singularity in a
particular face, the fins in this face pointing at this vertex will have
different parameter data, so it will be necessary to have more than n data
indices, where n is the number of faces that share the model vertex.
EXAMPLE:
The diagram shows the top, front and right hand side faces of a cube with
one four sided facet on each face (shown in an 'exploded' schematic form).
v4--f4---v3
/ / v11
f1 f3 / |
/ / f12 |
v1--f2---v2 / f11
v12 |
v5--f5---v8 | v10
| | f9 /
| | | f10
f6 f8 | /
| | v9
v6--f7---v7
f1 is the fin pointing at v1
f2 is the fin pointing at v2
. .
. .
. .
f12 is the fin pointing at v12
SHARED GEOMETRY:
In the example above v2, v8 and v12 all lie at the same point, but their
normals, parameters, derivatives and curvatures are different. Thus fins f2,
f8 and f12 will have different data indices. When this data index is used to
reference into the 'data_point_idx' table it will be found that each of these
data indices will give the same integer value - an index into the 'point_vec'
vector table. This reduces the volume of geometric data output.
The 'data_normal_idx' table is provided because the number of vertex normals
is different from the number of vertex point coordinates (there being more
than one normal across a model edge, at a singularity, or at a model vertex).
This level of indirection allows Parasolid to identify cases where vertices of
planar facets refer to the same face normal value and construct the
'data_normal_idx' table so that it refers to the same vector entry in the
'normal_vec' table.
The 'data_param_idx' table is provided as an index to the parameter table.
Parasolid does not identify common entries in these tables and so these have
the same number of entries as there are distinct fin data.
The 'data_deriv_idx' table is provided as an index to the derivative data
tables. Once again, this level of indirection allows Parasolid to identify
cases where vertices of planar facets refer to the same surface derivatives and
construct the 'data_deriv' table so that it refers to the same first and
second derivative entries in the 'deriv_dp' and 'deriv_d2p' tables.
The 'data_curv_idx' table is provided as an index to the curvature data
table. Once again, this level of indirection allows Parasolid to identify
cases where vertices of planar facets refer to the same face curvatures and
construct the 'data_curv' table so that it refers to the same curvature entry
in the 'curv_dirs' table.
For more details see associating fins with facet geometry.