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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.

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.

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

The Size Modifier scales the mesh. Different scaling factors can be applied along the x, y and z axes. The Size operator only changes the vertex position and does not affect the local coordinate system, i.e. the reference point for other modifiers, such as the velocity field, are not changed. Name: Provide a name for the modifier that closely describes its function. Lock: When enabled, this flag keeps all the scaling factors the same. The last change in any axis is adopted for all axes. x,y,z: The scaling factor by axis. Anchor: The anchor is the xyz position in space around which the scaling will be applied. This may shift the whole object towards or away from this position, depending on whether the value is smaller or larger than one. A change in anchor position does not affect the local coordinate system, it only moves the vertices of the mesh. Modifiers: Size

Modifiers The Boost Modifier is basically an enhanced version of a Boolean object or modifier. The idea is to use one mesh to regionally change the properties of another. However, instead of completely cutting out or adding to a mesh, it scales the properties by some factor that may vary spatially either through a function of space or a texture. In the example below a sphere contains a complex mesh structure which has a Boost Modifier that is linked to the spherical mesh. In the first rendering below, the boosting factor was set to zero, such the sphere is hollow in the region of the boosting mesh. In the second examples, the boosting factor for the density was set to 2, enhancing the density by that factor. The Boost Modifier is applied to the mesh to is meant to change another, in this case the inner mesh. Note that more than one boosting mesh can be applied to the main mesh. Parameters: Name: If multiple Boost Modifiers are used, make sure to name them adequately for ease of identification. Enabled: When deselected, the modifier will not be applied. Boost: This is the boosting factor that is applied to the main mesh. It can be a mathematical expression and function of the main variables such as n (density), T (temperature) or P (pressure). Note that these are the properties of the boosting mesh object, i.e. they relate to the modifiers within the boosting object itself. To make the hollow structure above, this factor was set to zero (0) and 2 for the enhancement of the structure. If set to "n" as shown, the factor is taken from the Density modifier in the boosting object. This may be a function of position, including the texture. This allows for a complex manipulation of the region covered by the boosting object. Variable: From this drop-down list select the variable upon which the boosting shall act on in the main object. Note that this is different from the variables in the Boost factor. Operation: Select the operation that the Boost Modifier shall perform on the main object. You can select from Scale, Add and Replace. Applied Object: From the drop-down list select the objects on which the Boost modifier shall act on. Several objects may be chosen. Hide itself: Generally the boosting object is used only to act upon other meshes, but is not rendered itself. This may, however, not always be the case. So, if the boosting object is a rendered object in itself, disable this flag, such that the boosting mesh itself is rendered, too. Modifiers: Boost

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.

