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* Manifolds.

Background.

TNT products and some other advanced commercial geospatial analysis systems are often referred to as 2.5 dimensional (2.5D).  The Z axis for features created, used, and visualized in these systems is measured in a vertical axis orthogonal to the 2D projection of these features onto a map plane.  Often this plane is defined at or referenced to mean sea level.  Generally, the available 3D data such as DEMs, bore hole profiles, seismic profiles, and 3D coordinates for maps fall into this category.  All these 2.5D systems store and use only minimal information about relationships that occur in the 3rd dimension.  For example, 3D topology is not maintained, in other words the topology is only 2D and refers only to the projected surface.  While vertical overlapping area features can be defined in a CAD or shape object, true 3D relationships (for example, caves, concavities, and the general idea of volumes) are lost in a polygonal topology vector or single raster object. 

The few 3D and 4D geospatial systems that do exist are specialized, expensive, and/or developmental in nature and focus on geologic, air-space and atmospheric, oceanic, and outer space related special applications.  Upon careful consideration you will find that geodata with Z coordinates that are not measured orthogonally from the projected map plane and/or preserve volumetric relationships is very hard to collect and, as a result, is very expensive and sparsely available.  Thus, it is natural that commercially oriented geospatial analysis systems focus upon the plentiful 2D geodata and on 2.5D when DEMs are available.  Desktop commercial geospatial analysis products, such as TNTmips and its competitors, are not viable unless they are based upon, and work with, widely available geodata.

Fortunately there are still many new and useful 2.5D applications of geospatial analysis similar to the introduction in RV7.0 of the use of manifold surfaces and stereo viewing.  Other recent MicroImages 2.5D introductions included the free TNTsim3D program for publishing your simulations and the continuing improvements for higher quality, faster 3D perspective viewing.  Future 2.5D opportunities might include editing 2.5D geodata in stereo; editing using several geolocked orthogonal views; or sketching in 2D, 3D, and or stereo views with the results simultaneously added to each. These past, present, and future developments can exploit the sources of Z-coordinate geodata just becoming widely available for use with your 2D geodata.  These include more widely available and accurate DEMs ranging from the global SRTMs to local laser-derived DEMs to collecting accurate elevations with a GPS unit.

Some applications of 2.5D geodata are obvious and are the basis for the myriad of  products that create a realistic 3D perspective view or real time simulation of a 3D surface.  These products strive for speed and realism in games and some use real geodata for applications like flight simulation or guiding the driver of a car.  However, in many site specific professional geospatial applications, the level of the integration of these 3D visualization subsystems into the total system is of even more importance than realism.  For example, can they use the same geodata layers and scripting tools?  Are the 2.5D capabilities and 3D capabilities tightly integrated with 2D capabilities for visualization, interpretation, and editing, such as in TNTmips and TNTedit?  Are high quality 3D and acceptable quality stereo created with or without a DEM to help visualize complex surfaces to create 2.5D geodata relationships, such as manifolds in 2D views?

Only now in wealthy nations are we getting into position with our data collection and analysis systems to keep our geodata systems updated rather than creating static, one-time geodata sets and their interpretations.  And this is generating a monstrous amount of digital data much of which may never be used.  Obviously these nations have a tremendous amount of effort at hand just organizing and using these 2D and 2.5D geodata. 

Recently a senior project manager for one of the largest intelligence and homeland security contractors to the U.S. government was overheard to say that it will take 25 to 50 years to actually integrate the local, state, and national geodata into a comprehensive and maintained 2.5D geospatial system.  It’s not just a technical issue—spend the money and get it done.  A myriad of local and other laws, institutional barriers, and political issues must be resolved.  Funding must be available, channeled to the working levels in local, state, and federal government, and standards truly adopted.  There will have to be unpopular sacrifices of and safeguards for personal freedoms within our basic democratic framework.  For example, even the limited amount of geospatial data available is already used to gerrymander election results. 

We have plenty of work cut out for us worldwide just coping with our 2.5D geospatial future. True 3D and 4D systems are truly long range goals that can be worked toward only if and when sources of appropriate 3D geodata become available.  The first step will be to move toward 3D geocentric and geodetic coordinate systems to properly record positions in a geodetic or geocentric system.

MicroImages and other developers are adding more of these 2.5D applications as demand, time, and most importantly the availability of 2.5D datasets allow.  However, as is characteristic of the MicroImages TNT products, working with new 2.5D applications as they are introduced will not require that you assemble the needed software from several pieces that are available only on a specific platform, OS, or use one graphics engine, such as DirectX or OpenGL.  As a result you will not become entangled in a variety of prices, release cycles, data formats, user interfaces, and so on. All those details end up controlling the ease of use and integration of your 2.5D geospatial applications. This may mean that other specialized products reach selected 2.5D goals faster in some cases, but a truly professional 2.5D geospatial analysis system requires careful integration.

Manifold Surfaces.

Definitions.

The word “manifold” has numerous and quite different meanings in English and in the Random House Unabridged Dictionary, for example, a manifold is a part of an automobile engine or a pipe network.  Alas, manifold is the word already accepted elsewhere in earth resources to refer to a curved surface in space.  It is this dictionary’s 12th definition that is most appropriate: “a topological space that is connected and locally Euclidean.”  Note that this definition says nothing about how the manifold surface will appear in space. 

This term can be extended to cover its use in the TNT products.  A TNT manifold object is a raster, vector, shape, or CAD object (internal or linked) that has been georeferenced in 3D to define its functional surface in 3D space.  Furthermore, its content must be appropriate to be viewed as a texture projected onto the TIN or manifold surface defined by these georeference points.  From this basic definition even more new terms have to be introduced and defined so that this new capability of the TNT products can be unambiguously explained here, and in future discussions of these types of TNT geodata and shapes.

Manifold Object.
A manifold object is a raster, vector, CAD, or shape object that has 3D georeferencing.  When a manifold object is selected in a 3D view, including in the Spatial Data Editor, a TIN will be formed from its 3D georeference points and the contents of the associated raster, vector, shape, or CAD object projected onto that surface as its texture.  Georeferencing is now both a 2D and a 3D process and is used to enter and edit the 3D control points needed to define a manifold object.  The GeoToolbox in Display and the Spatial Data Editor can directly create a vertical cross section manifold object.  Since a manifold object is georeferenced in 3D, it can be represented and visualized anywhere in a 3D space, and it may or may not intersect a terrain surface.  The surface of the manifold object can be planar, curved, or creased and folded.

