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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

Data Preparation Before we start getting into the preparation of data, let´s first get out of the way a common misunderstanding : Shape is not a software that processes observational data and as a result delivers a 3-D model. ​ What Shape does is to provide you with a set of tools that allow you to apply your scientific insight and creativity to generate a 3-D model that reproduces your data as closely as possible. During this process you might improve your understanding of the object of your research and with the final model you have a tool to help your peers to better understand your conclusions. ​ Selected Window: Data as a reference in the Render Module are included per Window , which may be an Image or a Position-Velocity (P-V) window. Clicking on a Window selects that window , which is indicated by a thicker white border of the window. ​ Once a window has been selected, the drop-down list at the top of the Properties tab gives access to the selected window by chosing Selected Window . ​ Two important choices to be made at the top are the flags Render and Master . By default all windows get rendered, but sometimes it may be prefereable to not render some windows. ​ Only one of the windows can have the Master switch on . Once you select Master for a window, the corresponding switch in the previous Master window is switched off. ​ The Master switch determines which rendered or reference image can be shown in the Render View of the 3-D Module as a reference background during the modelling process. ​ The potential of cross-checks between data and models : It has happened in several occasions that the model result hinted at problems with the data processing and resulted in the correction of mistakes. Hence, frequent critical cross-check between data and model can be beneficial in both directions. Usually the data inform the modeling process. Occasionally it also happen that the modelling leads to corrections , new processing or interpretations of the data . ​ ​ ​ ​ Data Preparation: Data for Shape basically consist of some form of image that is placed as a reference in the background of the rendered images, spectral images or the 3-D views in the 3-D Module. Shape provides tools to correctly place the images in their corresponding context. ​ ​ The key information that is needed to prepare these images are their scaling and corner positions in the chosen coordinates. ​ ​ So, for instance, if you wish to work on arcsecond scales and your side to side field of view is 10 arcsec, then you have two options . First, you crop your image to the same field of view. Then, after loading it into Shape, it fits automatically to the 10x10 arcsec field that you have set up. This is the recommendable option . The second , more complex, but often necessary option is to use a certain image as it is. Then the position, rotation and size are adjusted in Shape such that it is correctly placed in the field of view. ​ ​ These options are applicable for images, P-V diagramas, channel maps and graphs. ​ ​ If your images have scales with tick-marks , you can adjust the placement such that they coincide with the corresponding tick marks in the Shape image coordinate system. This can be done in position and velocity. ​ In the first example on the right (click on the image to see a larger version ) the observed image was first cropped to a square format that corresponded precisely to the original size of the default window size or range values. ​ As long as no rendering was done, the background image remains visible. The visibility of the background image is indicated by the red square in the top-left corner . Once your models become very realistic you may not immediately notice whether you are looking at the observed or rendered image. Then it may happen that you are wondering why your rendering hasn´t changed after your changes in the 3-D model settings... until you notice that there is a little red square that tells you that you have been staring at the observed image all the time. ​ To gradually switch between reference and rendered image use the Transparency slider . ​ In the second example on the right, a new P-V Window was added. A single position velocity diagram as shown further up was added as a background. The x0, y0, x1, y1 values were adjusted such that the image fits precisely in such a way that the tick marks in the observed image and render window overlay correctly. A small additional correction was applied by adding a Translation Modifier to the observed image with an adjustment in the x-direction. Other modifiers can be added to correct scaling and rotation of the reference image . Note that the order of the modifiers in the stack may be important, especially when there are rotation and translations combined. ​ Rendered images as references for changes: Often one needs to compare a previous rendering with the one that includes new changes to the model. Rendered images can be saved as reference images after you open the background Image drop-down list and select None . Then click on Save image. A new item in the image stack appears labeled with the time the image was saved. A whole sequence of rendered reference images can be build by repeating this process. To delete an image from the stack, select the image and press Remove image . ​