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

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

Filters for physical quantities in Shape can be defined here. Modules: Hydrodynamics Overview Hydrodynamic simulations are an important area of astrophysics. 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. Furthermore the results of the simulations can be directly incorporated in mesh-based renderings without the need of external software. From the hydrodynamics, just like any other mesh model, can be used to generate spectral information. Filtering using the Filter Module allows you to extract regions with particular properties based on the filter settings. Exporting of the hydrodynamic simulation data allows later incorporation of the data or parts of them into a completely different rendering project. The simulations in Shape are always intrinsically 3D on a uniform cartesian grid. The numerical algorithm in Shape was selected to run relatively fast in 3D with a minimum of variables to keep memory usage as low as possible, while still allowing to simulate the basic astrophysical phenomenology such as shocks and radiative cooling above a temperature of 10^4 K, typical to photoionized nebulae. The details of the numerical scheme used for the hydrodynamics, its limitations and example applications are described in the following research article: W. Steffen, N. Koning, et al., 2013, MNRAS, 436, 470–478 It is recommended to use numerical hydrodynamics tools in Shape or any other application only with sufficient understanding of the the possibilities and limitations of such tools. This module in Shape was made to make access to numerical hydrodynamics easier, but if you do not have insight into the potential artifacts the numerical schemes produce, especially at low spatial resolution, it is recommended to seek the assistance of someone who does. General Workflow The workflow involves three overall steps: First, you set up the elements of the simulation in the 3D Module. Second, the flow parameters are set up in the Hydro Module. The simulation is started and previewed here, too. Rendering and analysis is then done as usual in the Render Module vía a dummy rendering object that is set up in the 3D Module. See below for more details on how to set up a simulation in the 3D Module. User Interface The user interface of the Hydro Module consists of three main parts: The visual preview panels, the menu bar at the top and the parameter panel on the right. From the drop-down list at the top of the parameter panel you have access to four sub-panels: General, Flow, Boundaries and Camera. Menu Bar Calculate : The Calculate Button starts a hydrodynamic simulation. Preview : The Preview Button visualizes the initial setup of the simulation in the preview windows, where you can inspect the distribution of density, speed, temperature and pressure. Add : Add a new windows. You can add several new windows to the preview visualization area. This allows you to simultaneously supervise the evolution of different physical quantities or look at them from different viewing angles or filter conditions. Refresh : Refresh all views to the current state of the hydro simulation. Cascade & Tile : Select how to arrange multiple preview windows. They can also me manually arrange by clicking on the top bar and drag them around. Preview Preview : Each of the preview windows gets a new icon on the menu bar. Change the name in the camera parameters panel on the right to suitably represent the content of the window. Save & Load: Save or load the complete state of the hydrodynamic simulation for the current timestep. This allows you to stop the simulation at this time and restart the simulation where you left off after loading the data back with the Open button. The Open button opens the file dialog to select the previously saved file. Loading a file also allows you to use the result in a different project and render it with a different mesh based scene. After loading a data set click the Preview button on the Menu bar to see the simulation preview. How to set up a hydrodynamic simulation in the 3D Module Numbers that you need to start: The physical size of the computational domain in units of meters. Approximate densities (in particles/m^3) of background and active objects Initial velocities in km/s (in the 3D Module), which are then converted automatically to m/s in the Hydro Module and later back to km/s in the Render Module. Filters in the 3D Module require km/s, whereas those in the Hydro Module require m/s. The timescale on which the simulation is likely to finish in seconds (note that 1 year is approximately p x10^7 sec, which easy to remember) . Setup Render Module The first thing to do is to set the Scene Size and Resolution in the Render Module . Scene Size: The physical size from center to edge of the whole computing domain in meters (you may have to choose the correct units in the Units Tab of the Render Module). Resolution: The voxel resolution for the rendering. This does not need to be the same as the hydro simulation resolution with is set in the Hydro Module. Setup 3D Module Hydro Type: Each mesh object in the 3D Module has to be assigned a Hydro Type in the Hydro tab on the right. Background: The computing domain can not have any region that is completely empty. Therefore there has to be exactly one object with the type Background. The mesh of the background object has to enclose the full domain. Best to use a cube object with the size of the domain or larger. The background distribution of physical properties such as density or temperature may or may not be uniform as needed. Initialize: Object that receive all their properties at the beginning of the simulation and change only passively as a consequence of the simulation receive the hydro type Initialize. These could, for instance, be clumps or rings of high density gas. Boundary: Objects that are updated at every timestep or have to remain the same during the simulation are of type Boundary, since they act like a boundary condition. These could be stellar winds or jet that have to inject gas in a controlled, possibly time-variable manner. Variability is controlled in the Animation Module. Modifiers All