INTERPOLATE

The interpolate (or intrp) command is used to interpolate attribute values from nodes or elements of a source mesh to node or element attributes of a sink mesh. Normally the source grid is coarser or the same resolution as the sink grid. Consider using upscale to assign values from high resolution to coarse resolution.

Note: interpolate/map replaces the command doping/integer1 which copied source itetclr values to sink imt values. interpolate/voronoi replaces doping/integer2 which copied nearest node source imt to sink imt. interpolate/continuous evolved from the doping/table command. These commands are still similar to the old versions except that this interpolation has been updated to include attribute selections and expanded options.

SYNTAX

interpolate / intrp_method / cmosink, attsink / 1,0,0 / cmosrc, attsrc / [tie_option] [flag_option] [keep_option] [intrp_function]

interpolate /  map or  voronoi or  continuous or default &
  /cmosink, attsink / 1,0,0 /cmosrc, attsrc/ &
  [ tiemin or tiemax ] [ flag_value or   plus1 ] &
  [nearest, node_attribute ] [keepatt or delatt ]  [ intrp_function ]

PARAMETER DESCRIPTIONS

intrp_method defines the method of interpolation used from mesh object cmosrc to mesh object cmosink.

map method copies the value from the enclosing source element to sink node or element (centroid). Sink nodes located outside the source elements are tagged with values according to flag options. If undefined, the flag value will be a value 1 greater than the max source attribute values. To copy from a source of type node, use voronoi method.

voronoi copies the value from the nearest source node to the sink node. By selecting the nearest source points, Voronoi regions are generated around each sink point. The resulting sink point (node or centroid) is given the value of the attribute associated with the Voronoi generating point whose Voronoi cell the sink point lands in. The outside flag options do not apply for this method, even if a sink point is outside the source, a nearest node will be found.

continuous interpolates values from the enclosing source element nodes to the sink nodes (or centriod of element). The interpolation is the sum of vertice values multiplied by the relative volume of elements formed by the sink point location on or inside the found element. The element is divided into volumes as determined by the sink point location and its relationship to the vertices of the enclosing element. A triangle becomes three triangles each with a vertices on the sink point. A quad becomes four quads. A tet becomes four tets. The assigned sink point value is the sum of these values divided by the number of element vertices. The interpolation function belonging to the attribute is applied to the vertice values before being summed. See also the interp_function option. WARNING A hex becomes 8 hexs which depends on orthogonal hexs and so is not currently supported. Use hextotet to convert hex elements to tets.

default - If source attribute is element type then use map. If source attribute is node type then use continuous.

cmosink, attsink are the sink mesh object name and attribute to write interpolated values to. If the sink attribute is element type, centroids are calculated for each element and these are used for the interpolation methods.

indexed_set 1,0,0 (start,stride,stop) or pset,get,pset_name or eltset,get,eltset_name are the set of sink nodes or elements to write interpolated values to. 1,0,0 will select all sink nodes or elements. 

cmosrc, attsrc are the source mesh object name and attribute values interpolating from.

The following parameters are optional on the command line:

tie_option is used to break a tie when a sink point has more than one valid candidate source node or element. Along with kdtree search, nearestpoint() and retrieve_within_eps() routines return a list of candidate objects for a sink point. These can be either a list of closest points, or a list of elements the point is on or inside. tie_option chooses one candidate from the possible candidates. The result is a one-to-one correspondence with each sink point paired with a single source node or a single source element. See keep_option for saving attributes with this correspondence.

• tiemax selects the maximum value from candidate nodes or elements. This is the default selection.

• tiemin selects the minimum value from candidate nodes or elements.

flag_option is used to assign an error value, or to assign a value for points not inside the source mesh. These flag values indicate either that there was an error and a value could not be written to the sink attribute. The kdtree element search will assign a flag value if a sink point is located outside the source grid. This does not apply to Voronoi method which finds nearest node and does not depend on finding an enclosing element.

• plus1 will assign a flag value of maximum source value plus 1, this is the default behavior.

• nearest node_attribute will find the nearest source node and use the node’s attribute value as the flag value. The keyword nearest must be followed with the name of the source attribute name to be used for the flag values.

