Map to Geom panel

The Map to Geom panel allows you to map nodes, domains, morph volume edges, or morph volume faces in your model to a line, node list, plane, surfaces, elements, or an equation using edge domains and handles to guide the process. It also allows you to map a mesh to section lines, apply the difference between two lines or two surfaces to a mesh, offset a mesh in the normal direction, and map (or create) a mesh to a surface interpolated from a set of nodes or lines.

Panel Usage

The Map to geom panel does not include any subpanels, but its layout changes dynamically depending on the options chosen, beginning with the type of geometry you wish to map to.

map_to_geom_panel

You can complete inputs in any order, but since the panel layout can alter depending on the inputs chosen, it is best to work from left to right to avoid negating any settings you've already made if an "earlier" input setting changes the options for inputs you have already selected.

Examples

The following is an example of Map to Geom. The marked nodes and line are selected in the picture on the left and the fit to line option chosen. The picture on the right shows the results of clicking the automap button. Engineering Solutions distributes the selected nodes along the specified line, and the rest of the mesh stretches to accommodate the mapping.

morph_maptogeom

Here, the left-side handles remain fixed and all of the elements stretch.

Below is an example of map to geom with following handles. The same line is selected, but instead of a node list, the edge domain closest to the line is selected. Mapping by domains enables the user control button, which accesses a new panel. In this example the two handles on the left are chosen as followers before clicking the map button. The follower handles are given perturbations similar to those of the mapped nodes and follow along behind them.

maptogeom_usercontrol

Here, the left-side handles move with the mesh based on their distance from the line.

In the following example the highlighted morph volume edges are mapped to the line while the dimmed edges are selected as follower edges. The highlighted edges are mapped directly to the line while the follower edges are given a similar morphing.

Note:

The number of handles per edge was increased to three to improve the accuracy of the mapping.

mvolmapedge

The User Control panel can also be used to place handles and edge domains before the previously selected mapping operation takes place. This capability is useful when mapping a mesh to a surface. After selecting the mesh and surface you can go to the User Control panel and fit each edge of the mesh to the lines around the surface. Then when you map, the mesh will be fit to the surface.

Nodes and domains can be mapped directly to several different types of entity, or mapped using one of several indirect methods. See the options for (mapping type switch) in the Inputs table below.

Subpanels and Inputs

There are no subpanels on the Map to Geom panel. All inputs and command buttons are located on the main panel.

Panel Inputs

Input

Description

(at location switch)

When using map to equation, this switch allows you to choose the start point for the function:

•	at origin stars the function at the default global coordinate system's origin (0,0,0).

•	at node reveals a node selector, allowing you to pick a node to serve as the starting point.

•	at system reveals a syst selector, allowing you to pick a local coordinate system. Its origin serves as the starting point.

(covariance switch)

This switch displays when the map type is interpolate surf.

Covariance is the local variations of the interpolation around the drift (see drift switch below). The values h, h^2log(h), and h^3 give progressively more precise interpolations, while exp(-1/x) will give an approximate interpolation.

(drift switch)

This switch displays when the map type is interpolate surf.

Drift is the global trend of the interpolation. The values of no drift, constant, linear, quadratic, and cubic give progressively more precise interpolations while trigonometric uses a unique interpolation approach.

(interpolation method switch)

For interpolate surf mappings, this switch replaces the (map direction switch). It allows you to pick the method by which a surface will be interpolated.

•	infer plane is used for roughly planar interpolations. The plane normal is approximated so that the plane will pass through (or close to) the target nodes or lines.

•	planar is used for roughly planar interpolations but you may select the orientation of the planar "starting position."

•	cylindrical is used for interpolations which run about an axis. Select an axis that runs through the center of your target nodes.

•	spherical is used for interpolations which enclose a roughly spherical volume. Select a node in the center of your target nodes.

•	ellipsoid is used for interpolations which enclose a roughly elliptical volume. Select the global system, a local system, or a center node (which uses the global system axes) to orientate the ellipsoid.

