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

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 .

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.

The Taper Modifier is designed to smooth the edges of the density in a mesh as exemplified by the renderings below. It is a scaling as a function of inwards distance from the inner and outer surface of the mesh. The first image on the left shows a bipolar structure with a constant density. Here the emission goes right up the mesh and make evident the coarse mesh structure. In the second image a Taper Modifier was applied with the Taper function as shown below the render. As configured it generates a gentle glow around the surface. The render on the right has a different Taper function. It shows how it can be used to generate more complete multi-shell structures. Note that each hump in the Taper function generates two shells, one from the outside surface and a second from the inside surface. If the mesh has no inner surface, only one shell is generated. Note that for complex high resolution meshes the Taper Modifier is computationally expensive. So, balance between the computing time and the need for it. Much testing can be sped up by temporarily disabling the Taper Modifier while it is not needed. Name: Provide a name for the modifier that closely describes its function. Taper: Opens a graph to set the Taper function. The Taper function is most conveniently set up as a Point function. To smooth the edges, set the value to zero at position zero and transition to a value of 1 at the desired distance from the surface. Note that this transition scale does not change with position in an object. It may therefore not get to 1, if there is a shell that is thinner than the transition scale. This is the case in the example below, where the shell becomes thin towards the center and therefore the emission very low. This can be compensated for partially by adjusting the Magnitude graph. Magnitude: A graph that allows one to compensate for "lost" emission, from the taper in regions of these shells. Modifiers: Taper

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

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

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

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.