Obviously the raster, vector, shape, and CAD objects can be combined or merged in various ways before the 3D georeferencing is added to them to define a single manifold object.  However, they can also be kept as separate manifold objects and projected and viewed in order onto the same manifold surface.  For this purpose the 3D georeferencing of a manifold object can be conveniently transferred from one raster object to another or between vector objects as long as they have matching extents, just as with the georeferencing of 2D objects.  For example, you create a raster manifold object, a matching vector overlay manifold object to delimit boundaries, and a CAD manifold object containing annotations.

Manifold Surface.
A manifold surface is the TIN surface formed in 3D space each time the manifold object is used in a 3D view.  The shape of this TIN remains the same for every new viewpoint of it.  Its shape can only be changed in the Georeference process using the new tools provided for this purpose.

Manifold Texture Object.
A manifold texture object, or a manifold texture, is the special name that refers to the raster, vector, shape, or CAD object with the 3D georeferencing needed to use it as a manifold object.  The texture object is projected (called draping) onto the manifold’s TIN surface every time the 3D view is created, refreshed, or the viewpoint is moved.

Manifold Layer.
A manifold layer refers to the current view of a manifold texture object draped onto the manifold surface in a 3D view.  The 3D view can have other manifold and topographic layers in it.

Terrain Surface.
You are already familiar with the use of a terrain surface, which is the TIN formed in a 3D view using one or more elevation rasters.  Depending upon which of the 3D models is used, the shape of this TIN can change slightly to refine it for each new viewpoint.

Topographic Texture Object.
You are already familiar with the use of a topographic texture object, or a topographic texture, which is the 2D raster, vector, shape, or CAD object you select for projection (called draping) onto the terrain surface every time the 3D view is created, refreshed, or the viewpoint is moved.

Topographic Layer.
A topographic layer refers to the current view of a topographic texture object draped onto a terrain surface in a 3D view.  The 3D view can have other manifold and topographic layers in it.

Sample Applications.

Most software products used to build and view manifold layers and other volumes from geodata and visualize them in 3D are highly specialized and expensive.  A popular current application is to use them to build the walls in a seismic/geology immersion room used in oil exploration and costing hundreds of thousands even up to a million dollars.  A picture taken inside one of these rooms can be found in the article entitled The End of Cheap Oil by Tim Appenzeller in the National Geographic Magazine of June 2004.  In these specially built facilities, something like a very early holodeck, experts manipulate seismic profiles projected onto all the walls of the room as manifold layers.  Now in RV7.0 you and your standard TNT products can begin to explore the possibility of using these kinds of 2.5D manifold layers in your applications. 

The uses of manifold layers range from simple graphical representations in publications to complex 3D visualizations.  Their use is common in geology; geophysics; mineral and petroleum exploration; mining; archaeology; monitoring groundwater pollution and other subsurface environmental properties; geotechnical, road building, and excavation engineering; and others.  To introduce you to the appearance of these layers in a 3D TNT view, several different kinds of manifold and associated topographic layers are illustrated in the accompanying color plate entitled Manifolds in 3D Views. 

Most of the geodata available to MicroImages and suitable for constructing manifold objects is geological in nature.  Crisscrossing or “egg crate” like intersecting subsurface profile manifold layers are common in geology and are called fence diagrams.  Geologic cross sections are available on printed geologic maps and in their digital equivalent.  Any cross section can be created from a geologic map by a trained geologist.  Seismic data is widely used but quite proprietary in nature.  As a result, the orientation of the rest of the color plates used to describe this manifold process in this MEMO use these kinds of data sets starting with the general illustrations in the accompanying color plate entitled Visualize 3D Geology Using Manifolds.  Another accompanying color plate entitled 3D Subsurface Model Using Manifolds illustrates the distribution of an ore body determined from drilling, mine shafts, and expert interpretation.  It is hoped that you can make the extrapolation from these examples to creating and using manifold objects from your geodata.

3D Visualization.

A raster, vector, shape, or CAD object with the necessary 3D georeferencing is a manifold object and can be selected for display in 3D as a manifold layer.  Since this uses the same TNT 3D visualization models as rendering topographic layers, multiple manifold and topographic layers can be rendered in the same 3D or stereo view.  This is a unique way of visualizing the relationships between topographic layers or other horizontal reference layers in proper geospatial relationship to manifold layers representing subsurface or above-surface profiles, transects, and layers with other content and orientations. 

Depending upon the viewpoint, adding several topographic and manifold layers means that they can obscure each other.  The ordering of their 3D rendering is back (farthest away) to front (nearest).  Transparency can be used to help you see the underlying layers in a rendering, but can create confusion over which layer is actually being viewed.  Faster reorientation of a composite 3D, better means of temporarily unmasking obscured layers, adding the use of manifold surfaces in TNTsim3D, and stereo viewing are all areas of future development needed to provide more means of visualizing the 3D relationships manifested in these potentially complex multilayer views.

As you begin to more fully understand this new capability, you will also find that even the 2.5D geodata needed for this application is not widely available.  However, it can be put together from various sources starting directly within the TNT products (for example, your geologic interpretations of 2D geodata such as bore hole profiles and geologic maps).  Unlike all the 2D geodata already available or that you assemble, subsurface, oceanographic, atmospheric, and other such specialized data can be hard to find, often incomplete, and recorded in unusual units (for example, seismic propagation times).  Getting these external 2.5D sets organized into TNT manifold objects will require effort and potentially the use of the TNT geospatial scripting language (SML) for data conversion, formation, and importing into a manifold texture object with its 3D georeferencing.

Create a Manifold Cross Section.

You can use a new tool option in the GeoToolbox in a 2D view to quickly and easily create a simple vertical manifold object.  This is illustrated in the accompanying color plate entitled Create Cross-Section Manifold Objects.  This procedure uses a 2D vector object overlaying an elevation raster object in a 2D view. You use the GeoToolbox to draw any kind of connected line representing the desired cross section on this view in 2D.  The line does not have to be straight, but must be continuous.  When you are finished drawing and editing the line, use the Generate Cross Section icon in the GeoToolbox window to create your new manifold object. 

