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Maps Module Overview ​ Channel maps are spectroscopic images, where the image contains only emission from a certain small range of wavelength or line-of-sight velocity. They are typical for spectroscopic radio observations, but have come into more frequent use also in the optical and infrared spectral ranges. Usually they are presented in an array of many channel maps representing the complete spectral range that has been observed. The full set of spectral data is often referred to as a data cube, since the image can be arranged as slices of a cube. The Maps Module is divided in three main sections. The dominant region is the display of the channel maps. Above the maps is the main menu and to the right are the parameter tabs. There are three tabs for General parameters, those for an individual selected Channel and for the Output of the channel images (maps). General Workflow: In the General Parameters tab the minimum (initial) and maximum (final) velocities are applied. These are then divided in a number of channels that is the product of the number of channels in rows and columns. To set up this grid of channel maps click on the "Re-grid" button in the main menu and confirm. This generates the grid of image windows. Now render by clicking on the Render Button in the Render Module or press Ctrl-S. Parameter Panels: General: Render: This flag controls whether the channel maps are rendered at all. Make sure to have the tick mark set when using the Map Module. ​ Initial vel: The smallest velocity to be included (can be negative). This is the center velocity of the first channel map (top left in the grid). Final vel: The highest velocity to be included. This is the center velocity of the last channel map (bottom right in the grid). ​ Delta (D) : This is the width of the velocity channels. If set to zero, then the width is calculated from the difference between the final and initial velocity divided by the number of channels. If set manually, then the channels may be narrower than that or wider, in which case they overlap. The intensity taken into account is constant over the interval, which may or may no be the case for the actual observations. ​ Rows & Columns: The number of rows and columns that the channel map grid shall have. The total number of channels is then the product of rows and columns. ​ Transparency: The transparency of the rendered foreground image. It can be changed with the slider to transition between rendered and observed background image. This helps to compare the model with observations. ​ Light Echo: This function is deprecated. ​ Difference: Show the difference image subtracting the observed image from the rendered model image. ​ Export: Export the rendered image in ASCII format for further external processing. ​ Channel: ​ Select a particular channel by clicking on the image in the grid view of the channel maps. The selected channel is highlighted by a thin red line. The Channel parameter panel on the right then displays the settings of that particular channel. To view the image of this channel by itself at a larger scale, click on the "Expand" icon in the main menu of the Map Module. Vel (km/s): The velocity center of this channel. ​ D vel (km/s): The full width of the velocity channel. Image: A reference or observed image can be loaded to be compared with the observation. One can transition between the rendered model and the reference image by changing the Transparency in a numerical way (see below) or using the Transparency slider in the General parameter panel (see above). The reference image can be placed and processed using similar attributes as those used in the Selected Window section of the Render Module. Please see the pages on "Data Preparation " and the Render Module for more details on how to use the Location parameters and the image Modifiers. ​ Output: ​ The output parameters control the appearance and labeling of the grid image output using the Save Grid or Save Images button in the Main Menu of the Map Module. An example grid output is shown on the right. CrossHairs: Mark the center of each channel with a cross. ​ Labels: Label each channel with its central velocity. Color: The color for the labels. Change the color by clicking on the colored squared. A dialog opens to let you select a different color. Menu bar: ​ Re-grid: After you adjusted the General Parameters for the grid of channel maps, the Re-grid button sets up the grid using these parameters. When you change the General Parameters use this button again to apply these parameters. ​ Insert: Individual channels can be inserted before the currently selected channel. Note that this channel does not change the parameters of the pre-existing channel and is therefore not part of the regular sequence that was established using the Re-grid button. This new channel needs to be set up individually in the Channel parameter panel. Delete: Delete the currently selected channel. ​ Save grid & Save images: save the grid of image or individual channel images. Se the section on Output above for details. ​ Palette: Opens the image adjustment dialog for the channel maps. Here you can adjust brightness, scaling, and add other image modifiers. Note that the Gaussian Blur modifier handles the resolution of the maps. This is currently disconnected from the Seeing parameter in the Render Module and needs to be adjusted separately. In the Maps Module it works in terms of pixels, so it is depends on the resolution. This feature will be improved in a future release. ​ Properties: Opens the Properties dialog for the detailed appearance of the grid coordinates, tick marks, fonts and colors. Load obs: Load observed or reference images to the background of the grid. Here you can load a sequence of multiple images to fill all the channels. Select multiple image in the directory dialog that opens by clicking on the first of the sequence and then Shift-click on the last. Reference images for individual channels can be loaded or changed with the corresponding Image load button in the Channel properties panel. ​ Expand: Expands the selected individual channel image to full size of the image grid area for a detailed view. Clicking the same button again restores the full grid. ​ ​