Modifier Module Overview When a project becomes complex and there are many similar modifiers the Modifier Module helps to manage modifiers with bulk operations that change parameters for more than one of them simultaneously . On the right, the Modifier Module ​contains a list of all modifiers that have been set up in the project. The list has four columns that classify the modifiers and help identify and select them. Clicking on the head of a column groups the list according to that property in alphabetical order. This allows to easily work with a certain type of modifier. Different background colors for the fields further helps with the the classification and reduces mistakes in the selection of modifiers. ​ The first column contains the Type, which can be Density, Taper, Point, Bump, Squeeze, etc. ​ The second column indicates the Group the modifier belongs to, such as Particle, Transform or Geometry. ​ The third column contains the name that the user gave to the modifiers. If no name was given, then this field is empty. ​ The fourth column contains the name of the object the modifier is applied to. Select a modifier by clicking anywhere on its row in the list. Selected modifiers are highlighted in blue. On the right side, the parameters of a selected modifier are shown. The parameters can be changed there. ​ To select multiple modifiers keep the Ctrl key pressed while you click on the modifiers to be included in the selection. To select all modifier within a certain range in the list, select the first one and the use Shift-click to select the last one. All modifiers in between will then be included in the selection. The parameters shown on the right will be those of the first modifier selected in the set. ​ When you change parameters with more than one modifier selected, all selected modifiers will now have this parameter value. Filter: Use the filter function to display only a subset of modifiers. To achieve that start typing a word in the Filter text field. For instance, if you would like to see only the Texture Displacement modifiers, then type "Texture Displacement". You can use any word that may appear in the four columns to filter them.

Render Module Properties Panel: Selected Window Properties Panel: Selected Window ​ The Render Module can have several render windows, which can be of type Image or P-V (Position-Velocity). Each of them may have different parameters, which are listed and managed in the "Selected Window" panel. The selection is done by right-clicking on a window . The selected window is then highlighted by a white boarder that is thicker than that of the others. The parameter panel changes automatically when you change the selected window. ​ While there are some parameters that they have in common, the Image and the P-V windows have different sets of parameters . First we will discuss those of the Image window . Then we describe the additional parameters that correspond to the P-V window. The common parameters will not be repeated here . ​ 2D Image Render : This flag determines whether this window is to be update after the next rendering process (on) or shall keep the previously rendered image (off). By default this flag is set to on. If you have several image windows, it may be desirable to keep the previous result to compare with another window that is updated. Master: If you use the data of an image in an other module , this can be done only for one of the image windows. The one that is used is the one with the Master flag on . When you change the flag of one window from off to on, then the window that previously had the Master flag on is automatically switched off. Window Parameters: Under the Master flag there is a group of four icons that invoke utility commands . The first one copies the window parameters into a buffer . If you have additional windows of the same type and want them to have the same initial parameters, then you use the second button to paste the buffered window parameters to another window (after selecting it by clicking on the window). The third button saves the image of a window to file. Note that you need to provide the filename with the appropriate extension, e.g. .png. Shape selects the format of the image file according to the file extension that you provide. The fourth icon lets you print the image of the window to