This manifold texture object you are creating hangs down or projects vertically upward from the trace of the cross-section line on the terrain surface.  Thus you are prompted to enter the base level elevation of this vertical cross-section manifold texture object in the Cross Section Options window.  This elevation value is measured relative to the base elevation of the elevation raster object, typically mean sea level.  The value you enter will be used to position and create the edge of the manifold texture opposite the topographic profile formed by the trace of the cross-section line on the terrain surface.  Since you can enter any value for this elevation that is greater or less than that of the values in the elevation raster object, this manifold object can go up, down, or intersect the terrain surface. 

The polygon boundaries in this new manifold texture object are the map polygon boundary lines that the cross-section line intersects in the 2D view, projected vertically down or up to the horizontal edge you defined by the base-level elevation.  Wherever the cross section line intersects a 2D polygon edge, a vertical polygon boundary is created.  Thus, all the polygons in this manifold’s texture object have vertical edges that are parallel in 3D and intersect the cross-section edge at the same points as the 2D polygons.  These polygons in the manifold texture object are all automatically assigned the same styles and other attributes as their corresponding 2D polygons as they must match along their intersection of the 2D vector object and the manifold texture object.  The vector object created as the manifold texture object has polygonal topology.

The georeference control points created automatically for this manifold object define the TIN used to shape the manifold surface upon which the vector texture object is draped.  These control points define a vertical surface that starts at the terrain surface.  One set of points traces out a cross-section edge that conforms to the terrain surface.  These points vary in XYZ.  A corresponding set of paired points traces out the opposite edge as the vertical projection of these terrain surface points up or down to the plane of the elevation you entered.  These points all lie in the same X-Y plane and, thus, have the same Z value.  Since this manifold surface is vertical everywhere, no additional georeference points are needed to define its position in space, just these matching pairs of top and bottom points.

Editing a Cross Section Manifold.

The simple polygon shapes in the initial cross-section manifold texture object can be edited and shaped to meet the below/above ground conditions on this vertical manifold surface.  Load this manifold object in the Spatial Data Editor; it automatically displays in a 2D view and as a manifold layer for reference in a 3D view.  It will be stretched out and flattened in the 2D view by using the z coordinate on the y axis of the 2D view.  Proceed as usual to use the Spatial Data Editor to create the revised representation of the below ground polygons.  This editing to create a representation of this manifold texture object with the subsurface volume features is illustrated in the accompanying color plate entitled Edit Manifold Objects.

Any time you refresh your 2D edit view, you see how your current changes appear when projected as a texture onto the manifold surface in the 3D view.  As usual you can add any other manifold or topographic layers into this same 3D view for reference purposes.  For example, if you have already designed a manifold object that would intersect this new manifold object, you would want to view both layers in the 3D view.  If you are building a fence diagram, all polygons must match at the intersections of the manifold surface as illustrated in several color plates.  If you have a stereo viewing device set up on a second monitor, your 3D manifold layers and corresponding topographic layers can be rotated and viewed in stereo as you edit their polygon shapes in the 2D view.  

This cross section creation and editing procedure duplicates the way in which most vertical cross sections are created by drawing them.  It quickly provides an initial vector manifold texture object and its vertically-oriented manifold surface for your use as a starting point. It creates a basic manifold object as a starting canvas for your more complex 3D interpretations of a geologic, archaeological, geotechnical, or any other manifold layer.  For example, this replicates the way geologic sections are inferred and sketched and resketched by hand.  But instead of sketching them by hand, they are created as vector objects.  This provides that opportunity to view these scenarios and intermediate results in 3D as they are created.  This is especially important when multiple manifold layers are being created that will be interrelated in 3D.

Georeferencing a Manifold Surface.

Creating a complex manifold surface for a manifold texture uses a collection of XYZ points in a geospatial or a Cartesian coordinate reference system to define its surface.  These XYZ control points must be obtained by some method.  For example, they might represent the coordinates measured to various layers in a bore hole, from towed sensor arrays, or computed from transects.  These 3D control points become the vertices of the triangles that define the shape of a TIN onto which the manifold texture object is draped when viewed in 3D.  Using triangles to define a manifold surface could render a faceted surface.  However, modeling a surface in this manner is very common and used in many games, 3D viewers, and other 3D computer simulation products.  Whether or not the surface appears curved, folded, faceted, and so on depends upon factors such as the density of these points, the designation of edges as fold lines or some other special edge, distance to the triangle, surface texture projection and shading technique, and so on.  In RV7.0 these 3D georeference points and special triangle edge effects they define are added to a raster, vector, and/or CAD object to create a manifold object using a new procedure in the georeference process, which has been significantly expanded for this purpose. 

Choosing the new 3D Piecewise Affine model from the menu in the Georeference window permits you to enter XYZ coordinates for any position you select on the raster, vector, shape, or CAD object in the 2D view.  For example, suppose the raster object represents a single, flat vertical seismic slice.  To define this vertical plane, you will only need to select the position of 4 points near the corners of the raster and enter their XYZ coordinates in the control point table in the Georeference window.  Since these 4 points lie on a plane, the manifold surface will be defined by a TIN with 2 coplanar triangles.  If the 4 points are not coplanar, the TIN will have 2 triangles that are not coplanar and the common edge will be a fold edge in the manifold surface.  If you want the top of the manifold surface to conform to the terrain, then more control points are needed along the top.  If you want to curve the manifold, then you begin to enter XY values for points that do not define a plane.         

The accompanying color plate entitled Georeferencing Manifold Surfaces illustrates the positioning of these 3D georeference points and their tabular entries.  In this example, as is usually the case, the positions of known XYZ coordinates on the manifold texture object are not at the corners of the object.  If no georeference points are provided at the corners and along the edges, the TIN created would be smaller than the area of the manifold texture object.  The edge areas of the manifold texture object would have no manifold surface to project onto and would simply be clipped off and lost in a 3D view of this manifold object. 

To preserve all the surface area represented in a rectangular manifold object you may want to extrapolate from the measured and known georeference points to add additional control points at the corners of the manifold texture object.  This can be done automatically using a built-in procedure.  It extends the plane of the edge triangles defined by your georeference points.  It uses these planes to interpolate coordinates for the corners of the manifold texture object and adds them to the control point list.  This is also illustrated in the accompanying color plate entitled Georeferencing Manifold Surfaces.  Adding new control points adds new triangles around the edge of the TIN to increase its area.  However, these triangles are coplanar extensions of the edge triangles created by the 3D georeference points you entered.  You can edit the XYZ coordinates of these added control points in the table in the georeference window to modify the orientation of these added edge triangles.