Top of Page Basic Workflow Overview 3-D view ports Menu Bar Primitives Objects, Tools & Lights tabs Transform tools 3-D Module Basic Workflow Basic workflow: Interactively add the geometric elements of your object in the form of primitive polygon meshes (Primitives) that you can access at the top menu bar of the 3-D Module. These meshes will serve to encase the volumes that will constitute the different parts of the model. Then you modify the simple structure of the Primitives using what we call Modifiers, which give the objects new geometric structure and physical properties as a function of position in space. Using the Physics Module, you then assign the material and radiation properties to the meshes. Finally, the model is rendered with the Render Module and some of the observational properties can be displayed with the (Channel) Maps and Graph Modules, where the observational data can be included and compared with the model results. If the results are not satisfactory, the model will be adjusted until a satisfactory match is found between observations and model. Overview of the 3D Module : The purpose of the 3D Module is to set up your model interactively. This module is divided in several sections, the interactive 3-D view ports , the Menu Bar at the top, Objects, Tools & Lights tabs on the right and Transform Tools on the left. ​ 3-D view ports: By default there are four view ports that can simultaneously show you the same number of different views of your mesh model. Several of these camera views are aligned with the coordinate axes (initial defaults: Front, Right). The Free-Form view can be changed arbitrarily using mouse input after selecting the Camera > Orbit tool from the Transform Tools to the left of the 3-D view ports (see Transform Tools for details). A special view port is the Render view, since it represents the view that will be used for rendering in the Render Module. This view can be controlled interactively with the Mouse in the same way as the Free-Form view, but also numerically with Image and Camera parameters in the Render Module. ​ Right-click menu: When you right-click on the area of a 3-D viewport, a menu opens that allows you to set a number of properties of this particular view. Camera: Select a different camera view for this viewport. Save Image: Save the mesh images of the viewports. It saves the image of all viewports in one image. If you want to save only a single view, then use the Maximize command from the right-click menu to open a single view in the 3-D view space (to go back to the four viewports, right-click again and select Restore). Make sure to provide a filename with a valid image extension. Most common image formats are supported, such as .png (recommended), .jpg, .gif, etc. (example: image1.png). The Save Image function is the same as that of the Save button in the 3-D Module´s top menu bar. Saving your viewport images with this function does not include the colored coordinate axes or the viewport labels. To saves these you can make screenshots of these areas. Properties: In this dialog you can set a few parameters for the individual view port. Scene alpha: This parameter changes the transparency of the whole polygon object scene, so a comparison with observations or the rendered scene may be easier with lower alpha values. Background: This setting selects the background image of the scene between None, Observed and Rendered, which enables you to compared the corresponding images with the mesh. Including the Observed data is useful to place and shape mesh objects according to the observations. Note that a direct comparison with observed data makes only sense for the Render image. Sometimes, comparing the observed images with other views might be helpful when checking for symmetry properties. Maximize: For more detailed inspection, this command fills the space of the four viewports with a single one. Restore the four views using the Restore command in the right-click menu. 3-D view ports Overview Menu Bar Menu bar: The Menu Bar of the 3-D Module provides quick access to a number of commands (left section) and the creation of Primitive mesh objects (right section). ​ ​ ​ Save: Save the mesh images of the viewports. It saves the image of all viewports in one image. If you want to save only a single view, then use the Maximize command from the right-click menu to open a single view in the 3-D view space (to go back to the four viewports, right-click again and select Restore). Make sure to provide a filename with a valid image extension. Most common image formats are supported, such as .png (recommended), .jpg, .gif, etc. (example: image1.png). Saving your viewport images with this function does not include the colored coordinate axes or the viewport labels. To saves these you can make screenshots of these areas. Import: This command allows you to import objects from a different project. A file selection dialog opens to select the project from which to import objects. Then a second dialog allows your to select one or more objects (shift-click for selecting multiple objects). Note that it is divided into tabs for different types of objects which have to be imported separately. Options: The Options dialog contains settings for viewing coordinate grids in the 3-D viewports and other options that might be helpful during modeling and for publication of model meshes. Undo: This command opens the Undo Stack utility. It shows recent commands that can be undone and redone. You can select which commands to undo or redo and set the maximum number of commands to be held in the stacks. Additional Undo options exist for example for the Path vertex objects which can be undone with Ctrl-z or redone with Ctrl-y. Primitives: The most important functionality of the menu bar in the 3-D Module is to provide quick access to the creation of various Primitives, i.e. basic geometric mesh objects that can be described with only a few parameters. ​ ​ ​ ​ Create a new primitive object by a first click on the corresponding icon, then click on one of the 3-D viewports and immediate drag the mouse to the right to increase the first parameter of the primitive. When the first size is adequate, click again and drag to the right to increase the second parameter (if necessary). One click and drag to the right for each parameter (sphere has one, cone and plane have two, “cube” has three) of the primitive object and then one more click to finish. Your object appears in the Systems folder of the Objects tab located to the right of the 3-D viewports. By default the names of the objects is PS_#, where # is the number in order of creation. This name can and should be changed to something more descriptive in the General parameters menu of the drop-down list to the right of the Objects folder tree. The detailed properties of the individual objects can be changed after selecting it by clicking on the objects name in the Objects stack, where it will be highlighted and in the 3-D viewports the corresponding mesh will turn white, if the Show status flag in the General properties is activated (this is the default). The Object Properties drop-down list contains five different parameter sections: General, Particles, Modifiers, Primitive and Fields. Click on Object Properties for a link to a more detailed description of its content. Primitives