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Modules In this section we give an overview of the functionality of the different modules and provide links to more detailed information on how to use them and their subsystems. Click on the Module Icon to the left of the description for more information and access to video tutorials on the module. 3-D Module ​ ​ In the 3-D Module the geometric and most other properties of a model are set up interactively. Description Render Module This module takes care of the rendering of image and position-velocity diagrams and a number of settings for other render options. Description Physics Module Radiation transport properties such as emissivity, absorption or scattering are set up as materials (species) in the Physics Module. Description Desktop Module ​ ​ The Desktop Module is your hub to all the other modules, project files, ShapeX configuration and more. Description Video Tutorial Math Module The Math Module allows you to set up variables and relations between them that can then be used throughout Shape as "global variables". Description Modifier Module The Modifier Module lists all modifier that are currently in use and allows you to change parameters of a selection of modifiers simultaneously. Description Maps Module The Maps Module displays channels maps of the 3-D model. The number and velocity range between the first and last channel can be set up. Description Animation Module Most parameters in Shape can be animated over time. This can be used to generate time variation of the models either for scientific modeling of time varying phenomena or for visualization purposes. Description Filter Module Filters for various physical quantities can be defined here. They can then be applied to objects in the 3-D Module. Description Movie Module In the Movie Module one or more animation sequences can be concatenated to a movie and exported for viewing with an external movie player. Description Export Module The Export Module exports the 3-D model into various output formats that can then be used as data for external use. Description Hydrodynamics Module Shape is the first astrophysical tool to introduce an interactive mesh-based setup for such simulations without the need of programming or scripting by the user. Description

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: General Properties Panel: General ​ The initial panel contains the General properties of the 3-D volume that is going to be generated and the type of rendering algorithm that is going to be employed. ​ Resolution: The number of volume elements (voxels) that the computing domain is to have in each direction. The total number will the N^3. Note that the rendering time required therefore increases very quickly with this number and your system may run out of memory. Make sure Shape is run with sufficient memory allocated for the process at startup. Scene size: The width of the computing domain in terms of physical units, which by default is meters (m). This number corresponds to half the voxel size assigned to the Resolution parameter above. The physical domain runs from -(scene size):+(scene size). Scene center: The center of the cubic computational domain may be shifted in the physical scene that might be larger than the rendering domain. Setting a smaller domain with a shifted center may be useful for testing purposes or for achieving higher resolution outputs for certain regions. Renderer: Choose the type of renderer from this drop-down list: either the High-Definition (HD) render (default) or the Standard renderer (SD). The HD renderer does not use a predefined cubic voxel grid and works similar to a ray-tracing engine that integrates to the pixel plane. If there are computations that depend on light sources, such as dust scattering, it is computed along the way. This may require more time, but is much less memory intensive. Therefore higher resolutions can be achieved. Fast renders, e.g. for camera animation movies, is not possible, however, since the some information is not stored for quick rendering from the precomputed voxel grid. Grid: When the HD render mode is switched on and scattering or photo-ionization processes are to be calculated, you can activate the Grid flag to use a grid for the scattering and ionization calculations. This speeds up the computation, but may be less accurate and uses more memory, which may limit the resolution on systems with insufficient RAM. For the most accurate calculation make the grid the same size as the Resolution parameter. Smaller sizes are best set smaller by factors of 2. They speed up the computation, but are less accurate. Grid Size: When the Grid flag for the HD renderer is set, then you can choose the size of the grid with this parameter. Make sure it is not larger than the Resolution parameters. Step Size: The ray casting and ray tracing step size in units of the cell size of the domain. Setting it smaller than 1 can in some cases yield somewhat better accuracy. It does, however, take more computing time. Jitter: As an anti-aliasing method you can randomly displace the rays from the center of the image pixels. This is in units of the pixels size. # samples: The number of samples, i.e. rays to be cast, for each pixels. The position of the rays in a pixels are random. This may be used to increase accuracy slightly or as a measure to reduce aliasing. Auto render: If the HD is off or the Save grid flag is on, then data of the full grid have been saved and can be used to quickly render the scene for different camera views and animations. When you change the parameters of the camera the rendering updates automatically. The effect is not "real time" and may take a few seconds, depending on the resolution. Use window: For quick render in HD mode that require only a small portion of the image to be rendered, you can set a window using the Window Button above the image. Click on the icon with the square and then drag out a rectangle with the left mouse-button pressed. If the Use window flag is on, only this region will be rendered. This reduces the rendering times during model development when it is sufficient to see only part of the model. Overlay: Occasionally it is convenient to retain the previous image or images and add progressive images together. This is useful for diagnostics or simply as a nice "special effect.