• flag_value given as an integer or real value will use this numeric value for the flag assignments.

keep_option is useful during multiple calls to interpolate to use attributes pt_gtg and el_gtg instead of creating these search attributes for every call. The sink and source mesh objects and their index selection must not change. The interpolate command uses kdtree and candidate searches to create sink attributes that pair sink points to associated source node or element. By using the keyword ‘keepatt’ these attributes are not deleted. On subsequent calls to interpolate these attributes are used to look up associated node or element numbers. If map or continuous methods are used, the element attribute named el_gtg will be created. If voronoi or the flag_option nearest are used, the node attribute named pt_gtg will be created. The keyword delatt deletes any attributes created during the kdtree searches. By default these attributes are removed.

intrp_function replaces the interpolation function associated with the sink attribute. This interpolation function is applied to the final interpolated field value. Valid interpolate functions are linear, asinh, log, copy, sequence, min, incmin, max, incmax, and, or, user. Functions such as min and max pass the interpolation value unchanged.

DEBUG SYNTAX

cmo/setatt/ cmosink / idebug debug_level

For debugging purposes, setting idebug will output additional information from the interpolate routines. The integer value ‘debug_level’ is used to control the amount reported, 0 is no debug (default), 1 is minimum output and triggers calls to mmverify(), 5 is the middle, 9 and greater is verbose and includes information on every point and or element in the mesh.

Table 1 Attribute Types for Interpolate

This table indicates the type of attributes that can be used with the interpolation methods.

Table 2 Interpolation Methods and Options

This Table shows supported applications for each of the interpolation methods.

(parenthesis) means the option should work, but may be undefined.

NOT indicates Not Supported

Examples

interpolate / map / cmo_sink imt /1,0,0/ cmo_src itetclr

For each node in cmo_sink find an enclosing element from mesh cmo_src. Assign the element’s itetclr value to the corresponding imt attribute of cmo_sink. For sink points outside of the source elements, a value 1 greater than itetclr max value is assigned.

interpolate / voronoi / cmo_sink itetclr /1,0,0/ cmo_src imt / keepatt

For each element centroid in cmo_sink find nearest node in cmo_src. Assign the source node imt value to the corresponding itetclr attribute of cmo_sink. The keepatt option keeps the sink attribute pt_gtg with nearest node values for each element centroid.

interpolate / map / cmo_sink Pval /1,0,0/ cmo_src Vval / tiemin, log

This command will assign source Vval values to sink Pval for elements enclosing cmo_sink points. If the sink point is found within more than one element, the min value of the candidate elements will be chosen. Since the interpolation function “log” is named, it will be applied to the source Vval value before being written to sink attribute Pval.

interpolate/ voronoi / cmo_sink imt /1,0,0/ cmo_src imt

For each node in cmo_sink, find the closest node in cmo_src. Assign the imt value from the closest cmo_src node to the imt attribute of cmo_sink.

interpolate/ continuous / cmo_sink xval /1,0,0/ cmo_src Pv

For each node in cmo_sink, find a cmo_src element the node is inside. Interpolate the element node values in Pv on to the sink point and write to the sink attribute xval.

interpolate/ map /cmo_sink imt /1,0,0/ cmo_src itetclr / nearest, imt / keepatt

interpolate/ map /cmo_sink imtreal /1,0,0/ cmo_src itetreal / nearest, imtreal

The first call to interpolate will assign itetclr values from source elements to imt in the sink cmo for points inside the source elements. Any sink point not inside the source grid will be assigned the imt value of the nearest source point. Since keepatt is set, both attributes pt_gtg and el_gtg will be kept as sink cmo attributes and hold the node and element numbers for each sink point.

The second call to interpolate will find the sink attributes pt_gtg and el_gtg. The nearest point and enclosing element kdtree searches will be skipped. This time the element value in attribute itetreal will be assigned to the sink node attribute imtreal. For points outside the grid, values from nearest node attribute imtreal will be used. Note that the delatt keyword does not have to exist, the interpolate attributes are always deleted unless the keyword keepatt is used.

Demos

Examples: interpolate / voronoi Examples from test/level01/interp_voronoi

Examples: interpolate / map Examples from test/level01/interp_map

Examples: interpolate / continuous Examples from test/level01/interp_continuous