Objects, Tool and Lights tabs: The parameters of objects and different tools can be set in the Parameter Tabs on the right side of the 3-D Module. There are three tabs available for the parameters. Objects: handles the parameters of the objects in the 3-D viewports. Tools: allows access to the parameters of tools such as the Draw Tool or Erase Tool for particles accessed in the corresponding tab on the left of the 3-D Module). The parameters in the Tools tab appear once the tool has been activated. Lights: change the lighting properties of the 3-D viewports by changing the properties of the default Ambient Light or adding, deleting and changing the positions and parameters of other types of light. A more elaborate lighting scheme is often useful to create schematic illustrations using the mesh objects. ​ Objects, Tools & Lights tabs Transform tools: On the left side of the 3-D Module there is a set of tabs with a variety of tools, most of which interactively change the positions and orientations of various types of helper objects: Cameras: change the view points of Render or Free-Form view ports interactively. Systems: change the transform properties of individual objects (Systems) of the scene. Widgets: change the local coordinate system of the selected tool or modifier. Vertices: with these tools individual or a group of vertices of meshes are manipulated for very detailed local changes of the meshes. Particles: draw and erase Particles on and around meshes that serve as supports. This allows very detailed structures to be added to an object than can not be easily generated with meshes or procedural filament tools. The parameters of the Draw and Erase particles tools are set in the Tools tab on the right of the 3-D Module. Transform tools Objects Tree: The objects tree is a hierarchical list of the current objects in the scene. They can be collected in folders and sub-folder. With the tick boxes to the left of each object an object can be switched on or off. Similarly switching on or off a folder does the same for all objects in a folder. ​ New objects are placed in the default "Systems" folder. ​ New folders are created using the "Add new folder" button at the bottom left. Copy objects with the copy-button. The copy is then placed at the bottom of the list in the same folder. Move objects and folders around within the object tree by dragging and dropping. Delete objects and folder with the delete button at the bottom of the panel. ​ The color of the symbol to the left of the object name is the same as the mesh color and helps to identify the object in the 3-D views. If the object is not enabled, the color of the symbol is grey. ​

Render Module Properties Panel: Units Properties Panel: Units ​ Observational astronomers and theorists often work with very different units. This can be accommodated for in Shape by choosing the units that work best with your reference images or target audience. ​ World & Image units: Various units can be selected for the World (Coordinate System) in the 3-D environment and the Images. The appropriate unit is selected from a drop-down menu and by default is set to meters (m). Some of the units are in terms of typical linear and others are in angular sizes. Energy: The energy units refer to the intensity units of the images. In addition to the SI (International System) some of the typical astronomical units are also available. Distance: The units for distances are similar to those for the World & Images, except that the angular units are, of course, not available.

Render Module Properties Panel: Output Properties Panel: Output ​ The Output panel sets the type and file location for the output of the 3-D render cube information from the current scene. This information can then be processed and, with the Export Module, exported to other standard formats for external visualization. Enabled: Enable the output to be executed after the rendering is finished. Slices: When enabled, the output is done in the form of PNG format images slices. Each slice contains RGBA information in the XY-plane of the world coordinate system. Name: This text field takes the name of the output file without an extension. Unless Slices is enabled, the output will be a single file with the extension ILV. The ILV file can be loaded into the Export Module for further processing and output in other formats. Background Image: In this section you can control which the viewing of all the foreground rendered images and the observed background images in all windows. Image: From the drop-down list you can choose which images are used as background or reference image. The initial choice is between Observed and None. If Observed is chosen, the Observed images chosen in the Selected Window panel will be visible as background. If you choose None, then you can click on the button beneath to save in memory the current rendered images as a background or reference. Each image is identified by the time stamp of the moment of click on the save button in this panel. ​ The button labeled "x" allows the user to delete a saved set of rendered reference images from the drop-down list. Transparency: The slider controls the transparency of the foreground rendered image. Moving the slider to the right makes the foreground gradually more transparent, thereby allowing a comparison between the reference image in the background with the foreground.

Downloads The most up-to-date installers for Window, Mac OSX and Linux can be found found at: Installers Updates ​ Occasionally, updates will be issues without supplying new installers. This greatly reduces the size of the downloaded needed. The update packages will contain library files that simply need to be copied over the files that already exist on your system (whever you have installed ShapeX). Notes: ​ Since the last release, Shape has been revamped almost completely. In particular, the user interface (UI) and the rendering algorithms have seen profound changes. New modules and modifiers help with the workflow New manual & website help the user to get started User forum - ask questions, share tips & tricks, propose features Installers for Windows, MacOSX, Linux RPM & Debian ​ IMPORTANT NOTE: Remember that to take full advantage of your computers RAM, you need to manually set it in the ShapeX.cfg file. Search for this file within the installation directory. Open it with Administrator privileges and add the minimum and maximum RAM that you will allow Shape to use, say e.g. 14 GB of your actual RAM of 16 GB. Edit the .cfg file in a text editor with the following lines: [JVMOptions] -Xms1000m -Xmx14000m ​ Make sure that there are no spaces before or behind the lines with the numbers. Save the file and run Shape. At the bottom of the UI the "Total (Mb): " should now indicate approximately 1.4E4 .