Animation Module Overview Most parameters in Shape can be animated over time. This can be used to generate time variation of the models either for scientific modeling of time varying phenomena or for visualization purposes. A simple example application is the simulation of the lightcurve of an exoplanet or of eclipsing binary stars. ​ An application that aims more at purely visualization could be rotating the virtual camera around an object go generate a movie that shows the structure as seen from many points of view. ​ Since animation implies the generation of a large number of individual images that can be joined together in the Movie Module, care needs to be taken in preparation in order for the rendering process to not take an unacceptably large amount of time. The key question is which type of rendering do you need : Camera motion: If you animation will consist of camera motion only and the spatial resolution that you need is small enough to allow you to use the grid renderer, then you can save a lot of time. In this case the steps before the final ray casting to determine the image pixel values can then be precalculated and saved. Then they do not need to be repeated for every frame. ​ Another option to get a camera animation is to use the interactive iluvia software from ilumbra.com . Using the Export Module in Shape you can quickly output your model in a format suitable for iluvia and inspect your model interactively or very quickly set up and capture animations. Varying model parameters: If parameters of the model itself need to be changed over time, then the precomputed grid changes and a full render is needed for every frame. For complex models and high resolutions, this may take a lot of time to compute, depending on your computing equipment. ​ Once you decided which type of animation and spatial resolution you need, you can time the rendering and estimate the total time it will take to render the necessary number of frames. For each rendering, come basic stats are output in the Info Module that include the time it took to render. This information can be used to estimate the total time necessary to render out the full animation.​ ​ General workflow: ​ 1. Set up the timing and output parameters in the Parameters Panel on the right. 2. Select variables to be animated from the Parameter Tree. They appear in the Animation Parameter Stack. 3. Select each animated parameter in the Animation Parameter Stack and set up its animation graph as a function of time 4. Render the animation Animation Module UI: The Animation Module is divided into five main sections. A control bar is at the top and the parameter tree and the animation parameter stack are on the left. In the middle you find the animation graph for the animated parameters. At the bottom is the time line . Finally, the General and Output parameters are in the panels on the right. Control Bar: Animate: Starts the rendering of an animation. After each rendered image it advances one frame and renders again. ​ Refresh: Updates the Parameter Tree after new renderable parameters have been added somewhere in Shape. This does not happen automatically, so make sure to click on this button to see any new parameters. Up & Down: In the Animation Parameter Stack move selected parameters up or down. This has no effect on the result but is helpful to keep order in the stack when a large number of parameters is animated. ​ Remove: Removes selected parameters from the Animation Parameter Stack. ​ Copy & Paste: Copy the animation graph from a selected animation variable in the Animation Variable Stack and paste it to another that you select after copying the previously selected graph. Parameter Tree: The parameter tree is a hierarchical list of all animatable parameters. The parameters may be from the UI, general project parameters or from particular objects. Additionally global parameters that have been defined in the Math module will also show at the bottom of the parameter tree. To select a parameter for animation, open the parent branches in which it is located. Once the parameter appears, double click on the tick box to the left of the parameter name. When the tick mark is on, the parameter appears in the Animated Parameter Stack, where the time variation of the parameter is set up (see below). Note that newly created parameters or objects do not automatically show in the parameter tree. To have them appear click on the Refresh button in the menu bar at the