a printer or save it as a file in PDF format . It basically embeds the image in a PDF-file. Note that the image annotations, such as coordinates are not saved in a separate scalable font, but are incorporated in the pixelized image. Seeing: The combination of image degradation from atmospheric seeing and instrument resolution is simulated by a convolution of the image with a Gaussian kernel with a full-width half-maximum (FWHM ) of this value. It uses the same units as those chosen in the Units Panel of the Render Module. Slits: The slits drop-down list contains the slits that correspond to the P-V windows. In this list they can be switched off from this image window by unchecking them. If the "Move Slit " button above the image window is on, you can click on a slit and move it by pressing the left-mouse button and dragging it horizontally. After clicking on a slit and then moving the mouse-wheel, the slit-width can be changed interactively. ​ The color of a slit helps to identify the P-V window to which it corresponds. The P-V window has a thick vertical line of the same color. Background Image: This section of the Selected Image Window Panel controls the file, positioning and appearance of the reference image that is loaded into the background layer of the image display. ​ Image: From this drop-down list the current background image is selected. By default it is the "Observed" image, which can be loaded from file. Initially there is one other option called "None", which displays no image. However, when the None option is selected, the currently rendered image can be added to the list as a reference to be compared to later renders. It is often useful to compare renders from changed parameters with the previous version to see the effect of the parameter change. When selected, a button appears that allows one to delete such an image from the list when no longer needed. Transparency: In order to interactively compare the rendered image with the background image, the transparency of the rendered image is changed using the slider. If the slider is moved to the right, the transparency increases and the background image gradually appears. To help identifying whether the rendered or the background image is visible, the background image is marked with a red square in the top-left corner. Filename: The file path and name of the Observed background image. Click on the icon on the right of the filename field to select a file from disk. x0, x1, y0, y1: The coordinates of the bottom-left (x0,y0) and top-right (x1,y1) corners of the observed image. If all values are left at 0 (default), then the image fill the current image range. Setting custom values allows a precise placement of the image. Modifiers: The appearance and positioning of the Observed image can be adjusted using various operators, called modifiers. They can be selected from the "Available Modifiers" drop-down list. It is then added to the Modifier list that is applied to the image. Each of them has it´s own set of parameters, which in most cases are self-explanatory. PV Window The first few parameters of a P-V Window are the same as those of an Image Window. Please refer to that section above for an explanation. Slit color: In many projects data for several slit positions are available. To more easily relate them with the slit marking in the image window and the parameter panel, you can set individual slit colors. Default colors are assigned randomly. Slit X, Slit Y : The horizontal and vertical position of the slit, respectively. It can be set numerically in this field or interactively with the mouse cursor by dragging the slit on the Image Window. Make sure to activate the "Move Slit " icon above the Image Window first to enable the interactive functionality. By default the slit can only be moved horizontally. To interactively move it vertically press "y" at the same time as you drag it up or down. Slit width, Slit height : The slit width can be changed interactively after activating the "Move slit" button above the Image Window using the mouse wheel. By default the width is changed. If at the same time you press the "y" key , the height of the slit is changed interactively. Naturally, you can also change the values manually in the number fields. Velocity : The reference velocity for the spectroscopy is set in the "Spectrum " section of the Render Module. In the scale of the P-V window the zero-velocity for the graph can, however, be shifted by the value of this parameter. I maintains the same total range as before . Range : The total width of the P-V Window in units of velocity. Resolution : The P-V image is convolved with a Gaussian kernel of this full-width half-maximum (FWHM ) in horizontal direction in units of velocity. Background Image : This section is similar to that for the Image Window as described above. Please refer to that section.