The Texture Displacement Modifier uses a procedural texture to deform a mesh. The value of the 3-D texture at position of a mesh vertex in space determines how far the vertex is pushed away from its original position. The magnitude of the position change of the vertex as a function of the grey value of the texture. The direction can be chosen to be radial (set the radial flag) from the local coordinate system or you can use the widget to set the direction. The Magnitude dialog: In the Magnitude dialog you set the function that determines the distance a vertex is pushed based on the grey-scale value of the texture at its original position in space. The values of the texture is in the range [0,1]. The variable that carries these values is "x". So, if you use the default "x" as a function, the vertices will move between 0 and 1 units. The example mesh show in the figure below uses a "clumpy" texture with a few hundred clumps distributed in the spatial domain. The function that is used as magnitude of the displacement is 15*(x-0.5). The reason we subtract 0.5 from x is to allow the texture to not only push outwards making the shell necessarily larger, but also inwards, such that the average radius stays approximately the same. The factor 15 then extents the maximum range for the displacement to that value. Texture : Use the Texture dialog to choose and customize the texture that controls the Texture Displacement modifier. See the page on the Texture key subsystem for information on how to setup a texture. Modifiers: Texture Displacement

Desktop Module Video Tutorial The Desktop Module is your control and navigation center. It allows to open modules and customize the quick navigation bar at the top, open recent projects with a single click, customize general parameters and open utilities. Module area: You can left-click on the icons for the different modules to switch to them. Right-click opens a little button that allows you to pin the icon to the main Menu Bar at the top of the user interface. Alternatively, you left-click and drag the icon onto the Menu Bar. Menu Bar: The Menu Bar is the quick navigation tool and stays there on all Modules. Drag-and-drop icons from the Desktop here and arrange them according to the needs for the most efficient workflow on your project. Right-click on an icon to unpin it from the Menu Bar. Files: In this section of the Desktop you have access to project files. You can save the current project with its current name and location (Save) or save it with a new name or location in the file system (Save As). Furthermore, you can open an exiten project (Open) or clear the current project and start a new one (New). Recent Files: In this section of the Desktop you have access to project files that you have been working on recently using a quick access button. Just click on the button of the project that you would like to open. If the displayed file name is not enough to identify the correct project, just hover over the button to display the full file path as a tool tip. Information tools: There are a few tools that will display useful information or where you can configure a few general parameters that you might need to change from their defaults in order to optimize the performance of ShapeX on a particular system. The Memory tool will show the memory usage as a function of running time. The Progress tool shows how the difference forground and background processes are progressing. The Help tool opens this website. The Config uration tool allows you to set multi-threading and autosave parameters (how often the current project file is backed up automatically), as well as a project directory, where ShapeX will start to look whenever you open a file dialog. System information about the interactive Java3D libraries and other Java system data can be found in the J3D and System information tools. Commands: There a few additional tools that are either just commands to be executed or open a tool that did not fit into the other categories. The Shape It! button simply executes a rendering and is equivalent to the Render button located at the left end of the Menu Bar. The Reset button resets the Menu Bar to its default configuration with the minimum necessary modules. Finally, the Units tool open a utility that allows to convert between different units, such as cgs to SI, which come in handy since many astrophysics books use cgs units, while ShapeX works with SI units.

The Warp Modifier rotates the mesh vertices as a function of distance around an axis. ​ To actually be a warped surface, the axis of the Widget for the Warp Modifier needs to be at an angle to a reference plane such as a flat disk. ​ Name: Set a name that allows you to identify this modifier easily. ​ Enabled: When this flag is turned off, the Warp Modifier is switched off. ​ Deg: If set, the the rotation as a function of distance in the Magnitude Graph is given in degrees per unit distance. When switched off, then it will be radians per unit distance. ​ Magnitude: Opens the function graph to set how the rotation angle is as a function of distance from the local coordinate system set by the Widget. ​ Widget: The Widget opens the Widget Dialog. It allows you to change the direction of the Warp Modifier. The turquoise arrow indicates the direction around which the rotation will be performed. In the example it was rotated around the original x-axis by 30 degrees. Modifiers: Warp

Filter Module Overview A variety of box filters can be defined in this module and applied to objects in the 3-D Module. To apply the filter look for the Filters drop-down list in the General Parameters tab for mesh objects. All filters defined in the Filters Module appear in this drop-down list. Select the filters to be applied. The Filter Module has three main areas, the Tool Bar at the top, the Filter List on the left and on the right the Options for the selected filter. ​ Menu Bar: Add: Use the Add button to add a new filter to the Filters list. When you click on this button a pop-up opens with a list of Filter Types from which to choose one. In the Options Panel change the Name to something recognizable, e.g. the name of the object to which it will be assigned or something that describes the function it is meant to do. Remove: Remove the selected filter from the Filters list. Make sure you have selected the the filter that you really mean to delete. ​ Copy: Copy the selected filter within the Filters list. Best to rename the filter to make it uniquely recognizable. Change the parameters in the Options Panel. ​ Sort: Sort the filters alphabetically in the Filters list. ​ Open: Load a previously saved filter from disk. A file opening dialog will open for you to select a file. ​ Save: The selected filter will be saved to disk. A file saving dialog opens. Select the directory and filter name to be saved. Add an extension that helps you to recognize the file as a Shape-Filter. While you can choose any extension, we recommend to use .shf. ​ ​ Options: ​ Name: Set a descriptive name for the filter. This name appears in the Filter selection drop-down list in objects in the 3-D Module. ​ Enable: The check box activates or disactivates this filter for all objects that use it. ​ Mode: Here to can chose the Mode of the filter, which refers to whether the range between the Min and Max values is to be included or excluded. ​ Clamp: If checked then all values above the Max values are set to the Max values. If unchecked, then the value is set to zero. ​ Min & Max: The minimum and maximum of the filter range.

