Map to Geometry

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.

1. From the Morph ribbon, click the arrow next to the Morph tool set name and select Map To Geometry.
2. In the Morph: Map to Geometry dialog, define parameters.

   Parameter	Action
   Action	Select the type of mapping operation that you wish to perform. Interpolate Surface Map the selected entities (or an automatically generated mesh) to a surface interpolated from nodes or lines. Line Difference Map 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. Map To Elements Map the selected entities to the elements specified in a standard elems collector. Map To Equation Map 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 Figure 1, 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. Figure 1. Map To Lines Map the selected entities to a chosen line. Map To Node List Map the selected entities to a specified node list. Map To Plane Map the selected entities to a plane, specified via a standard plane and vector selector. Map To Surfaces Map the selected entities to the surfaces specified in a standard surfs collector. Map To Sections Map the selected entities to the lines of one or more section cuts. This reveals the lines / line list toggle and follower nodes selector. Normal Offset Offset the selected entities in the positive normal direction of specified domains, by a specified amount. Surface Difference Map 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.
   Extend Edges	Select the Extend Edges check box 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 check box 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 check box is not selected, the mapped nodes will be projected on to the interior or edges of the surfaces or mesh. Figure 2 shows three surfaces that 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. Figure 2. Restriction: Only available when Map to Elements or Map to Surfaces is selected for Action.
   To	Select the starting line or node for your mapping. Restriction: Only available when Line Difference is selected for Action.
   From	Select the starting line or node for your mapping. Restriction: Only available when Line Difference is selected for Action.
   Mapping Style	Select the To Lines or From Lines To Lines. In the Select field, below, select the destination lines. Restriction: Only available when Map to Sections is selected for Action.
   Select	Select the elements you wish to move. Restriction: Only available when Map to Elements is selected for Action. Select the line(s) you wish you map to. Restriction: Only available when Map to Lines or Map to Sections is selected for Action. Specify the nodes that you wish to serve as the mapping target. Restriction: Only available when mapping by any direct method (Map to Lines, Map to Node List, Map to Plane, Map to Surfaces, Map to Elements, or Map to Equation) and Node List is selected for Map Entities. Select the domains you wish to move. Restriction: Only available when mapping by any direct method (Map to Lines, Map to Node List, Map to Plane, Map to Surfaces, Map to Elements, or Map to Equation) and Domains is selected for Map Entities.
   Map Entities	Choose between map domains and elements. Restriction: Only available when Map to Sections or Normal Offset is selected for Action. Choose between domains and nodes. Restriction: Only available when Line Difference or Surface Difference is selected for Action.
   Mapped	Specify the morph volume edges that you wish to serve as the mapping target. Restriction: Only available when mapping by any direct method (Map to Lines, Map to Node List, Map to Plane, Map to Surfaces, Map to Elements, or Map to Equation) and Morph Volume Edges is selected for Map Entities.
   Add Followers	Select the Add Followers check box to use followers. 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. Restriction: Only available when mapping by any direct method (Map to Lines, Map to Node List, Map to Plane, Map to Surfaces, Map to Elements, or Map to Equation) and Morph Volume Edges is selected for Map Entities.
   Origin	Choose the start point for the function. At (0,0,0) Start the function at the default global coordinate system's origin (0,0,0). At Node Select a node to serve as the starting point. At System Select a local coordinate system. Its origin serves as the starting point. Restriction: Only available when Map to Equation is selected for Action.
   Autofill Options	This field displays 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 equation field. You can modify these equations, or type in your own. The equation 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. Restriction: Only available when Map to Equation is selected for Action.
   Normal Method	When mapping along a normal offset, choose how the normal direction is determined. Averaged Normals Define the normal direction for each node as the average of only the elements touching the node. Smoothed Normals Calculate the average normal direction for all elements and then smooth them so that transitions near corners are not abrupt. CFD Corners Use a sophisticated algorithm to smooth the normals for all the elements such that the elements will not get folded when their nodes are morphed. Figure 3 shows how the mesh is projected to a curved surface using each available option. For cases where your mesh contains sharp corners, 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 averaged normals option can also give a smooth final mesh. Figure 3. Example: Calculate Using Methods Restriction: Only available when Normal Offset is selected for Action.
   Calculate Normals Using	Choose to use either all elements when calculating the normal direction or to use only the elements being mapped. Restriction: Only available when Normal Offset is selected for Action.
   Target Entities	Choose between nodes or lines, and select the nodes or lines through which the surface will be interpolated. If you selected lines, specify the number of nodes per line. 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. Restriction: Only available when Interpolate Surface is selected for Action.
   Map Entities	Choose what you wish to map to the target entities. Domains Map morphing domains to the target. Morph Volume Edges Map one or more morph volume edges to the target. Edges may come from multiple volumes. Node List Map a collection of specified nodes to the target. Restriction: Only available when mapping by any direct method (Map to Lines, Map to Node List, Map to Plane, Map to Surfaces, Map to Elements, or Map to Equation). Choose what actually gets mapped to the section lines. In either case, you must select the domains or elements that you wish to map to the section lines. Restriction: Only available when Map to Sections is selected for Action. Choose what 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. Restriction: Only available when Line Difference is selected for Action.
   Followers	Follower nodes are not mapped to the sections, but follow the basic morphing of nodes that are mapped. Restriction: Only available when Map to Sections is selected for Action.
   Select: Domains	When mapping domains, select the domains you wish to move.
   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.