top of the Animation Module. Animated Parameter Stack: The Animated Parameter Stack is the list of parameters that are selected from the Parameter Tree to be changed, i.e. animated over time. ​ The first column shows the Parent branch in the Parameter Tree, the second is the name of the parameter. The third column contains the value of the parameter at the current time of the animation time line. ​ To select a parameter click on the row for that parameter. Automatically its animation graph will be shown. Animation Graph (not shown): In the Animation Graph you set up how the parameter selected in the Animation Parameter Stack changes over time. Note that in this graph the x axis is in units of time as defined in the Parameter Panel on the right (see below), whereas the Time Line at the bottom is in terms of the frame number. ​ The graph is not shown here . It work the same way as other graphs in Shape. For more information on how to set up a graph see the manual page on Graphs . Parameter Panel (right side) ​ General: Timing and frame numbers are set up in this tab. Name: The base name of for the output frames of the animation Start Frame: The frame number at which to beginn the animation. It may be necessary to start from a position different from 0 or 1 when an animation was interrupted or if several will be concatenated. ​ # Frames: The total number of frames for the duration of the animation from the Start Time to the End Time . ​ Start Time & End Time: in terms of time units (see below) when is the animation meant to start and end. ​ Time Units: Select the desired time unit from the drop-down list. The default is Years. Make sure the unit in the Variable tab is the same or consistent with the needs for this model. The animated variable that is selected and displayed in the graph uses the units from the Variable tab . Occasionally these units need to be different from each other. ​ Fields: Include the calculation of field lines, magnetic or velocity. ​ Distribute: Recompute the distribution of particles for each frame. ​ Render: Do a full render at each time step. Camera animation with "Autorender" on in the Render Module does not require this, since the model grid does not change and is calculated either before the animation is started or with the first frame. After that autorender is used if the Render flag in the Animation Module is off. Variable Some control parameters for the animated paramater that is currently selected in the Animated Parameters Stack . ​ Time Units: The time units to be used for this variable. Make sure it is the same as the Time Unit in the General tab or you are certain of the animation graph in this context of a different general time unit. Enabled: Enable the animation of this variable. If for some reason you disabled this variable, then later you might wonder why it doesn´t change in an animation. It may well be that you forgot that you disabled it. So, if something in your animation doesn´t change as expected, make sure all the variables that you need change are actually enabled for animation. ​ Stamp: The total number of frames for the duration of the animation from the Start Time to the End Time . ​ Stamp Format: The number format for the numerical stamp. ​ ​ Output: Here you define the output format and what you wish to output and where on disk it is to be placed. ​ Directory: Set the output directory for the individual animation frames. Note that the name of the files is set in the General Tab. Image Type: Specify the image type by writing the standard extension for the image. For instance, if you wish to output PNG format images, then write ".png". ​ 3D Mesh: Output and image of the 3D Mesh. Note that it is not the mesh itself that is output, but rather an image of the view in the 3-D Module. ​ Hydro: Output the full data from the hydrodynamics module at each time step. Note that, depending on the resolution, this might lead to a large amount of data to be output. ​ Plots (Images): Output images of any graphs that the animation might generate in the Graph Module. You can adjust the image resolution for these outputs. ​ Plots (Ascii): Output the ASCII values of any graphs that the animation might generate in the Graph Module. ​ Math Variable: Output any math variables that change over time during the animation. ​ Stereo: Output stereo images. ​ dStereo (deg): The parallax anglee. This is the difference between the horizontal camera angles for the two stereo images. ​ ​