Key Sub-S ystem: Graphs In Shape graphs are used to display functions. The functions are either analytical or set interactively by adding control points to a curve. The control points of an interactive curve can also be loaded from an external ascii file. ​ In modifiers the graphs are usually applied to set and display spatial variation of a quantity that is passed on to some quantity as a multiplier. In the modifiers the graphs may be single coordinate functions or they may depend on all three space coordinates in different types of coordinate systems (spherical by default, Cartesian or cylindrical). Generally the result is a single number, but in the case of the velocity field, for instance, the output can be a vector. ​ In the Physics Module graphs commonly are a function of wavelength. ​ The functionality and appearance of the graphs varies slightly depending on the particular context. ​ The image of the graph on the right is taken from the Squeeze Modifier, which controls the shape of a cylindrically symmetric mesh. The function display at the top shows a line of how the function f(x) changes with the independent variable (always x). In this modifier it is the position along the axis of the object. ​ At the bottom is a list of tabs to set a variety of f unction properties . ​ ​ Workflow: ​ Analytic: By default the function is set to Point , but can be changed to Analytic with the Function drop-down list. ​ In the analytic mode, the graph is controlled by a mathematical expression, that by default is the constant function f(x) = 1. ​ Templates: From the Templates drop-down list a few commonly used functions can be selected that are the inserted as mathematical expressions in the editor line for the function. These templates can then be edited as needed. In our example we have typed the function manually. In additional to several standard mathematical operators such as "exp" and "abs", it includes the variables "a" and "b". Variables can have alphanumerical names. Reserved variables include "n", "t" and "Pi", referring to density, temperature and the number p. ​ Variables: The numerical value of the variables is displayed in the Variables tab . Here the value can either be written manually or be assigned from the Math Module. If the variable was defined in the Math Module, then the flag labeled "Use global variables" needs to be set. If the flag is not set, the local manually set value is used (Local variable ). Global variables are then marked by a grey background. Global variables are accessible from any function throughout Shape. ​ Constraints: Frequently used functions such as the Gaussian vary over an infinite range. In many practical situations the function is required to smoothly reach zero or some other fixed value within a finite range. This can be achieved by setting constraints in the Constraints tab. Here the function can be made to smoothly Fade in and Fade out within the ranges set there. The value form and to which the function converges is the "Default" which can be changed by the user. In the graph the region that is covert by the Fade in is shaded in blue and the Fade out in red. ​ ​ Point Graph: ​ A point graph is set up using manually placed points. These point may also be loaded from a file (Load Ascii button). To obtain a continuous function the values between the points are interpolated. ​ There are two modes for interpolation . By default the interpolation is linear between the points. The second is a spline interpolation that is controlled manually with separate handle on each side of the points. ​ ​ ​ ​ ​ ​ The spline interpolation is activated by clicking on the following icon: A green color in these icons at the top of the graph indicates that they are activated. To move the points in the graph use the left-click and drag mouse functionality. To move the spline handles , use Crtl- left-click and drag . ​ Additional interactive functions to manipulate the points individually or collectively are available by activating some of the icons on the toolbar above the graph. ​ If you hover over a button or icon, a tool tip shows a short description of the functionality, which are very self-explanatory in this case. The hand tool is active by default and allows one to move points by left-clicking on and dragging them. The magnifying glass: zoom in and out in the graph The next icon allows you to pan left-right and up-down in the graph. The box with a pencil is for selecting multiple points by dragging a rectangle around them, while the cursor symbols with the arrows activates moving the selected points together. ​ Selected point are deleted by clicking on the cross icon . Note that unselected individual points can be added and removed from the right-click menu (see below). ​ The range of the graph is adjust ed to the points in them by clicking on the icon with the two curvy arrows . As mentioned above the next icon activates the spline interpolation with two handles on each point. The wrench icon opens a pop-up windows that gives access to detailed options for the appearance of the graph . These should be largely self-explanatory. Right-click menu: The right-click menu give quick access to additional functionality for graphs. In particular there are four functions for point graphs at the top of the list. ​ Add Point add a point to the curve where the curser is currently located. Remove Point removes a point over which the cursor is hovering. Set Point opens a small pop-up window where the exact x and y values of a point can be set. Mirror Point is a very useful function when a perfectly symmetric setting is required. When clicked while you hover over a point with coordinates (x,y) a copy of the point is added to the graph at (-x,y). ​ The second set of functions toggle on and off various functions, which are self-explanatory. ​ The Save Ascii function will open a dialog that allows you to save the point values of the graph in a file in ascii format. The Save Image function saves an image of the graph. In the file dialog that opens, the filename has to be give a suitable file extension for the image to be correctly saved. The extension can be one of typical file formats, such as .png or .jpg, etc. ​ Finally, the Properties functions opens a dialog where the graph´s appearance may be