Once you have entered four 3D georeference points for your manifold texture object, as near to the corners as possible, you can now open a 3D view in the Georeference process.  It will show you how your manifold surface or object is shaped and positioned in space from any viewpoint using a wireframe view of the current TIN or with the manifold texture object projected onto it.  Since this is a standard 3D view, any other manifold and topographic layers can be added to it for reference purposes.  Views with multiple manifold layers are common and are illustrated on the color plates.  You can then proceed using the 3D view as reference to edit the positions of the four 3D georeference points or add more, add 3D interior points to shape the manifold surface, extrapolate from the interior points to the corners, add exterior points to expand the surface, and edit the edges of the TIN using procedures discussed in the following section.

Editing a Manifold Surface.

Sparse Known Control.

The number of 3D georeference points you have to enter to define the manifold surface can be few in number; a minimum of 4 are required.  However, georeference points that are known in 3D position and can be located on the corresponding manifold texture object (the raster, vector, and/or CAD objects) are difficult and expensive to obtain for manifold objects extending above and below the earth’s terrain surface.  The new 3D Georeference process permits you to use your understanding of the shape of the manifold surface represented by the manifold texture object to add in additional XYZ control points.  These points can be used to modify the shape and edges of the TIN that will define the manifold surface.

Expanding the Control.

You can insert control points into the list of georeference points for the manifold surface without knowing their XYZ coordinates or locating their positions on the manifold texture layer. In positioning and editing these control points to improve the shape the surface you can use anything you have available:

  • the current 3D view of the manifold layer and various topographic layers, such as a drape of a surface geologic map, or natural color or enhanced image overlay, such as image ratios;

  • boreholes, radiosond or other atmospheric observations, towed sensor arrays;

  • all other available non-digital map, image, historical data, and lore about the area and its volumetric relationships; and

  • most importantly, your personal expertise and skills in 3D inference.

This new feature in the Georeference process also permits you to edit the triangles of the TIN formed from these control points to extend and shape the outer edge of the TIN to conform to the rectangular or irregular edge of the contents of the manifold texture object.

Matching Texture and Surface Objects.

The manifold texture object will be larger than the coordinate area covered by the TIN connecting the 3D control points unless there are points at each corner of the object. Conversely you may have a manifold texture object that has null area representing irregular edges and holes.  Holes present no problem as they automatically become transparent holes even though the manifold surface is defined for them.  Irregular or null edges can create irregularities when this manifold layer is viewed with a topographic layer and other manifold layers.  You may want to use a single manifold texture object that does not curve around in space but has definite folds.  You may want to add 3D points to your TIN to better shape it in 3D space and in the view.  These special considerations and conditions require that you edit the TIN you are creating in the georeference process.  You edit the TIN defining the manifold surface in a 2D view.  However you can monitor the results by opening a 3D view of the manifold object in the Georeference process.  If you have a stereo viewing device set up on a second monitor, your 3D manifold layer and its corresponding terrain surface can be rotated and viewed in stereo as you edit the shape of the manifold surface in the 2D view.

Available Tools.

Choosing the Georeference process opens the table for entering 3D coordinates and a 2D view of the current TIN and manifold texture object in flattened 2D form in the Object Georeferencing window.  Choosing the 3D Piecewise Affine model opens a new Piecewise Control window to provide tools to specify the special connectivity properties to use when the lines are generated in the TIN to connect all the control points.  This new window and its use and the effects of using these edit tools are all illustrated in the accompanying color plate entitled Editing Manifold Surface Triangulation. 

Adding Hard Edges.
You can use this tool to select any edge in the TIN and designate the connection between these two control points is to be a hard, or fold, edge.  This hard edge will be preserved through any activities applied to the TIN built from these control points.  Hard edges are drawn in the TIN in a different color to differentiate them from soft edges. 

Removing Hard Edges.
This tool is used to select a previously designated hard edge and remove this special connectivity property from the pair of control points.  Thus, the designation of this edge as hard is deleted and the points may be connected by a soft edge in the TIN.  

Remove Edges.
This tool selects an exterior triangle’s exterior edge, thus designating that 2 control points at its end should never be connected in the TIN.  This removes the area of this edge triangle from the TIN usually because it is null and not covered in the irregular area of the manifold texture object or because it obscures some other layers when viewed with this manifold layer.

Add Control Point.
This tool inserts a control point into or outside a triangle without requiring that its coordinates be manually entered.  If the position of the point is inside any triangle, its XYZ values are interpolated from the surface of that triangle.  It then becomes a valid control point and all the surrounding points connected to it with soft edges.  If the point is selected outside the area of any current triangle, its XYZ position is extrapolated by extending the plane of the nearest triangle.  New triangles are formed to redefine the edge.  In either case, once these points that have been inserted into the list and TIN by this tool, or any other, their XYZ values can be manually edited in this list in the Georeference window to move them from their initial interpolated/extrapolated positions.  In this manner, the added interpolated control points can be used to shape the interior of the TIN or the extrapolated edges.  When used together with the Remove Edges tool, you can shape the outer edge of the TIN to match the irregular edge of the manifold texture object or match a terrain layer.

Remove Triangles.
When a triangle is selected that has an outer edge not shared with any other triangle in the TIN, the outer edge is removed and its area is no longer included in the TIN.  While this tool has the same result as the Remove Edges tool, it is sometimes easier in a complex TIN to select a triangle using its interior rather than directly selecting its outer edge.

Extrapolate Boundary Control Points.
This tool insures that the TIN is a parallelogram onto which all the rectangular manifold texture layer can be projected.  This tool has been discussed above in the section on Georeferencing Manifold Surfaces as it is often used immediately in connection with entering the known 3D georeference points and viewing the initial manifold surface in a 3D view. Its use is illustrated in the accompanying color plate entitled Georeferencing Manifold Surfaces.

Recover Deleted Elements.
This icon will undo all previous control point editing back to the last save of the georeference object.  Using this tool with periodic saves will untangle your editing results when the triangulation gets too complicated.

As previously discussed above in more detail, all this edit activity with these tools is performed on the current representation of the TIN formed from all the current control points and their connectivity relationships.  However, while you appear to be adding and removing triangle edges, you are actually merely establishing new relationships between pairs of points in the 3D georeference subobject for the manifold texture object(s).

Create a Manifold Object Using a Script.