   Interpolation Shape	Choose the method by which a surface will be interpolated. Cylindrical Used for interpolations which run about an axis. Select an axis that runs through the center of your target nodes. Cylindrical About Nodes and Cylindrical About Line 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. Ellipsoid 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. Infer Plane 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 Used for roughly planar interpolations, but you may select the orientation of the planar "starting position." Spherical Used for interpolations which enclose a roughly spherical volume. Select a node in the center of your target nodes. Tube About Nodes and Tube About Line 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. Figure 4 shows 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. Figure 4. Figure 5 shows 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. Figure 5. Figure 6 and Figure 7 show a mesh created on a surface interpolated from a series of cross sections along a line using the cylindrical about line method (Figure 6) and the tube about line method (Figure 7). Notice the smooth transitions between the varying sections. Figure 6. Figure 7. Restriction: Only available when Interpolate Surface is selected for Action.
   Projection	Choose the direction of mapping. Along Vector Map nodes to the selected geometry in the direction specified by the vector. Normal to Elements Map 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 Elements (Smoothed) Map 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. Note: Available when mapping to a plane, surfaces, elements, or an equation. Normal to Elements (CFD Corners) Map 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. Normal to Geometry Map nodes to the selected geometry in a direction normal to the geometry (which could be a different direction for each node). In Figure 8 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. Figure 8. Restriction: Only available when the following actions are selected: Map to Lines Map to Node List Map to Plane Map to Elements Map to Equations Choose 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. Figure 9. About Axis Apply mapping 360 degrees around the model's center axis, effectively changing its radius to match the mapping. Recommended for nonlinear situations and cylindrical or sphere-like models, such as bulb-shaped housing. Figure 10. By Line Axis Establish a straight line running through each section line and project nodes to the section line normal to that line. By Line Normal Establish a plane for each section line and project nodes normal to the plane. Recommended method for section mapping. By Plane Establish a straight line running through each section line and find the vector which is normal to that vector which lies in the specified plane. Nodes are projected to each section line along that vector. 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. Recommended for section mapping where the section lines do not lie in similar planes and also cross each other. By Vector Project nodes to the section lines along the specified vector. Select the vector to lie in the plane of the mesh and normal to the section lines. Recommended for section mapping where the section lines do not lie in similar planes and run generally in the same direction. Kriging Use 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. Restriction: Only available when Map to Sections or Line Difference is selected for Action. 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. Restriction: Only available when Surface Difference is selected for Action.
   Mishandles	Choose between keeping the current number and arrangement of handles on the morph volume edges, or specifying a different number (up to 5 handles) for each morphed edge. Restriction: Only available when mapping by any direct method (Map to Lines, Map to Node List, Map to Plane, Map to Surfaces, Map to Elements, or Map to Equation) and Morph Volume Edges is selected for Map Entities.
   Covariance	Covariance is the local variations of the interpolation around the drift. The values h, h^2log(h), and h^3 give progressively more precise interpolations, while exp(-1/x) will give an approximate interpolation. Restriction: Only available when Interpolate Surface is selected for Action.
   Drift	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. Restriction: Only available when Interpolate Surface is selected for Action.
   Rotate Nodes	When mapping nodes from a straight line to a curve, select the Rotate Nodes check box if you wish the curvature of the new line to affect the whole mesh. Figure 11. Line Difference with Rotate Nodes Figure 12. Surface Difference with Rotate Nodes Restriction: Only available when Line Difference or Surface Difference is selected for Action.
   Blending	Select the type of blending that you want between the mapped sections and the fixed nodes. All Elements 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. Attached Elements 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. None Functions like having no fixed nodes except that you may fix nodes in the mapped region without any blending occurring. Figure 13. Restriction: Only available when Normal Offset is selected for Action.
   Offset Method	Absolute Distance Measure the offset from each node to the closest point on the target. Along Projection Direction Measure the offset from each node to the target along the direction of projection. In Figure 14, three nodes are being offset from a plane along a vector which is at a forty-five degree angle to the plane normal. When Absolute Distance 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 Along Projection Direction is selected, the offset is measured from each node to the plane along the projection vector. Notice that when using the Along Projection Direction option, the nodes can end up closer to the nearest point on the target than the value of the offset. Figure 14. Example: Offset in All Dir. and Offset in Proj. Restriction: Only available when the following actions are selected: Map to Lines Map to Node List Map to Plane Map to Surfaces
   Offset	Specify 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. Restriction: Only available when the following actions are selected: Map to Lines Map to Node List Map to Plane Map to Surfaces Map to Elements Map to Equation
   Constrain Nodes	Create a new morph constraint for the mapped nodes. The selected nodes will be constrained to the chosen entities during subsequent morphs.
   Moving Bias	Higher values result in nodes between the mapped nodes and fixed nodes following the mapped nodes more closely. Restriction: Only available when Line Difference or Surface Difference is selected for Action.
   Fixed Bias	Higher values result in nodes between the mapped nodes and fixed nodes staying closer to fixed nodes. Figure 15 shows the cyan and yellow components are mapped to the line, first with no fixed nodes, then with both the moving bias and fixed bias set to 1.0 and the magenta component fixed, then with both the moving bias and fixed bias set to 2.0 and the magenta component fixed. 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. Figure 15. Restriction: Only available when Line Difference or Surface Difference is selected for Action.
   Nugget	Nugget controls how close the interpolated surface will fit relative to the control points. If nugget is not selected or the value is set to zero, the interpolated surface will pass through all the control points. If nugget is selected and the value is not 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. Restriction: Only available when Interpolate Surface is selected for Action.

3. Click Map.