Key Sub-S ystem: The Modifier Stack A model in Shape is build starting from a few basic mesh objects such as spheres, cylinders, tori or imported ones. ​ Very few objects have such regular structure, however, and the fundamental purpose of Shape is to enable the user to reproduce any structure the universe comes up with at us as closely as possible. There these "primitives" have to be "modified". That is why the operators in Shape are called modifiers . Since there is a large variety of modifiers, the are assembled in a modifier stack (see the image on the right). This list of modifiers operates on the primitive mesh in sequence from the top to bottom. ​ It is very important to note that for some operator combinations, such as rotations, the order in which they are applied makes a difference. ​ When a new modifier is added from the drop-down list that opens by clicking on the plus (+) sign below the stack, it is added to the bottom of the list. They can be reordered by dragging and dropping them into the desired position. To delete one or more modifiers select them in the stack and then click on the "x" at the bottom of the stack. ​ For good practice we recommend to order the modifiers by type as long as the order can be chosen without affecting the result. Modifier that apply to physical quantities such as density and temperature should go at the top, as shown in the example. Copy-Paste modifiers: ​ ​ ​ Modifiers can be copied within the same stack or to the stack of a different object. To copy the modifier to the buffer click on the Copy icon at the bottom of the stack. Then click on the paste button right beside to paste it to the same object. ​ To paste the modifier to a different object, select the target object and click on the paste button. When you do that, a small pop-up window opens with two option to select from. You can paste the modifier as a "new copy " or as an "instance ". The new copy of the modifier will act independently of the original. The instance of the original will work in unison with the original. This means that changes in the parameters of one instance will be automatically transferred to the other. You can have several instanced copies of the same modifier, thereby saving time by changing only one of them to affect all the others in the same way. This is an easy way to maintain the same structure for several meshes or other features of an object. ​ Modifiers: ​ There are basically three categories of modifiers: physical, geometry and transform . In the modifier stack these are identified by having a green, orange and white background respectively. The physical modifiers act on the local physical properties that determined the interaction of the gas with the radiation. Examples are the density, temperature, velocity or boost and points . The geometry modifiers move the vertices of the mesh to turn the primitive starter shapes into more complex structures. Examples for these are the bump, squeeze, twist and size modifiers. These modifiers do not move the origin of the local coordinate system. ​ Contrary to the geometry modifiers, the transform modifiers precisely do move the local coordinate center . The physical and geometry modifiers then take the new local coordinate center as a reference. ​ Links to descriptions of each modifier can be found in the Index . ​ ​ ​ ​ ​ ​

Modifiers The Image Displacement Modifier ​uses an grey-scale image to move vertices as a function of the image pixel intensity. This allows one to use actual images to influence the model structure. As shown in the example mesh on the right, a potential application is in the modelling of spiral galaxies. An external drawing device can be used to design structures almost interactively with the automatic update functionality. ​ For this example the image of a spiral galaxy was smoothed and a flipped copy of it generated. The flipped version is needed for the top-bottom symmetry of the galaxy structure. The image on the right is the rendered image. The Image Displacement Modifier (IDM) works in a similar way as the Bump Modifier with the basic difference of using an image as data source instead of a simple function. The handling of the Gizmo for placement is similar. One difference is that the Gizmo of the IDM include a preview of the image to help with the precise placement and scaling. ​ In this example of a spiral galaxy two IDM are required, one for each side, as shown in the example modifier stack on the right. 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. ​ Filename: Click on the button on the right to open the file selection dialog to open the image file to be used to the IDM. 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. ​ Radial: Select this option if you wish the displacement to be radial from the origin of the Local Coordinate System of the mesh. ​ 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. 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. ​ Note on Rendering IDM objects: Below are a few renderings of the example galaxy object. The first one shows the rendering at an intermediate viewing of the disk. At the center the bulge is seen as a vertical uniformly lit structure. This is typical for the applications of the IDM, especially with small-scale features. These turn out to look like little vertical "sticks". ​ There are a number of measures that one can take to remedy that depending on the feature and the application of the IDM. For the smooth structure of the galaxy, for instance, one can use the Taper Modifier to taper off the emission towards the surface of the mesh. This is shown below where the galaxy has been rendered edge-on. The upper image is without and the lower one has a Taper Modifier applied. ​ In addition to the IDM to strengthen the spiral features in the galaxy an Image Texture Modifier was applied with the same image. Modifiers: Image Displacement