Both a manifold texture object and its manifold georeference subobject can be created using new classes and functions added for this purpose to the TNT geospatial scripting language (SML).  Using these tools, you can build a complete manifold object in geospace or in some arbitrary Cartesian coordinate space.  The manifold texture object can be imported or computed from equations using SML.  Similarly the control points to define a manifold shape can be imported or computed from equations  The simplest application would be to convert a large tabular collection of XYZ points, too numerous to enter by hand, into a large georeference table.  The introduction of these new classes and functions along with more suggestions for their uses occur in the section below entitled Geospatial Scripting Language (SML).

Backward Incompatibilities.

If any object is georeferenced with 3D points only in RV7.0 for use as a manifold object, that object and the Project File that contains it can not be used in any V6.9 or earlier TNT product.  The reasons for this are identical to those explained above in detail in the section entitled Coordinate Reference Systems / Backward Incompatibilities.  To avoid this limitation, it is suggested that any objects you intend to georeference in 3D for use as manifold objects be kept in a separate Project File if you are also still using V6.9 of your TNT product.

Cartoscripts.

MicroImages’ Reseller in Italy has made their collection of geologic line styling Cartoscripts available for you to download and use at www.spaziogis.it/index.php?
option=com_docman&Itemid=71.  While these represent lines accepted for use in Italian geologic maps, you can use them as starting points and modify the scripts for your own nation’s map conventions.

Georeferencing.

There have been major changes in this process and these are discussed in detail in the section above entitled Manifolds.  Some of these changes, such as the ability to name your control points, will effect you if if you are not using any manifold operations in this process.

Raster Resampling Using Georeference.

This interface has been redesigned to use a window with tabbed panels.  The Rasters tabbed panel shows the list of selected rasters along with properties, including dimensions, georeference extent, and Coordinate Reference System.  The Settings tabbed panel shows all available settings so there is no longer a need to browse each of the menus to see what the various options are set to.

When resampling to match a reference raster in cell size and orientation, the output raster cells will now exactly align with the reference raster cells regardless of the Extents setting.  This is useful when there is only a partial overlap with the designated reference raster.

When resampling to geographic (latitude-longitude) coordinates, the cell size is now specified in degrees/minutes/seconds.  As usual, values may be entered in decimal degrees, though they will be shown for the cells in degrees/minutes/seconds.

Options are now available for choosing the pyramid computation method.  Available choices are None, Average, Sample, and Automatic.  The default Automatic choice will use sampling when the resample method is nearest-neighbor and averaging when bilinear or cubic convolution is used.

The reference raster and related settings are automatically reset when a new set of input rasters is chosen.

A null mask subobject is no longer created for the output raster if the input raster does not have a null value defined and set.

Raster Mosaic.

The TNT products are superior to any other in displaying and managing massive images.  Integrating all the pieces of your images (for example, DOQQs or orthoimages) into a single, large layer can be very convenient for your further analysis, for use in a TNTatlas, TNTsim3D, TNTserver, and so on.  This is even the best procedure if your ultimate objective is to break up the image into new, smaller geographic units after your analysis.  A common example is to assemble orthoimages into a single, large image with a common coordinate system, work with this mosaic, and then divide it into new pieces and the map projection required in some other system.

Your use of the mosaic process to create these massive but convenient images has been discussed briefly in the Editorial section above.  Additional detailed information about the creation of compressed massive images was discussed in detail in the MEMO entitled Release of RV6.9 of the TNT products and dated 31 December 2003 in the section entitled JPEG2000 Compression.  RV7.0 of the mosaic process has no dramatic change in its interface or many features.  However, considerable attention has been addressed to increasing its robustness and optimizing its performance for these large tasks.

Null Mask.

Mosaic now automatically generates a null mask layer and its pyramids to define non-data areas and null cells in the output raster.  It, and any other process that displays this output raster, will automatically use this null mask as will other processes converted to do so.  This also significantly improves the mosaic’s handling of input rasters that have no null value or different null values.

First Raster Overlap.

An overlap mode of First Raster has been added whereby cells from the first raster in the list covering each output cell will be used.  The mode of Last Raster was available in RV6.9 and earlier, but now you do not need to reorder your selections to use the first raster.

* Output to JPEG2000.

RV6.9 of the TNT products required that you mosaic your raster and then use the Extract process to apply JPEG2000 compression to it.  The mosaic process in RV7.0 permits you to apply lossless or lossy JPEG2000 compression to your mosaicked output raster object.  The many objects you select for input to mosaic can be any of a mixture of uncompressed or objects compressed with JPEG, JPEG2000, or in any mixed coordinate reference system (CRS).  Note that DPCM, or Differential Pulse Code Modulation, is now called Standard Lossless compression in TNT dialogs.  Also selected and mixed in can be linked external rasters with or without compression such as GeoTIFFs, MrSID, ECW, TIFF, and others as long as they are georeferenced and their CRS identified internally or via an auxiliary file.  To permit this flexibility, the Mosaic process still requires that it be provided with adequate drive space to create the entire mosaicked raster object in its final uncompressed and also compressed form if compression is specified.  Also, as discussed earlier in this MEMO, using tiles during the compression procedure to avoid creating temporary storage for the full uncompressed raster then compressing it, can have detrimental effects at the tile edges and legal ramifications.  The accompanying color plate entitled Mosaic Directly into JPEG2000 provides sample results from mosaicking 100 GeoTIFF images directly into a single JPEG2000 raster object.

Temporary Storage Requirements.

In RV7.0 each input raster object is uncompressed as needed and resampled into this large raster object using your desired CRS, sampling method, overlap method, and so on.  The size of this uncompressed temporary mosaic can be closely estimated in advance from the extents of your input objects, compressed or not, and your setting for the mosaicking process.  However, if you are requesting that your mosaic produce a compressed output raster object (for example, a lossless JPEG2000 result), this temporary raster must coexist in your storage system at the same time as the uncompressed result.  However, the exact size of a compressed raster may not be accurately estimated.  It can be closely estimated for a JPEG2000 compression (for example a request of 10:1 lossy compression). However, the size of a mosaic object using JPEG compression or JPEG2000 Best Quality is not so easy (for example, a request for a 75% JPEG lossy result).  If you target a compressed raster output, then at the onset the mosaic process will liberally estimate this additional storage requirement and warn you if the temporary and total drive space available would likely be insufficient to complete the final compressed or uncompressed mosaicked object.

Sample Applications.

The following kinds of test applications have been used to challenge and confirm the robustness of the Mosaic process especially for producing a JPEG2000 compressed raster object.