•	cyl about nodes and cyl about line are used for interpolations which run around a node list or line. Select a node list or line which runs through the centerline of your target nodes.

•	tube about nodes and tube about line are used for interpolations which run around a node list or line and have a closed end. Select a node list or line which runs through the centerline of your target nodes.

Click to see some examples.

The following examples show a mesh that has been morphed to match a surface interpolated from the nodes around its perimeter. The effects of the different shapes for the form of the interpolation can be seen clearly with the shapes ending up looking more like the form of the interpolation selected in each case. However, in all the cases, the interpolated surface fits through the control points.

interp1

The following example demonstrates how a mesh can be morphed to a smooth interpolated surface given a handful of target points. The basic form was an inferred plane and the Kriging parameters used were: linear drift, h^3 covariance, and no nugget.

map_interpolate

The next set of examples show a mesh created on a surface interpolated from a series of cross sections along a line using the cyl about line method (top) and the tube about line method (bottom).

Note:

The smooth transitions between the varying sections.

interp2

interp3

(map direction switch)

This third switch displays for all direct mapping types (to lines, nodes, planes, surfs, elems, or equations). It determines the direction of mapping:

•	normal to geom - this option maps nodes to the selected geometry in a direction normal to the geometry (which may be a different direction for each node).

•	along vector - this option maps nodes to the selected geometry in the direction specified by the vector.

•	normal to elems - this option maps nodes to the selected geometry in a direction normal to the elements on which the nodes lie, which may be a different direction for each node.

•

normal to elem (smoothed) - this option maps nodes to the selected geometry in a direction normal to the elements on which the nodes lie, which may be a different direction for each node. This option will smooth the normals, averaging the directions between neighboring nodes, which may give more even results and reduce mesh distortion for meshes with sharp corners. This option is only available when mapping to a plane, surfaces, elements, or an equation.

•

normal to elem (cfd corners) - this option maps nodes to the selected geometry in a direction normal to the elements on which the nodes lie, which may be a different direction for each node. This option uses the “cfd corners” method to calculate the normal direction, which will give more even results and reduce mesh distortion for meshes with sharp corners. This option is only available when mapping to a plane, surfaces, elements, or an equation.

•	fit to line - this option distributes the node list or edge domain evenly along the selected geometry.

Note:

Relative spacing between the nodes will be maintained. This option is only available when mapping to a line or node list.

•

fit to target - this option distributes the selected entities evenly within the selected geometry. The edges of the selected entities will be matched to the edges of the target geometry and the interior will be projected normal to the geometry. This option is only available when mapping domains, elements, or morph volume faces to surfaces or elements. When mapping domains or morph volume faces to surfaces you may switch the toggle between map as group and map one to one. The map as group option will treat all the entities as a single entity when fitting them to the target surfaces. The map one to one option will try to map each selected entity to only one of the selected surfaces, fitting the edges of the entities to the surface edges. This option works best when the number of selected entities and surfaces are equal but can sometimes give good results if they are not. If the map one to one option does not map the entities as desired, you can use the user control option to fit the trickier areas by hand and then map the rest automatically.

For other mapping types, this switch is replaced by the (map by switch) (for section or line difference), the along vector / about axis toggle (for surface difference), or the interpolation method switch (for interpolate surf.) Each of those alternative inputs is described separately in this table.

Examples:

map_to_geom_panel_options

In the images above, note how the mesh (viewed in profile) is projected to a curved surface using each available option. The fit to target option is ideal for mapping an edge or 2D domain to a line or surface. It will stretch or shrink the mesh to fit the target geometry, distributing the interior nodes evenly, while the other options simply project the nodes on to the target (or to the closest edge of the target) in the chosen direction. The normal to geom option works well for most mapping cases but will occasionally fold, bind, or stretch the mesh. For cases where your mesh contains sharp corners and you wish to use the mesh to determine the projection direction, the cfd corners option will produce the smoothest projections. However, it can be time consuming, and for meshes without such sharp corners the smoothed normals option will work quickly while giving good results. For a gently flowing mesh, the normal to elements option can also give a smooth final mesh.