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

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.

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

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.

Physics Module Overview In the Physics Module you define the radiative properties of gas and dust components. Materials or "species" are set up which then are assigned to the objects from the 3D Module . This section covers how to access and use the interface functionality. For a more detailed account of the underlying physical and numerical procedures and assumptions, please refer to the Theory section of the manual or to the PDF document "Radiative Transfer in Shape" . ​ In general, we have tried to keep the physical calculations in line with the general philosophy of Shape, i.e. keep it simple and fast, but good enough to capture the most important phenomenology to allow qualitative and first order quantitative analysis. ​ Units: Note that contrary to most of the astrophysics literature, in Shape we use Standard International (SI) units, i.e. MKS units based on meter, kilogram and seconds. For example, astronomers used to thinking in terms of particles per ccm should multiply all the densities by 1e6 before they put them into the density modifier. If needed, unit conversions can be done easily on a number of websites, e.g. at UnitConversion. ​ Workflow ​ The basic procedure is to define material species in the Physics Module where you specify the radiative properties. The species are then assigned to a selected object in the 3-D Module using the Species drop-down list in the General tab. ​ By default, i.e if you do not specify a species, an objects has purely emitting species that is proportional to the density squared (n^2) ​ To change that default species you first select a basic species from the Species list that opens by clicking on the blue "+"-button on the toolbar at the top. Select the species in the species list and edit its properties. ​ ​ ​ ​ ​ ​ Selected species can be removed from the list by clicking on the Remove button on the main menu. Copy ing is a good why to use an existing species as a basis for a new one by just modifying some of its properties. The Sort button sorts the species in alphabetical order. ​ Selected species can be saved to disk individually or in groups using the Save button . This allows one to create a library of repeatedly used species. They can be loaded into any other project using the Open button. ​ ​ ​ Custom Species: The most likely and general species that you can choose is the Custom species. It allows to define all its properties manually. We discuss this species in some detail. ​ On the right there is a screenshot with the general options . ​ Name your species in a descriptive way that makes it easy to identify. This becomes important in complex projects with many different species. ​ Enable tick box: Species can be disable by switching off the Enable tick box . If more than one object use this species, they will all be switched off. ​ n scale: The n scale parameter allows you to multiply the density n of all objects that use this species by this factor. The resulting density will be used only for this species. Other species that an object may also use will not be affected by this factor. This allows to use different scales for the density depending on the species but specifying a single object mesh and density distribution. ​ Emitter boost: If the scattering and/or ionization options are used, then for this species only, the local brightness of the received emission from the emitter is multiplied by this factor. This is useful, for instance, when you need to brighten the objects scattered light without changing the emitter itself or the intervening absorption. ​ Color: In the color rendering mode by default an object is rendered with the color assigned to the mesh in the 3D Module. However, the rendered color can be changed easily without changing the mesh color by clicking on the color swatch (white rectangle) and selecting a different color. For this to take effect switch on the Override Color tick box. When selected, the color swatch above the flag determines the color of the object and overrides the color resulting from the physics setup. NOTE: There are many other ways to change the rendered color of an object using the spectral settings for the emission. They are explained below in their respective parameter settings. ​ Contribution : In the Contribution section different contributions to the radiation transfer can be enabled or disabled. They include the Emission (on by default), Absorption, Scattering, Ionization. We can also specify whether for ionization. If you do not wish to define the Absorption explicitly, then it can be calculated using Local Thermal Equilibrium (LTE) conditions. For that switch on the Absorption, LTE and Calculate K(j) flags. ​ You define the emissivity, absorption and scattering coefficients as a function of wavelength. First activate one of these coefficients in the Contribution area (there may be more than one active). Then Edit their wavelength dependence by setting up the panel that pops up in a separate window after clicking on the corresponding Edit button. ​ Coefficient: The pop-up panel for each coefficient mainly consists of an analytic function f(x) that is set up in the Function tab at the bottom, A display and control panel of such functions in the middle and the graph of the functions