Lossy JPEGs into Lossless JPEG2000.

Lossy compression should never be applied to images to save storage space when those images will be used for some form of computer image analysis.  However, using lossless JPEG2000 or standard lossless compression (formerly called DPCM) can be specified for a mosaic result intended for additional analysis.  Keep in mind that Mosaicking images, depending upon your settings, may alter them by resampling, by feathering the edges, and so on.  However, many orthoimages, especially those collected by digital cameras from the air, are being distributed as JPEGs or as lossy compressed TIFFs.  To avoid excessive additional changes in these already lossy compressed images, you might want to link to and select them as input for your mosaic and choose lossless JPEG2000 as the compression method for your mosaicked raster object. 

Over 6000 units of color Digital Ortho Quarter Quads (DOQQs of 3.75' by 3.75' ground areas) are available from the site of the Nebraska Department of Natural Resources.  http://www.dnr.state.ne.us/databank/fsa03.html.  These DOQQs were acquired using an airborne digital imaging system and are in 24-bit color with 1-meter resolution.  They are provided for downloading in both UTM and Nebraska State Plane CRSs using JPEG compression.  Remember, JPEG is always lossy compression!  Although the JPEG compression is about 20 to 1, no JPEG artifacts are evident and image quality color balance between units is good.  These JPEG DOQQs (*.jpg) files are each provided with a georeference via a companion world file (*.jgw) file of the same name.  It is a simple matter to select hundreds of them in mosaic, which will autolink to them.  Mosaic can then assemble them into a single JPEG2000 lossless output raster object representing a county or some other project unit.  Since the input objects were heavily compressed JPEG files, the lossless JPEG2000 mosaic is also of a significantly reduced size.  A future development in mosaic would be to permit it to use a region defining the irregular boundary of a county or project to control the portion of the input objects to mosaic and even to automatically select the objects needed from a common directory(s).

Lossy MrSID into Lossy JPEG2000.

Landsat 24-bit color orthoimages of 15-meter resolution can be downloaded for almost all the earth except for the poles for circa 1990 and circa 2000.  These NASA sponsored orthoimages are in 6 by 6 degree units and are compressed about 30 to 1 into MrSID files.  These MrSID images (*.sid) can be downloaded with their georeference provided in a companion world file (*.sdw).  Mosaic can then link to these files and convert them into a single province- or country-covering raster object and apply lossy or lossless JPEG2000 compression.  Now you can prepare and substitute a 15-meter color image coverage of your nation in place of the 1-kilometer MODIS images distributed with RV6.9 on the Global Reference Geodata DVD.  Using reasonable compression for your JPEG2000 results will permit you to use these large coverage images in your projects including their free distribution with TNTatlas, TNTsim3D, and via TNTserver.   

Predefined Raster Combinations.

Statistics for corresponding cells in a set of rasters can be computed using the Statistics operation under the Algebraic combination category.  This procedure computes two output raster objects, one containing the cell-by-cell mean and the other the cell-by-cell standard deviation for the selected input raster objects.  This operation might be used, for example, to compute cell-by-cell statistics for a time-series of vegetation index rasters (or rasters containing any other measured or computed numerical value).

An Exclusive Union (XOR) logical operation can be performed on a set of binary raster objects.  Like the previously-available logical AND and logical OR operations, the XOR operation produces a binary raster object.  When performed on a pair of input rasters, XOR produces a cell value of 1 if either input has value 1, but not both.  Thus the result is 1 if the two corresponding input cells have different values (0 and 1) but 0 if the two input cells have the same value (1 and 1 or 0 and 0).  When you select more than two input objects, the operation is performed sequentially: input 1 XOR input 2, result 1 XOR input 3, result 2 XOR input 4, and so on.  In general, the cell result will be 1 where the number of input 1's is odd and 0 where the number of input 1's is even.

Raster to Vector Boundary.

This process will now warn you if you are requesting it to convert a highly variable input raster into a vector object.  Since this is a somewhat qualitative appraisal by the program, you can override this warning and attempt to proceed.

Converting a raster object to a vector object is generally applied to categorical or theme rasters or to the results of automated image processing which categorizes the image into a few classes grouped into clusters of cells of equal value.  It is not usually meaningful or useful to convert a highly variable raster object such as an unprocessed image to a vector object.  Representing a cell as a vector polygon with topology will inflate the storage for that cell by about 100 times.  This is not due to the vertices for the polygon but the overhead associated with the definition of a polygon.  This overhead is not increased appreciably when the polygon bounds a meaningful area of uniform cells, but is prohibitive when each cell or a small number of cells make up each polygon.  It is also very time-consuming to make this large number of conversions.  Thus, this inappropriate kind of conversion will either take so much time to complete that you would conclude that it was not working or produce a huge object.  Another result would be that it would run out of storage space since the storage can not be estimated before the vector object is complete—it could easily grow to 100 times the count of the cells in an image.

Import/Export.

Vector Import.

CARIS ASCII graphical data files can now imported.  CARIS is a vendor of GIS-oriented products focused upon hydrographic and coastal applications.

MapInfo MIF files now import with improved support for text fonts, color, and styles.

Vector Export.

Geography Markup Language (GML) files conforming to version 2.x can be exported from vector or CAD objects.  GML (*.gml) is the OpenGIS’s XML encoding for the transport and storage of geographic information, including both the geometry and properties of geographic features.  Specifications for GML can be found at www.opengis.org/ specs/?page=specs.

ESRI shapefile export can now export vector or CAD label elements as shapefile point elements with the label string as the database record entry for the point.

Raster Import / Linking.

ESRI ArcGrid files can now be imported in all forms including even when they are compressed.

Images in the Robinson projection can now be imported from the ArcGrid format.

PNG (*.png) import will now recognize the ICM color profile tag in the PNG file and import the ICM color profile as a subobject of the raster object.  If the ICM color profile does not exist but the gamma and chromaticity values do, then an ICM color profile object is created under the raster to contain the gamma and chromaticity values.

MrSID files (*.sid) can now be imported or autolinked on Mac OS X, Windows, and Linux/UNIX.  In V6.9 this capability could be used only on Windows-based platforms.   

TIFF import and auto-link  will now convert the metadata in the TIFF directory to a metadata subobject in the Project File.

Sun Raster (*.ras) import will look for the companion world file (*.snw) of the same name and transfer its georeference into the corresponding raster object.