(map by switch)

When the mapping type is section or line difference, this switch replaces the (map direction switch). It determines what type of entity or feature guides the mapping process.

The first four methods of linear mapping differ in how the nodes are projected towards the section lines, which determines how each line influences the nearby mesh. With linear mapping the entities are mapped directly:

mapsections1

•	map by line normal establishes a plane for each section line and projects nodes normal to the plane. This is the recommended method for section mapping.

•	map by line axis establishes a straight line running through each section line and projects nodes to the section line normal to that line.

•	map by vector projects nodes to the section lines along the specified vector. This method works well for section mapping where the section lines do not lie in similar planes and run generally in the same direction. Select the vector to lie in the plane of the mesh and normal to the section lines.

•

map by plane establishes a straight line running through each section line and finds the vector which is normal to that vector which lies in the specified plane. Nodes are projected to each section line along that vector. This method works well for section mapping where the section lines do not lie in similar planes and also cross each other. The normal direction for the specified plane should be aligned with the mesh, meaning that if the mesh and the section lines lie generally in the xy-plane, the axis for the plane should be in the z-direction.

•	The last linear method, kriging, uses the kriging algorithm to fit the mesh to the section lines. The kriging method yields smoother results, but may not match the section lines precisely.

•	For nonlinear situations, mapping about axis is useful for cylindrical or sphere-like models such as a bulb-shaped housing. The mapping is applied 360 degrees around the model’s center axis, effectively changing its radius to match the mapping.

(mapping type switch)

The first switch on the panel allows you to select the type of mapping operation that you wish to perform, and influences which additional input fields display. Options include:

•	map to line: Maps the selected entities to a chosen line.

•	map to node list: Maps the selected entities to a specified node list.

•	map to plane: Maps the selected entities to a plane, specified via a standard plane and vector selector.

•	map to surfaces: Maps the selected entities to the surfaces specified in a standard surfs collector.

•	map to elements: Maps the selected entities to the elements specified in a standard elems collector.

•

map to equation: Maps the selected entities to a function. This option enables the (at location switch) and the F(xyz) (function type switch), as well as several alphanumeric boxes to accept functions. Additional buttons allow you to flip to the prev or next pages of function boxes for large numbers of functions. .

In the following example, the mesh for a flat plate is mapped to an equation defining a torus centered at the selected node. The mesh nodes were projected normally to the plate to preserve the uniform spacing.

maptorus

•	map to sections: Maps the selected entities to the lines of one or more section cuts. This reveals the lines / line list toggle and follower nodes selector.

•	line difference: Maps the selected entities from one line to another. The entities to be mapped do not need to lie on the line. The relative positions of the entities to the first line are maintained when mapping to the second.

•	surface difference: Maps the selected entities from one surface to another. The entities to be mapped do not need to lie on the surface. The relative positions of the nodes to the first surface are maintained when mapping to the second.

•	normal offset: Offsets the selected entities in the positive normal direction of specified domains, by a specified amount.

•	interpolate surf: Maps the selected entities (or an automatically generated mesh) to a surface interpolated from nodes or lines.

(map what switch)

When mapping by any direct method (to lines, nodes, planes, surfs, elems, or equations), the second switch on the panel defines what you wish to map to the target entities. Options include:

•	map domains: map morphing domains to the target.

•	map node list: map a collection of specified nodes to the target.

•	map mvol edges: map one or more morph volume edges to the target. Edges may come from multiple volumes.

•	map mvol faces: when mapping to a plane, elems, or an equation, this additional option allows you to map one or more morph volume faces to the target. Faces may come from multiple volumes.

When mapping with indirect methods (to sections, line difference, surface difference, normal offset) this switch is replaced by the map what toggle described below.