Key Sub-System: Particles Many astronomical objects, especially nebulas have filaments with complex structures. Often these can not be reproduced easily as analytic or point functions of coordinates. Particles are a way to place emission in specific regions without the limitations of a functional description. The particles serve as small spherical regions where the overall gas distribution will be sampled for rendering. The advantages are, however, somewhat balanced by disadvantages related to the non-continuous nature of particles and the way they are placed in the model. Therefore careful evaluation should be applied to whether this is a suitable tool for your goal. ​ On the right is an example of spiral arms applied with the Draw tool on the surface of a flat disk. Below are the renderings with (right) and without smoothing (artificial "seeing") applied. General Workflow ​ Particles can be applied to a mesh by two methods: 1. using the "Draw" tool to place them at specific positions on a mesh using a 3-D cursor that slides over the surface mesh.2. randomly over a surface or filling the volume. The volume particle number density can be controlled by the Distribution function. ​ Once a first set of particles has been applied and the density the distribution of particles can be adjusted using the Draw or Erase tools. ​ The physical properties of the particles, such as density or temperature, can then be adjusted as a function of position using the usual modifiers. General Parameter Panel For the particles to render at all, in the General Parameter Panel of the object select "Particle" from the Input drop-down list . Particles tab ​ In the Particles tab you control the uniform but random distribution of particles in the mesh volume or along its surface. ​ Num: The number of particles to be distributed Size: The size of the marker circle in the 3-D views of the 3-D Module. ​ Displayed: The percentage of the total number of particles that is to be displayed in the 3-D views of the 3-D Module. If the number of particles to be rendered is very large, it may be convenient to display only a fraction of them in the 3-D views. Seed: The seed of the random distribution of particles. Change this number to change the distribution. Container: From this drop-down list you can select between Volume and Surface. For Volume the particles will be evenly distributed within the volume of the mesh. When you choose Surface, they are placed on the surface. Buttons: ​ At the bottom of the Particles tab is the button (left) that needs to be pressed to apply the particles or redistribute them according to the parameters of this panel. ​ ​ The second button is used to save the parameters in an ASCII file including all its attributes, including their position in Cartesian World Coordinates, their velocity, the density n and pressure p. ​ The third button open a dialog to load external data as particles. This allows one to visualize a variety of external data, including hydrodynamic simulations in order to extract spectral information such as position-velocity diagrams. Using this dialog a variety of ASCII data formats can be loaded. Draw particles: ​ In order to place particles in specific positions that can not be described with functions, Draw and Erase tools is provided. ​ You access the particle tools via the buttons in the Particles tab on the left side of the 3D Module as shown on the right. ​ When the Draw or Erase buttons are activated an orange 3D cursor in the form of a cylinder appears on the surface of the active mesh. You can move it around with the 2D cursor, it will stick to the surface and place particles on the near side of the mesh at a certain rate within the volume of the cylinder. Using Alt-left-drag places the particles on the far side . Draw tool parameters: ​ The parameters for the Draw tool can be adjusted in the Tools tab on the right side of the 3-D Module. This tab displays the parameters of the currently active tool. The Name parameters identifies the currently active tool. ​ Since the Draw tool is a cylinder , its geometric parameters are: Radius and Length in units of the spatial domain. The orientation of the 3D cursor is always with its axis perpendicular to the local surface mesh triangle. ​ Transparency: using the slider the transparency of the 3D cursor can be adjusted. ​ # Particles: The number of particles that will be placed at random positions in the volume of the 3D cursor per unit of mouse movement. The value should be 1 or above (not as shown in the image or the parameter panel on the right). If set to 1, a single click places 1 particle at a random position in the volume. To place individual particles at very specific positions, choose a small radius and length for the curser and click at the desired position. ​ Density: The density of the particles. This can be modulated or scaled as a function of position using density modifiers in the mesh object with the Scale or Add options, including textures. ​ Particle Size: This parameter is currently decripated. The radius of the rendered particle is now set in the Render Size parameter located in the Input parameters of the objects Input type (Particles). If you enable the Pixels flag, the Render Size is in terms of pixels in the Render Module. ​ Modify: When activated the 3D cursor does not generate new particles but modifies the properties of the particles that come into its volume to have the current properties set for the tool, mainly the density. ​ ​ ​ Erase tool: The Erase tool is activated with the corresponding button in the Particles tab to the left of the 3D views. It deletes particles inside its volume. It has only the parameters of Radius , Length and Transparency for the cylinder that makes up the tool. ​ The Input Parameters dialog that opens when you click on the Options icon after selecting Particles as Input in the General tab of a mesh object. ​

Movie Module Overview In the Movie Module you concatenate individual animation frames into a movie. It can be reproduced in the integrated movie player and saved to disk for viewing in an external movie player. Several movie can be displayed side by side. These can then be saved into a single movie file. This is useful when comparing different visualizations of the same object simultaneously. Menu Bar: Create: Once you loaded the animation sequence of images, click on the Create Button to render the movie in a single file for viewing in external movie players. ​ Add: Add a second or more movie panel to the right of the current one. Several frames can be rendered side by side into a single movie. ​ Delete: Remove the currently selected movie panel. Select by clicking on the panel with the left mouse-button. ​ Load: Load a sequence of animation frame into the currently selected movie panel. When you click on the Load button, a file dialog open. Select the first of the frames. Then go to the last one of the sequence and Shift-Left-Click it to select all the frames from the first to the last. Click "Open" to load them into the frame buffer of the selected movie panel. 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.