customized in more detail by changing colors, tick-mark spacing, coordinate grids, etc. ​ ​ Special variants of graphs: ​ Some contexts in Shape have specific features in addition to the basic functionality described above. These are explained in their specific contexts, such as the graph for the velocity modifier, which has a number of special functions. ​ There is one common feature of the extended graphs that depend on more than one variable, which we describe here. Most function graphs have as output a single number that controls a modifier or displays some property. An exception is the velocity modifier, which has a vector as output. ​ The basic graph that has been described above depends on a single variable. Many modifiers do, however, depend on more than one spatial dimension. Those have a separate graph that describes the spatial dependence of the output on each spatial coordinate. They are accessible through tabs at the top of the graph. The active coordinate is marked in grey. ​ Using the default Custom Mode one can select from three different types of coordinate system in the Coordinates drop-down list: Spherical (default), Cartesian and Cylindrical. The labels of the access tabs for the graphs change their labels accordingly. ​ Note that for the spherical coordinates the label convention is that of the North America, with q being longitude and f the latitude. ​ SEPARABILITY: an important property of the default behavior of these graph is that the resulting function F(u,v,w) is separable in their component functions: F(u,v,w) = f0 * f(u) * f(v) * f(w) ​ where f0 is a constant parameter set by the user under the Coordinates drop-down list. ​ Non-separable functions: a non-separable analytic function can be set up when enabling the Analytic mode from the the Mode drop-down list. This feature requires an analytic description of the function and a point-graph can not be used. ​ As before, one chooses the type of coordinate system from the Coordinates drop-down list. Then in the function editor a formula is types as a function of the general coordinates (u,v,w) as shown in the example on the right. The coordinates have to be in terms of the letters u,v and w, no matter which type of coordinates is chosen. Their meaning changes automatically to (x,y,z), (r, q,f) or (r, q, z ) for Cartesian, spherical or cylindrical coordinates, respectively. The image on the right shows a rendering of the density that was described by the analytic function above it. It illustrates the how the wavelength of the sinusoidal pattern can be continuously changed by mixing the coordinates appropriately. ​ ​ ​

Modifiers The Image Texture Modifier ​uses an grey-scale image to control density or other physical properties as a function of the image pixel intensity. It is similar to the Image Displacement Modifier (IDM) . Refer to the page of the IDM for details. Here we will describe only the differences to the IDM. This allows one to use actual images to influence them model density distribution. As shown in the example on the right, a potential application is in the modelling of spiral galaxies, where we also made use of the IDM with the same base image. The Image Texture Modifier (ITM) was used to better define the density and brightness structure in addition to the overall shape produced by the IDM. The ITM "projects" the density distribution given by the image along the direction of and starting at the position of the Gizmo through the mesh. If not modulated by other modifiers, the ITM produces a constant density along the direction of projection. For a more realistic distribution it should be further processed in that direction using, e.g. the Taper Modifier. Parameters: ​ Name: If multiple Modifiers are used, make sure to name them adequately for ease of identification. ​ Enabled: When deselected, the modifier will not be applied. ​ Variable: Select the physical variable on which the ITM shall operate. ​ Operation: Select the operation the ITM shall perform on the physical variable. ​ Radial: Select this option if you wish the displacement to be radial from the origin of the Local Coordinate System of the mesh. ​ Filename: Click on the button on the right to open the file selection dialog to open the image file to be used to the ITM. The filename will be displayed in the text field. ​ Width & Height: The full size of the image in the 3-D Module in local x & y directions. Magnitude: Set up the how the mesh displacement shall be as a function of the pixel brightness of the image assuming that it has an interval from x=(0-1) for greyscale values of (0-255). You can use an analytic function of x (the pixel value between 0 and 1) or a corresponding point function. Widget: Opens the Widget panel shown on the right and enables the preview of the displacement image that helps to place it correctly. To see the preview image, the Display has to be enabled and the object needs to be selected in the object tree. The not only the Widget arrows are show, but also the preview image as shown below the Widget panel on the right. ​ Auto Update: If you change the image texture using an external software such as Gimp or Photoshop, then you can enable the automatic loading of the image by clicking on Start. Make sure to Stop it again after you finish. Since the image is read from disk, you need to save it after every change you want to be updated in Shape. ​ Interval (ms): The the interval between Updates of the image from disk. ​ Modifiers: Image Texture