Raster Export.

When export georeference to “descriptive text” all Coordinate Reference System (CRS) details are included.

PNG export process now exports the opacity mask for the file as the alpha channel.  The export will also export the ICM color profile if one exists under the raster object.

TIFF export now optionally provides “pack bits” compression for 8-bit rasters and uses it by default  instead of LZW compression.

GeoTIFF export now optionally creates a conamed companion world file (*.tfw) containing its georeference data.  Some other products read a GeoTIFF as a TIFF and expect the georeference information to be available in this world file.  The scale factor for the Lambert Conformal Conic projection is now also included in the GeoTIFF.

Font Management.

Previous issues of this MEMO have discussed in detail the issues of font management that plague this industry due to font copyrights, varied font rendering methods, and other similar issues some of which must date all the way back to Gutenberg.  Your problems arise when you move projects and results between various computers and are even more likely when the move is between platforms with different operating systems.  This even occurs when your cross platform activities (for example, Windows to Mac) are totally within the TNT products.  The new location or operating system may not have the same fonts available and you may have used one that can not be moved due to a copyright, can not be rendered well on the device (paper versus monitor), and so on.  At that point the software at the destination has no choice but to make font substitutions with or without your input.

Font substitution is likely to occur in published results such as the TNTatlas, SVG layouts, and PDF documents that can be designed to run across all platforms.  To minimize the impact of this, MicroImages has continued to improve how font substitutions are made within the TNT products and your project results.  Two forms of font substitution are now used in RV7.0: “considerate automated substitution” or in the order of your preprogrammed list of “designer specified substitution.”

Considerate Automatic Substitution.

TNT font substitution is automatically used when you have specified only one font and it is not available.  It is “considerate” because it does not make arbitrary substitution, which is common, but matches up fonts that have similar appearance, for example sans serif fonts are replaced by other public domain sans serif fonts.  These TNT substitutions are preprogrammed for various font styles.  The substitutions are listed in a table on the accompanying color plate entitled Font Substitution in the TNT Products.

Designer Font Substitution.

When you choose a font name or family during the design of your project, you are attaching that font name to that text string (for example, {~FArial-Bold.ttf}), which would render the character string with this format code in Arial Bold.  However, you can define your preferred substitution using the form {~Farialbd.ttf,Helvetica.dfont;2,Arial-Bold.ttf}.  This will be interpreted by TNT processes to mean use the Microsoft version of Arial bold if it is available, if not try for Helvetica, then try for the Sun version of Arial bold.  If none of these fonts can be found, then automated substitutions will be made.  The superior results of using designer or considerate automatic font substitution for a DataTip created with Arial fonts in Windows and then moved to a Mac to find and use Helvetica is illustrated in the accompanying color plate entitled Font Substitution in the TNT Products.

Map Calculator.

The map calculator use and operation remains about the same as RV6.9.  However, it now takes complete advantage of the new Coordinate Reference System (CRS) introduced in RV7.0.  See the above major section entitled New Coordinate Reference System for details on these many new, possible conversions.

* Advanced Geometric Object Conversion.

Diverging Objectives.

CAD software has a very large user base; why doesn’t this software dominate the GIS application area?  Vector topology provides the basis for many useful area oriented operations; why is it not maintained in GIS systems?  Geo-oriented games have the largest installed user base of all and have their own graphical storage structures.  IT managers are in charge in large, centralized enterprises that build their business infrastructure on databases software including any geographical data.  Web servers have their own preferred graphics formats, which they try to adapt to fit their geographic requirements.

All of these important spatial endeavors are built up on graphical data structures.  However, all these various structures are quite different since their primary application, while it may be spatial in nature, is quite different.  All of you have experienced this in attempting to convert CAD data to GIS data and vice versa in some software package.  It can be done, but the results can be unusable.  Converting a CAD drawing with many blocks and individual lines with their own part description into a vector object can produce a very bloated vector object with complex topology.  Converting a vector object to a CAD object can also produce complex results as everything can be in pieces and no concept of organized subparts, such as blocks, will be represented. In fact, shape type data storage structures evolved into existence to better fill the gulf in the middle of the CAD, vector, and database structures.

Resulting Complications.

Alas, if you are truly engaged in geospatial analysis, not just isolated in GIS, engineering, database management, … you will quickly learn the value of these different structures.  You also quickly learn that the geospatial analyst has to deal with each and all of them with facility.  A typical simple urban project will have property information in CAD form, ownership records in some database structure, historical data such as deeds in paper form or as scanned PDFs; requirements to upgrade it all with MrSID, JP2, or JPEG images; images of buildings in JPEG; a desire to go online to serve its internal needs (intranet) or public access (Internet); and so on.  And this simple problem is repeated over and over worldwide with varying degrees of existing data preparation and quality.  Major nations do not even have a documented cadastre or records of where things are on or in the ground.  These kinds of issues get much more complicated when the source materials that do exist are not only in these different formats, which are “optimal” for their current use, but also jealously guarded in that format for compartmentalized business or military turf or other compartmentalized reasons.

Integrating Disparate Strategies.

All of this is already clear to many of you who, by buying your TNTmips, understood the need to deal with using each of these project components in its optimal form.  You also realize that at some point in a geospatial analysis process, you will need to move geodata between these formats with as much facility as possible or use them together such as in a TNTatlas.  Perhaps this is merely a requirement to link to that data structure and add it as a display layer.  Perhaps you need to edit that data structure.  Eventually you will need to move from one structure to another.

As an encompassing geospatial system, not a GIS, CAD, database … system, TNTmips and its associated products are focused upon meeting all these diverse requirements.  RV7.0 makes significant gains in improving the integrated use of these common, but marketed different data structures that you will encounter and use.  This is an evolutionary process and never will be truly easy.  Gradually TNTmips is supporting the direct use of these data structures as layers, without import, directly from their various native formats.  Shapefiles can now be used in this manner.  JPEG and PNG rasters have also been added to this list.

Geometric Conversion Engine. 

Improved Integration.

RV7.0 introduces into several key processes a new Geometric Conversion Engine, which consolidates the fragmented code used in the processes to convert between vector, shape, CAD, TIN, and region data structures.  This immediately made it possible to create and plan for many new features in those TNT processes that previously only extracted and/or copied geodata within a specific object type.  Using this new engine, Copy and Paste and the processes to Extract and Merge can now automatically convert data between these geometric data types (for example, CAD to vector).  This powerful new engine also incorporates all the “transparency” properties you expect in a TNT process.  For example, the Coordinate Reference System (for example, projection) of the source data (which means, the copied area) may be different from that of the destination (which means, the paste layer) and will be converted as it is inserted.