(map what toggle)

When mapping with indirect methods (to sections, line difference, surface difference, normal offset) this switch allows you to pick between map domains and map elements, or in the case of line difference or surface difference, choose between map domains and map nodes.

along vector / about axis

For surface difference mappings, this toggle replaces the (map direction switch). It allows you to specify an axis to map around or a vector to map along. Either option presents a standard plane and vector selector, though the resulting vector is used differently.

blend %

When the map type is interpolate surf, also input the blend %, which is how much of the difference between the selected entities and the interpolated surface will be applied to the mesh. At 100%, the entities will be placed on the interpolated surface. At 50% the entities will be placed halfway between the interpolated surface and their initial positions.

constrain nodes

Check constrain nodes if you wish to create a new morph constraint for the mapped nodes. The selected nodes will be constrained to the chosen entities during subsequent morphs.

To remove a constraint, use the release nodes subpanel in the Morph Constraints panel, or simply delete the constraint.

domains

When mapping domains, use this selector to pick the domains you wish to move.

elems

When mapping elements, use this selector to pick the elements you wish to move.

extend edges

When using map to surfaces or map to elements, the extend edges checkbox will appear, enabling you to extend the edges of the surfaces or mesh in a direction perpendicular to the normal at the closest point on the surfaces or mesh. If this checkbox is selected, the mapped nodes will be projected on to an extended representation of the surfaces or mesh, allowing you to project nodes beyond the edge of the surfaces or mesh as well as within any holes. If this checkbox is not selected, the mapped nodes will be projected on to the interior or edges of the surfaces or mesh.

map_to_geom_extend_edges

In the example above, three surfaces float above an angled mesh divided into two 2D domains. Both domains are selected to be mapped to the surfaces in the normal to geom direction. With extend edges selected, the nodes of the domains are moved either to the surfaces or to virtual surfaces which are extended perpendicular to the normal direction at the edge of the surface. Notice how the nodes end up placed inside the hole in the center of the largest surface. Without extend edges selected, the nodes of the domains are moved to the nearest point on the surfaces. Notice that whenever you map nodes and elements which are part of domains, the handles are mapped first, expanding or compressing the surrounding mesh, which helps to reduce mesh distortion. In this case it succeeded in reducing mesh distortion around the edges of the surfaces, but not around the hole.

F(xyz)
(function type switch)

This switch displays when using map to equation, and presents a number of preset functions and function groups that you can choose from based on geometry. When you pick an option, such as hyperboloid 2, the relevant math function(s) automatically fill in the first available alphanumeric boxes located below the switch. You can modify these equations, or type in your own.

The function F(xyz) may contain x, y, and z variables with the rest being numbers or expressions. If using the selector to obtain a function for a standard shape, you should replace constants a, b, c, r, and R with numbers. The surface defined when the function is set to zero will be used as the target surface for the mapping. Use the prev and next buttons to create additional pages for your function if there is not enough space in the first page.

fixed nodes / no fixed nodes

This toggle displays when the map type is map to sections or line difference.

If you select fixed nodes then you may also select the type of blending that you want between the mapped sections and the fixed nodes.

•	blend all will blend all unfixed nodes in the model based on the distance between the sections and the fixed nodes.

Note:

Blending will affect unattached elements and elements which lie beyond the fixed nodes.

•	blend attached will blend only the nodes which lie on elements between the sections and the fixed nodes. Unattached elements or elements which lie beyond the fixed nodes are unaffected.

•	no blending functions like having no fixed nodes except that you may fix nodes in the mapped region without any blending occurring.

If you do not select any nodes as fixed nodes, but the toggle is still set to fixed nodes, HyperMorph automatically selects the nodes nearest the selected domains or elements that do not lie on those domains or elements.

mapsections2

follower nodes

This selector displays when the map type is map to sections.