The Bump Modifier is designed to add individual bumpy extrusions to a mesh. Position, orientation and detailed shape of the bump can be controlled. ​ To add a Bump Modifier to the Modifier Stack, click on the Add Modifier button (the + sign under the Modifier Stack) and select Bump. ​ The modifier appears at the end of the stack. It is important to note that the detailed effect of the modifier may depend on the position within the stack. Therefore experiment how it interacts with other modifiers before or after in the list. ​ Different properties of the Bump Modifier is controlled in different places. ​ The Control Panel under the Modifier Stack has several check marks: ​ Enable: Enable or disable the Bump Modifier ​ Symmetric: By default the bump will be cylindrically symmetric around its direction axis that can be seen when the Widget is on. Then the check mark is on. When the Symmetric flag is off, then the bump will be infinite in one direction and controllable in the other. ​ Radial: When the Radial flag is checked, then the bump will be applied radially from the coordinate center of the Widget. Otherwise it is parallel to the directional axis (pink) of the the Widget starting in the plane that contains its coordinate center. Widget: Posititon & Orientation The position and orientation are controlled with the Widget. The numerical control panel for the Widget can be opened by clicking on the Widget button in the Control Panel. Alternatively, use the interactive Widget controls on the left side of the 3-D views. As usual, during interactive control use the x, y and z keys to restrict moving and rotating actions to a particular axis. Magnitude: Shape & Size The shape and size of the bump are controlled from the Magnitude Graph that is accessed in the Control Panel under the Modifier Stack. ​ The Magnitude Graph works the same way as other graphs in Shape. For details see the user manual entry for Graphs . ​ The shape of the bump is set using an Analytic function or a Point graph, where the "x" is the distance from the local coordinate system (widget axis) is cylindrical coordinates. For the "symmetric", i.e. cylindrically symmetric case, the values at negative x are ignored. ​ By default the shape of the bump is set to a Gaussian function. ​ The overall size of the bump can additionally be controlled using the f0 parameter in the top left corner. Magnitude: Change the bump structure The detailed shape of the bump can be arbitrarily complex. This can be achieved by changing the Analytic function as shown in the examples on the right. Alternatively, for even more arbitrary complexity use the Point function by clicking on the Function drop-down list. Edit the Point function following the instructions in on the Graphs page . ​ Mesh resolution: Note that the application of the Bump Modifier may lead to poor mesh resolution in the bump. Currently the mesh resolution can not be improved locally. Therefore, if necessary, the overall mesh resolution can be increased by increasing the number of Segments in the Primitive tab of the object. Modifiers: Bump

Top of Page Overview General Considerations Computing Power Batch Processing Typical Modeling Applications Morpho-kinematic Modeling Photo-realistic Models 3-D Hydrodynamics Exoplanet transits Schematic illustrations Basic Workflow Need a new ShapeX feature? . Overview General Considerations Overview Your first question is likely to be: Is Shape suitable for my modeling problem? ​ Here is a short summary of the types of problems that have been worked on with Shape and others for which we know that the software can be used. We shall also discuss the limitations that might prevent your problem to be attacked with Shape. General considerations: ​ Polygon meshes: Polygon mesh objects are the most basic building blocks in Shape. The software generates them in a similar way as common 3-D animation programs such as the open-source Blender and many other commercial packages. However, these programs have been designed to model mostly opaque objects that surround us and hence compute their visual appearance according to the color assigned to their surface as a function of position and the lighting conditions. Only exceptionally volumetric effects are computed for clouds, fire or other phenomena that are not opaque. ​ In astronomy and astrophysics almost everything is about gas and dust clouds that are at least partially transparent. Real surfaces are very rare and can be found only on rocky planets and other solid bodies. Some stars can be considered to have "surfaces" since the transition from the optically thin to thick regimes is very small compared to their size. ​ The polygon meshes in Shape are therefore mainly used as containers of gaseous or dusty volumes, which are then assigned physical properties as a function of position within that volume rather than on the surface. Computing Power Batch Processing Computing Power: ​ An old saying claims: "There is no such thing as too much computing power." ​ This is also true for Shape applications that wish to push the limits of what is possible. But for many scientific applications today´s power of almost any laptop suffices. Since Shape is a highly interactive software, for your own comfort and an effective workflow make sure to use a mouse instead of just the mouse-pad. More sophisticated devices such as graphics tablets are of additional benefit for some applications. ​ Most processes in Shape make use of parallel computing on multi-core CPUs. Especially the rendering processes and hydrodynamic simulations benefit from many-core CPUs and multi-threading. ​ While the benefit of parallel computing mainly lies in reducing the time required for a computation, memory influences the spatial resolution that can be achieved in a rendering or hydrodynamic simulation. So, if you have ambitions to produce high resolution photo-realistic visualization and animations, then you might want to use a high-end workstation. Individual images can be rendered at high resolution with a special HD renderer that does not require a lot of memory. It does, however, have to do the full rendering process for each image. When you only need to change the camera view point for an animation or time series, other renderers only need to redo the last rendering step, because they keep the pre-processing information in memory, thereby speeding up the process. Batch processing can, at this time, not be done, e.g. as background processes on servers or supercomputers. This is a project for a future version. Typical modeling applications for astrophysics ​ Morpho-kinematic modeling The original design purpose of Shape was the modeling of the 3-D morphology of nebulae using as additional constraint the kinematics observed in spatially resolved high resolution spectroscopic data. As the structure becomes more and more complex, the traditional approach of direct coding of the volumetric density or emissivity as well as velocity distributions becomes impractical. Therefore the technology of interactive polygon mesh construction as volume containers was