at the top. ​ In the graph, when using an analytical function, the reserved variables n and t give direct access to the density (by number) and temperature fields, respectively, as provided by the corresponding modifiers in the 3D Module. ​ The x variable in this graph refers to the wavelength in meters. Remember that the meaning of x varies by context throughout Shape. ​ Spectral distributions from external data can be used, too. To do this remove the default function first by selecting it in the center section of the panel and clicking on the Remove button. Now click on Add and from the pop-up menu select Point-Function. Now you can load the external data file by clicking on the Load button. The data format is ASCII in vertical column with the wavelength in meters in the first column and intensity in the second column. ​ For the Scattering and (Photo-) Ionization coefficients the same setup is required as a function of wavelength as for the emission coefficient. ​ For scattering, in addition, a scattering function as a function of angle may be defined via the Phase Function . In this context the variable x is the angle in units of radian. By default there is a Henyey-Greenstein with the coefficient g=0 (isotropic scattering) applied. The coefficient g can be set in the Variables tab (or in the Math Module vía a Global Variable). ​ Note that for scattering to work, you need at least one emitter objects in the 3D Module. ​ ​ ​ Dust Species: The dust species has the options to contribute by Emission , Absorption and Scattering . ​ The grain attributes include the range of radii (assuming a power-law distribution with parameters a, a_min, a_max, q), the index of refraction with the real part n and the complex part k. k controls the absorption. Both, n and k can be set as a function of wavelength, by editing the corresponding graph (click on the Edit button). ​ The default option Custom in the Type drop-down menu has a simple default setup, which can be changed as required. There are a few additional options from the Type drop-down list approximating different types of grains. Here the index of refraction n and the absorption coefficients are based on data. A graph of these can be seen by clicking on the corresponding Edit button . To fully appreciate you might have to adjust the settings of the graph (right-click) ​ The Scattering currently is single scattering. Dust scattering calculations have the option to include a scattering phase function. To see and edit the function click on the Edit button to the right of the label Phase Function . The preset is the Henyey-Greenstein function . The single parameter g of this function can be changed in the variables tab of the graph. The user can change this function. Note that in this context the variable x stands for the angle in units of radians . For scattering calculations remember that you need at least one Emitter object in the 3D Module. The properties of the Emitter can be set after you select Emitters from the Object Type drop-down menu at the top-right of the 3D Module. ​ The default dust model is an approximation to the Mie model. For a the full Mie computer enable the corresponding flag. For more details on the approximate Mie calculation see the document "Physics in Shape" . ​ ​ Atomic Species: ​ The atomic species allows to calculate the emission properties based on the atomic transition coefficients and the physical conditions like density and temperature in the object. ​ NOTE: Usage of atomic species for the calculation of emission and absorption requires detailed knowledge of the underlying physics. We recommend the application of this option only for users that are experienced in this area. Testing of the atomic calculations in Shape has been limited so far. It is advised you solve your own test problems comparing the results either with analytical calculations. ​ You have the choice from two databases for the atomic coefficients: Kurucz and Chianti . To apply one or the other database select the Database at the bottom of the Species Panel. ​ Now select the Ionization State of the species in the Misc panel of the Options. For hydrogen the ionization state has to be set to "0", because lines only occur for neutral hydrogen, even thought they might come from a recombination. Processes that involve free electrons, i.e. Bound-Free (BF), take the next higher ionization state into account automatically. Now select the Database for this particular species from the drop-down menu. Click on the Reload button to read the lines. If the background of the Element label changes from red to green, then you successfully read the lines. If it is still red, one or more of the settings are incorrect. ​ To see a listing of the lines and their atomic properties click on the View Lines button. It opens a table of the atomic properties in the database. If you want to see only the lines in a certain wavelength interval, you can set Constraints for a minimum and maximum wavelength, as well as for the minimum and maximum Einstein coefficients (e.g. to select for allowed or forbidden lines). ​ The Contributions area allows you to select from various radiative process to be included in the calculations. The label B stands for Bound and F for Free. Note that not all processes are available for all the atoms, except for hydrogen. ​ The numerical factor the right of the contributions is a scaling factor. By default it is set to 1. The toolbar of the Physics Module