Follower nodes are not mapped to the sections, but follow the basic morphing of nodes that are mapped.

from line:

This selector displays when the map type is line difference and works in conjunction with to line (described elsewhere in this table.) Use it to select the starting line for your mapping.

fx bias =

This numeric field displays when the map type is line difference or surf difference.

Higher values result in nodes between the mapped nodes and fixed nodes staying closer to fixed nodes.

In the example below, the cyan and yellow components are mapped to the line, first with no fixed nodes, then with both the mv bias and fx bias set to 1.0 and the magenta component fixed, then with both the mv bias and fx bias set to 2.0 and the magenta component fixed.

Note:

The nodes in the transition region are nearly linear when both bias factors are set to 1.0 and follow a gentle curvature when both bias factors are set to 2.0.

maplinediff

handle placement: use current / handles/edge

When the (map what switch) is set to map mvol edges or map mvol faces, use this switch to choose between keeping the current number and arrangement of handles on the morph volume edges, or typing in a different number (up to 5 handles) for each morphed edge.

line list

When using map to line or map to sections, use this selector to pick the line(s) that you wish to map to.

lines / line list (toggle)

When using map to section, this toggle allows you to select the lines or line list to which you wish to map. Use the separate line list selector (above) to designate the destination lines.

map domains / map nodes

This toggle displays when the map type is line difference.

This setting determines what actually gets mapped to the section lines. In either case, you must select the domains or nodes that you wish to map using the line difference.

map elements / map domains

This toggle displays when the map type is map to sections and the lines / line list toggle is set to lines. This setting determines what actually gets mapped to the section lines. In either case, you must select the domains or elems that you wish to map to the section lines.

mapped edges

When the (map what switch) is set to map mvol edges, use this collector to specify the morph volume edges that you wish to serve as the mapping target.

mapped faces

When the (map what switch) is set to map mvol faces, use this collector to specify the morph volume faces that you wish to serve as the mapping target.

mv bias =

This numeric field displays when the map type is line difference or surf difference.

Higher values result in nodes between the mapped nodes and fixed nodes following the mapped nodes more closely.

node list

When the (map what switch) is set to map node list, use this collector to specify the nodes that you wish to serve as the mapping target.

no follower edges / follower edges

When the (map what switch) is set to map mvol edges, use this toggle to choose between using follower edges (which must be picked with the supplied collector) or not using any. Follower edges mimic the shape change of the mapped edges.

You can also change the number of handles on follower edges via the handle placement toggle, if desired.

no follower faces / follower faces

When the (map what switch) is set to map mvol faces, use this toggle to choose between using follower faces (which must be picked with the supplied collector) or not using any. Follower faces mimic the shape change of the mapped mvol faces. The procedure will map the edges of the selected faces to the selected plane, surface, mesh, or equation which will generally map the face as well. However, since morph volume faces are defined purely by their edges, the middles of the mapped faces may not perfectly match the features to which they were mapped.

You can also change the number of handles on follower faces via the handle placement toggle, if desired.

normal calculation: use selected elems / use all elems

When mapping along a normal offset, use this toggle to use either all elements when calculating the normal direction or to use only the elements being mapped.

normal calculation: averaged normals / smoothed normals / cfd corners

When mapping along a normal offset, use this selector to define how the normal direction is determined.

•	averaged normals defines the normal direction for each node as the average of only the elements touching the node.

•	smoothed normals calculates the average normal direction for all elements and then smoothes them so that transitions near corners are not abrupt.

•	cfd corners uses a sophisticated algorithm to smooth the normals for all the elements such that the elements will not get folded when their nodes are morphed.

freehand_panel_calculate_using

nugget: off / nugget =

This switch displays when the map type is interpolate surf.

Nugget controls how close the interpolated surface will fit relative to the control points. If the nugget is off or set to zero, the interpolated surface will pass through all the control points. If the nugget is on and non-zero, the interpolated surface will not necessarily pass through all the control points. The larger the nugget value is, the farther away the interpolated surface is allowed to be from the control points.

offset =

When mapping to a line, a node list, a plane, surfaces, elements, or an equation, you have the option of setting how far the nodes will be offset from the target. Although the mapped nodes will be moved in the specified projection direction, the offset will be the absolute distance, in model units, the mapped entities will end up from the target regardless of the direction in which they were moved.