Translations and rotations are non-deforming transformation that change the position and orientation of an object, respectively. ​ In Shape there are three groups of these transformations that distinguish themselves through their effect on the local coordinate system or the restrictions on their directions with respect to the observer. ​ The Translation , Rotations and PA/Inc Rotation Modifiers have the important property that they carry along the local coordinate system and operate in the coordinate system that is obtained after previous translations and rotations. Contrary to these, the Displacement and GeoRotation modifiers only transform the geometry. i.e. the mesh position and orientation as an enclosure for the region to be rendered. All coordinate information for the local properties, such as density, velocity, etc., does not change. These are according to any prior transformation of the other type. ​ Commutative Properties: Since several of the Position Transform can be concatenated in the Modifier Stack, it is important to know whether the order in which they are applied changes the result or not. Translations among themselves can be interchanged without changing the outcome (they are commutative). However, combinations of rotation with translations or other rotations are not commutative and therefore the order in the Modifier Stack is very important. So, make sure they are in an order that produces the desired result. Translation: Moves the object to a new position in the World Coordinate System. The local coordinate system is carried along. ​ When using the interactive System Translation from the System tab on the right side of the 3-D Module, a new Translation Modifier is added to the Modifier Stack if there is not one already at the end. This modifier can then also me changed numerically. By pressing the x,y or z keys while interactively moving an object, the translation can be restricted along these axes. Rotation: Rotates the object in the current coordinate system. The local coordinate system is carried along. If there is a Translation applied before, then the Rotation is still applied around the translated coordinate system. ​ When using the interactive System Rotation from the System tab on the right side of the 3-D Module, a new Rotation Modifier is added to the Modifier Stack if there is not one already at the end. This modifier can then also me changed numerically. By pressing the x,y or z keys while interactively rotating an object, the rotation can be restricted around these axes. PA/Inc Rotation: Rotates the object in the coordinate system observer´s coordinate system as inclination Inc and position angle PA . PA rotates around the line of sight with zero along the world y-axis (up). Inc rotates around the horizontal line in the plane of the sky with zero in the plane of the sky. The inclination Inc is applied first and the the position angle PA.. Displacement & GeoRotation: These two modifiers have the same functionality as Translation & Rotation, except that they only transform the mesh, but do not alter the current coordinate system. This means that other modifiers such as density, velocity, etc., will remain centered at the same position. This is often useful when a mesh is a substructure of a larger object. In such a case it is often useful to have instanced copies of modifiers that are meant to remain the same as those of the main structure or other sub-structures. Modifiers: Position Transforms Translation, Rotation Displacement, GeoRotation PA/Inc Rotation

Radiation Transfer The mathematical description of the radiation transfer physics used in Shape is described in the following PDF document.