The Squish Modifier changes the distance of a vertex perpendicular to a plane (default: local xz-plane), The action is similar to the Squeeze Modifier , except that it´s planar, not radial around an axis. ​ The Magnitude dialog allows you to define the squish 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. ​ Widget: The Widget opens the Widget Dialog. It allows you to change the direction of the Squish Modifier. The purple arrow will indicate the direction of its action. Modifiers: Squish

Render Module Properties Panel: Spectrum Properties Panel: Spectrum ​ Shape calculates the physical radiation properties over a user-supplied range of wavelengths. By default this range is given in terms of velocity (km/s) from a reference wavelength (5e-7 m). This allows a straightforward calculation of position-velocity (P-V) diagrams from a default setup. These defaults can be changed to a range in terms of wavelength in meters (m) that typically ranges from 3.5e-7 to 7e-7 m for the optical spectrum. For the modeling of radio observations the spectral unit can be set to Hertz (hz). ​ Min & Max: The start and end of the spectral interval. Lambda_0 (l_0 ): The reference wavelength (rest wavelength) for the calculation of red- and blue-shifts in terms of velocity. # Bands: The number of spectral bands to be computed. The spectral range is divided in this number of sections of uniform width. If the shape of the spectrum is important or spectral line structure is meant to be computed, this number is set between 20 and 100 or so. When the overall color of an image rendering is all that is needed, then between 5 and 10 bands is usually sufficient.

Overview ​ For many astronomical objects spatially resolved observations of the velocity structure are a key constraint to find their 3-D structure. Therefore it is essential to have a way to model the velocity structure of an objects in Shape. This is provided in the form of a Velocity Modifier that can be assigned to any geometric object . ​ Since velocity is a vector , the velocity modifier is probably the most complex modifier and, in some aspects, conceptually different from scalar modifiers such as the density modifier. ​ The main control panel of the velocity modifier is similar to other modifiers exposing the f0 scaling factor that is also incorporated in the Magnitude graph. ​ The main difference to other modifiers lies in this Magnitude graph , which we are going to discuss in some detail. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Similar to other modifiers there is the set of graphs on the right and the options on the left. We will therefore focus on the drop-down lists on the left side for the General options, the types of Vector Field and the Dependencies. ​ General: The general options are again similar to other modifiers where you can choose as modes Custom and Analytic, as well as the type of coordinate system (Cartesian, Spherical, Cylindrical). Here you can also set the f0 scalar factor that multiplies the final vector. f0 is also exposed at the higher level main panel for the velocity modifier. ​ Vector Field: This is one of the two key differences compared to other, scaler modifiers. This drop-down list allows you to choose from a variety of predetermined vector fields , including Radial, Disk Rotation, Elliptical, Collimated, Random, Custom, and Path . ​ The practical importance of these options is that all except the Custom field preset the direction of the velocity vectors in space. For these one only needs to set the magnitude as a function of position using the graphs on the right. For these fields the graphs on the right work the same as in other modifiers yielding the scalar magnitude of the velocity vector . Except for the case of the Custom field the coordinate tabs do not represent the velocity components! The Custom field is described below. ​ There is however an important difference. By default it is the same function, separable in their coordinate directions, as for other modifiers. In the velocity modifier it is, however, possible to choose on which spatial variable (u,v,w) each of the vector components (vu, vv, vw) depend on. Here (u,v,w) corresponds to the coordinates in the different types of coordinate systems. In Cartesian coordinates, for instance, the vx component may be defined as a function of the y-coordinate. It is important to note, however, that the actual variable in the analytic expression always x. What changes is its meaning according to the options that have been chosen. This allows to set up quite complex velocity fields. Additional complexity can be obtained by adding several velocity modifiers in the modifier stack. ​ Radial Type Velocity Field: The Radial Field sets all the velocity vectors to point away from the local coordinate system of the velocity modifier. lf the magnitude is negative, the vector points towards the coordinate origin. A typical use case for this vector field are expanding nebulae such as supernovae and planetary nebulas. ​ Disk Rotation Type Velocity Field: The Disk Rotation Field sets all the velocity vectors in the direction perpendicular to the cylindrical radial and the z-direction from the local coordinate origin of the velocity modifier. This velocity field is suitable for rotating disks such as spiral galaxies or accretion disks. ​ Collimated Type Velocity Field: The Collimated Field is an easy way to set up a jet-like outflow with an opening angle as a parameter, which by default is zero. ​ Custom Type Velocity Field: The Custom Field is fundamentally different to the others in that each of the graph tabs on the right actually represents the corresponding vector component instead of just a factor to the magnitude. Hence, the total magnitude and direction of the vector is given by the vector addition of these components. ​ An important tool help with the velocity field modeling is the Field modifier , which allows one to visualize the vectors in the 3-D views of the 3-D Module. ​ Modifiers: Velocity