A positive value for the offset will place the nodes short of the target, a negative value for the offset will place the nodes beyond the target, and an offset of zero will place the nodes on the target.

When mapping along a normal offset, the offset distance is how far the selected elements are moved from their present positions in their normal directions.

A positive value will offset the elements in the direction of the element normal and a negative value will offset the elements opposite the direction of the element normal.

offset in all dir. / offset along proj.

When mapping entities to a node list, line, plane, surface, or mesh while using a non-zero offset, you may select offset in all dir, which will measure the offset from each node to the closest point on the target, or offset along proj, which will measure the offset from each node to the target along the direction of projection.

freehand_panel_offset_in_all_dir_offset_along_proj

In the picture above, three nodes are being offset from a plane along a vector which is at a forty-five degree angle to the plane normal. When offset in all dir is selected, the offset is measured from each node to the closest point on the target plane, in this case along the plane normal. When offset in proj is selected, the offset is measured from each node to the plane along the projection vector. Note that when using the offset in proj option, the nodes can end up closer to the nearest point on the target than the value of the offset.

rotate nodes:

This checkbox displays when the map type is line difference or surf difference.

When mapping nodes from a straight line to a curve, check rotate nodes if you wish the curvature of the new line to affect the whole mesh.

maprotate

Line difference with rotate nodes.

rotatenodes_surfdiff

surface difference with rotate nodes.

target nodes: / target lines:

When the map type is interpolate surf, this toggle allows you to select between target nodes and target lines and pick the nodes or lines through which the surface will be interpolated.

If you selected target lines, type in the number of target nodes per line in the n/line field. The larger the number of nodes per line, the more accurate the mapping will be.

As a general rule, select no more than 3000 target nodes, as the surface interpolation algorithm will use a large amount of memory and CPU time.

to line:

This selector displays when the map type is line difference and works in conjunction with from line (described elsewhere in this table.) Use it to select the starting line for your mapping.

Command buttons

The following action buttons appear:

Button	Action
auto mapping	Performs the mapping operation based on all available input.
map	Performs the mapping operation based on all available input.
redo	Redoes the last "undone" operation.
redo all	Redoes all "undone" operations.
reject	Undoes the creation of an entity, such as a constraint or shape.
return	Exists the panel.
user control	Launches the user control subpanel to allow manual completion of the mapping operation.
undo	Undoes the most recent morphing action (movement of nodes, but not creation of entities such as constraints).
undo all	Undoes all recent morphing actions (movement of nodes, but not creation of entities such as constraints).

Map to Geom panel

Map to Geom panel

Map to Geom panel

Panel Usage

Examples

Subpanels and Inputs

Panel Inputs

Input

Description

(at location switch)

(covariance switch)

(drift switch)

(interpolation method switch)

(map direction switch)

Examples:

(map by switch)

(mapping type switch)

(map what switch)

(map what toggle)

along vector / about axis

blend %

constrain nodes

domains

elems

extend edges

F(xyz) (function type switch)

fixed nodes / no fixed nodes

follower nodes

from line:

fx bias =

handle placement: use current / handles/edge

line list

lines / line list (toggle)

map domains / map nodes

map elements / map domains

mapped edges

mapped faces

mv bias =

node list

no follower edges / follower edges

no follower faces / follower faces

normal calculation: use selected elems / use all elems

normal calculation: averaged normals / smoothed normals / cfd corners

nugget: off / nugget =

offset =

offset in all dir. / offset along proj.

rotate nodes:

target nodes: / target lines:

to line:

Command buttons

Button

Action

auto mapping

map

redo

redo all

reject

return

user control

undo

undo all

See Also:

F(xyz)
(function type switch)