adapted to astrophysical needs from conventional 3-D modeling in Computer Graphics. ​ This type of modeling is still the flagship application of Shape. The user builds a 3-D volume distribution of density or emissivity, assigns a velocity field and then produces images, position-velocity diagrams and/or channel maps. ​ This is the main approach for modeling the structure and kinematics of circumstellar gas, be it expanding or rotating, such as in planetary nebulae, supernovae or proto-planetary disks. An extension of this methodology is the application of carbon-monoxide (CO) radiation transfer using the ShapeMol module. This is useful to model high-resolution observations with the ALMA or other radio interferometers. A large number of scientific papers contains models of this type and can be referred to as examples. See the list of publications with Shape and Shape models. Morpho-kinematic Modeling Typical Modeling Applications Photo-realistic Models Beyond scientific application ShapeX can be applied to produce photo-realistic visualizations of a variety of nebulas, stars, galaxies and other types of objects. This type of application often requires a mixture of various modeling techniques, using polygon meshes, particles and hydrodynamics. Since high spatial resolution and substantial model complexity is likely to be required for this type of application, substantially more computing power and processing time might be necessary compared to more basic applications. More detailed information and examples of photo-realistic models, in particular with mixed techniques that include polygon mesh and hydrodynamics can be found in Steffen & Koning (2017) . Photo-realistic Models 3-D Hydrodynamics 3-D hydrodynamics The Hydro Module in Shape allows the simulation of basic astrophysical hydrodynamic phenomena at moderate spatial resolution (depending on the computing power in terms of CPU cores and RAM) solving the basic hydrodynamics equations. A simple radiative cooling scheme is included designed for fast computation above 10000 Kelvin. The details of the numerical scheme have been described in Steffen et al. (2013) . The novel feature of the hydrodynamics in ShapeX is that the user does not require programming the initial conditions. For this task the interactive 3-D polygon modeling interface is applied. The full integration of the hydrodynamic module in ShapeX allows a highly flexible analysis of the simulations and mixture with other modeling techniques. This yields very realistic visualizations for scientific and outreach applications. ​ If you have been using a hydrodynamics code that is not part of Shape and find that your visualization and analysis software does not meet your needs consider Shape for it. You can import data from hydrodynamic simulations and use Shape to generate spectral kinematic output (P-V diagrams, channel maps) and images for any viewing angle. It is also possible complement your model with additional features constructed with Shape´s polygon mesh techniques for scientific modeling or illustration, and much more. Exoplanet transits Exoplanet transit lightcurves The lightcurves of exoplanets are a rich research field for which Shape is very well suited using its animation module for setting up the orbital motion, the rotation of the star with star spots and limb darkening or brightening. Shape can not reconstruct the systems parameters automatically from data, but the user can construct not only the time series of a single transit, but automatically vary a number of parameters and setups that allow the construction of a catalog of transit lightcurves and corresponding videos that shows the transit together with the lightcurve. In addition to the scientific value, the movies can be of use for outreach and press release illustrations. Schematic illustrations Schematic 3-D model illustrations ​ The 3-D polygon mesh models can be used for schematic illustrations of model ideas, even if you are not interested in a physical model. For papers and presentations such models can not only be static illustrations, but as interactive demonstrations or movies they can be powerful tools to convince an audience of one´s ideas. Need a new ShapeX feature? Basic workflow: Interactively add the geometric elements of your object in the form of primitive polygon meshes (Primitives) that you can access at the top menu bar of the 3-D Module. These meshes will serve to encase the volumes that will constitute the different parts of the model. Then you modify the simple structure of the Primitives using what we call Modifiers, which give the objects new geometric structure and physical properties as a function of position in space. Using the Physics Module, you then assign the material and radiation properties to the meshes. Finally, the model is rendered with the Render Module and some of the observational properties can be displayed with the (Channel) Maps and Graph Modules, where the observational data can be included and compared with the model results. If the results are not satisfactory, the model will be adjusted until a satisfactory match is found between observations and model. Need a new Shape feature? ​ Don´t hesitate to contact us , we might be able to help either by finding a solution with the current software or implement a new feature for you, thereby helping other potential users with similar applications. Basic Workflow

The Shear Modifier changes the distance of the mesh vertices perpendicular to a chosen axis (default: local z-axis) along another axis. The orientation of the shear axis and direction of the shear can be changed by changing the values in the Axis boxes. Choose a value of 1.0 to select a particular axis (setting the others to 0.0). Intermediate value result in an intermediate axis. A better way to set the reference axis is using the Widget. The Magnitude dialog allows you to define the squeeze amount as an Analytic Function of position along the reference axis. You can also use a Point graph where you can generate an arbitrary function by manually placing points and setting the spline interpolation. To do this, select Point from the Function drop-down list under the graph. The example graph on the right shows the way it was done for the example mesh displayed below. Modifiers: Shear