Expanded Capabilities.

In these reincarnated processes, you can use any of the TNT selection procedures to determine what source elements to use in the conversion process.  This inherent TNT capability also takes advantage of the new and greatly expanded Coordinate Reference System released in RV7.0 and discussed elsewhere in this MEMO.  You can now also elect to use a complex region boundary to define the area to be converted in these processes in addition to how the edge effects should be handled (which means, partially inside, completely inside, …).  And bigger objects being converted to vector form use the faster and more powerful validation engine and its new abilities to resolve conflation problems when the source and destination objects have many complex overlapping features as discussed in detail elsewhere in this MEMO.  With these powerful new capabilities now in place in RV7.0, you can expect more capabilities along these lines to appear in the TNT products to further define what a geospatial analysis system should be capable of.  The current new conversion capabilities are summarized in the following subsections and a sample is illustrated in the accompanying color plate entitled Geometric Object Conversion.

Faster Operation.

Merge, Combine, Extract, and copy/paste operations to a vector object is now faster due to improvements in the topological validation step.  While this step is faster in RV7.0 its result is greatly improved as it is checking for and resolving conflation problems in the output vector object.

* Geometric Object Conversions.

Using the new integrated common code Geometric Conversion Engine “Vector to CAD,” “CAD to Vector,” “Region to Vector,” and “TIN to Vector” processes have been replaced by a new set of processes called “Geometric to Vector,” “Geometric to CAD,” and “Geometric to Region.”  The term “Geometric” refers to any spatial object that is not a raster, raster set, or hyperspectral object.  The current geometric set includes vector, CAD, TIN, shape, and region objects.  Therefore, the new “Geometric to Vector” process will allow selection of CAD, TIN, shape, and region objects to convert to vector objects.  “Geometric to CAD” will allow the selection of the vector, TIN, shape, and region objects to convert to CAD objects.  “Geometric to Region” will allow the selection of vector, CAD, and shape objects to convert to region objects.  All of the “Geometric to…” processes now support selection of multiple files.

The Geometric Conversion Engine that is used in the conversion processes can accept subsets of the source objects using the options “By Script,” “By Attribute,” and “By Element” to generate which elements to convert.  “By Script” is used to select elements via query, “By Attribute” is selecting elements via record attachment, and “By Element” uses the elements selected via the user interface.  These all work in conjunction with the region selection capability.  For example, you can choose a CAD object, select some of its elements via a script and limit the area using a region to convert or merge to a vector object.

In the Geometric to CAD process if a vector object is selected, a line is created in the destination CAD object if the vector line has an attachment to a record in a user defined table, even if the vector line is part of a polygon that was transferred to the CAD object as well.

* Merging Objects.

Process / CAD / Merge… and Process / Vector / Merge… now allow selection of other geometric objects to be merged into the destination vector or CAD object.  These geometric objects include vector, CAD, TIN, shape, and region objects.

The Geometric Conversion Engine that is used in the Merge processes can accept subsets of the source objects using the options “By Script,” “By Attribute,” and “By Element” to generate which elements to convert.  “By Script” is used to select elements via query, “By Attribute” is selecting elements via record attachment, and “By Element” uses the elements selected via the user interface.  These all work in conjunction with the region selection capability.  For example, you can select a CAD object, select some of its elements via a script and limit the area using a region to convert or merge to a vector object.

The vector Merge process now allows the selection of the topology type (polygonal, planar, and network) for the resulting vector object or the merge process will automatically determine the best topology level given the source objects.

* Vector and CAD Extraction.

These Extract processes are now integrated into the Geometric Object Conversion process discussed above.  They can still be accessed on the menu under this older entry to avoid confusion.

CAD Object Warping.

CAD object warping now supports densification of the elements.

Spatial Data Editor.

* Copy.

The Copy / Paste operation now has significantly expanded capabilities using the new Geometric Object Conversion engine discussed above.  You can now copy from a vector, CAD, TIN, region, or linked shape object (which means, shapefile) including linked objects.  During the copy operation, you can select the irregular area to copy from any using a region object.  This copy area selected from a vector, linked shape, CAD, or TIN layer can be optionally controlled as appropriate to the source object type to be Partially Inside, Completely Inside, Clip Inside, Partially Outside, Completely Outside, and Clip Outside the source object.  An example of the application of this feature is illustrated in the accompanying color plate entitled Copy/Paste between Geometric Objects.

* Paste.

Regardless of the type of geometric object selected for the copy operation, the subarea can be pasted into a CAD object or into a vector object and their relational database structures will be reconciled.  The topology will also be validated if the target is a vector object.  Future capabilities will permit other geometric objects as the generic paste destination (for example, a shape object).  This strategy is another big step forward in permitting your TNT application to understand, interchange, integrate, and take advantage of the unique and useful properties of each of these widely, but usually separately used geometric data structures.

Toggle Through Mixed Elements.

Right Mouse Button operations will now allow you to toggle through nearby elements (not just vector element types as in previous TNTedit versions) for vector and CAD editable objects.  For example, two or three vector labels lie on top of each other as a result of label auto generation.  Pressing the right mouse button will select one of the labels, then pressing the tab key will toggle through the other labels and any lines, polygons, nodes, and points that are nearby, allowing the selection of the label you want to move.  For CAD elements, holding the right mouse button and pressing the tab key will toggle through all of the CAD elements it found within its search distance allowing you to edit elements that are hard to select.  These time saving actions are illustrated in the accompanying color plate entitled Step through Elements with Tab Key.

Manifolds.

Creation and / or editing of a spatial object with a manifold georeference is now supported.  When opening a reference or editable spatial object with a manifold georeference, the editor will generate a set of dialogs for a separate 3D view.  This 3D view will contain a layer referring to the manifold georeferenced object in the Editor’s View window.  Any other reference layers can be viewed in the 3D view window.  Creating a new object over the reference manifold georeference object will copy the manifold georeference to the new object.  All reference and editable layers in the Editor’s View window must have the equivalent manifold georeference.  When all of the layers that have a manifold georeference are removed from the edit view, the associated dialogs are closed.

Undo.

Changes made in the Numeric Edit tool can now be reversed using the “Undo” button.


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