Coordinate Systems ​ The hierarchy and types of coordinate systems is key to the flexibility of the modeling of structures and velocity fields. Video Tutorial The Modifier Stack ​ Graphical representations of functions are a fundamental tool to control parameters that vary in space, time or wavelength. Video Tutorial Graphs ​ Graphical representations of functions are a fundamental tool to control parameters that vary in space, time or wavelength. Video Tutorial Textures ​ Textures are either random procedural 3-D structures or external images that determine structures of density, temperature or others. Video Tutorial Particles Particles are used to generate complex specific structures by spraying them interactively on surfaces and into volumes. Video Tutorial

Render Module Properties Panel: Camera Properties Panel: Camera ​ The Camera parameters include various rotation angles in different coordinate systems. The are either observer oriented, such as position angle (PA) or inclination. Or, they are rotations around the Cartesian world coordinate axes. ​ One can change from Orthogonal camera projection (on by default) to perspective camera. Furthermore various filters or "modifiers" can be applied to the data prior to the final render or after the render. These modifiers are discussed in more details below. Scene size: The width of the computing domain in terms of physical units, which by default is meters (m). This number corresponds to half the voxel size assigned to the Resolution parameter above. The physical domain runs from -(scene size):+(scene size). Scene center: The center of the cubic computational domain may be shifted in the physical scene that might be larger than the rendering domain. Setting a smaller domain with a shifted center may be useful for testing purposes or for achieving higher resolution outputs for certain regions. HD: The high-definition (HD) render is activated with this flag. It does not use a predefined cubic voxel grid and works similar to a ray-tracing engine that integrates to the pixel plane. If there are computations that depend on light sources, such as dust scattering, it is computed along the way. This may require more time, but is much less memory intensive. Therefore higher resolutions can be achieved. Fast renders, e.g. for camera animation movies, is not possible, however, since the some information is not stored for quick rendering from the precomputed voxel grid. Scatter Grid Size: When the HD render mode is switched on and scattering or photo-ionization processes are to be calculated, a sub-grid needs to be set that comfortably fits into RAM, but is as large as practical to avoid potential artifacts at grid limits. Recommendable is about half of the size that you can fit, if HD is off. Save grid: The grid data used for the final render step are retained in memory. This allows the Autorender (see below) to work. It requires more memory though and hence limit the achievable resolution smaller than with this option off. So, if you are doing quick tests or plan on rendering camera animations, then this option is convenient to be on. Auto render: If the HD is off or the Save grid flag is on, then data of the full grid have been saved and can be used to quickly render the scene for different camera views and animations. When you change the parameters of the camera the rendering updates automatically. The effect is not "real time" and may take a few seconds, depending on the resolution. Use window: For quick render in HD mode that require only a small portion of the image to be rendered, you can set a window using the Window Button above the image. Click on the icon with the square and then drag out a rectangle with the left mouse-button pressed. If the Use window flag is on, only this region will be rendered. This reduces the rendering times during model development when it is sufficient to see only part of the model. Overlay: Occasionally it is convenient to retain the previous image or images and add progressive images together. This is useful for diagnostics or simply as a nice "special effect.

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