hydro objects need to have at least one set of modifiers that describe their physical properties. These can either be [Density, Temperature, Velocity] or [Density, Pressure, Velocity] . Density, Temperature and Pressure must not be zero at any position in the domain otherwise the simulation will proceed only for a limited time or crash immediately. The Velocity may of course be zero. Other modifiers may be added as usual to control the shape, orientation and animation of the objects. Any of the modifiers may be animation including those for the physical properties. To some extent Boundary objects can be interactively moved around with the cursor or by changing numerical parameters while the simulation is running . Set up Hydro Module General Tab Grid Size: The number of cells in each direction of the cubic simulation domain. It is the same in all three dimensions. Note that the computational time and memory required for a simulation strongly depend on the Grid Size. While memory increases with the power of three , the required time increases as the fourth power of this grid size, not third power. This is so, because for smaller cells in the same physical domain the time step is also smaller. Therefore to reach the same final time, more time steps are necessary. So, ramp up this number from below, say starting at 64 and monitor memory and computing time as you increase the resolution. The numbers may be any number, no need to be multiples of 2. End time step: The number of time steps to be executed before the simulation is automatically stopped, unless the End Time is reach first. End time: The physical time in seconds after which the simulation shall be stopped automatically, unless the End Time Step is reach first. Resume: If a simulation as stopped or has been loaded from file, enable the Resume flag to continue the simulation. Click the Calculate Button on the Menu Bar to start resuming the computation. Animate: If Boundary Type objects in the 3D module vary in time in their properties, geometry or position/orientation via the Animation Module, then the Animate flag must be on for this time variability to take effect. Pause: Set this flag to temporarily pause the simulation. This can be useful to save the current state to file or generate a rendering of it in the Render Module. To continue the simulation remove the flag. Filters: For visualization purposes various filters can be selected from the drop-down list that select certain regions according to their physical properties. The filters themselves are set in the Filters Module. Note that SI units are used, including m/s for speed (in the 3D and Render Module the speed it in km/s, so different filters are required for the same filter range). You may combine more than one filter. Flow Tab Courant #: The Courant number is a number that controls the stability of the solution of the numerical differential equations of fluid dynamics. This so called CFL condition expresses that the distance that any information travels during the timestep length within the mesh must be lower than the distance between mesh elements. In other words, information from a given cell or mesh element must propagate only to its immediate neighbors. The number should be less than 1, recommended to be less than 0.5, depending on the particular conditions, incl. the strength of the cooling. Note that making the Courant # smaller, also decreases the time step and hence increases the total computing time. Gamma: The adiabatic index of the gas in the equation of state. For monoatomic gas the value is 5/3 (1.66). Eta: The numerical viscosity coefficient. This exchanges some fraction of the conserved physical quantities between neighboring cells and helps to maintain stability. The cost for the stability is diffusion, i.e. for instance high-density regions expand into low-density ones without the need of a pressure gradient. So, the value should be as small as possible, e.g. 1e-4 or smaller. High contrast regions are particularly affected. T0: The minimum temperature in Kelvin to be maintained if cooling becomes too strong within a timestep and would reduce the temperature below zero. For photoionized regions this value may be set to values of order 1e4 K. Otherwise to a reasonable lower value that represents physically plausible low values. Cooling: Enable or disable explicit cooling. See the paper by Steffen et al., (2013) for details. Cooling factor: Apply this factor to the explicit cooling calculation. Boundaries Tab For each side of the cubic domain the boundary condition may be set to Outflow or Reflection . If your simulation is symmetric with respect to a certain plain, then this plane could be one of the boundaries and then a setting of Reflection can be used. Most other applications will have an Outflow condition everywhere. The difference between the two conditions is only how the velocity components of the second to last cell is copied to the last cell. For the Outflow condition the component perpendicular to the boundary is copied as it is, whereas in the Reflection it is inverted. Camera Tab Controls the camera viewpoint and physical variable to be visualized in each preview window. Click on the preview window for which the parameters shall be shown and set. Name: Set the name of the preview window. It is convenient to set it similar to the physical variable to be displayed or some other name that somehow identifies the content. Variable: Select the physical variable to be visualized in the preview window. Note: When you move the cursor over the preview window a value for the physical quantity at the cursor position is shown in the top-left corner of the preview window. This is the integrated value along the line of sight. To see the local value use the Render Slice functionality (see below) to extract a single slice. Then the value shown represents the local value of the variable. Enable: Enable or disable this camera. Ortho: Enable or disable orthographic projection for this camera. Image: Edit the image display parameters for this camera. X Y Z pos: Set the camera position. The X Y positions are currently not functional. When the Ortho mode is disabled, the Z position in terms of the size of the domain (=1) changes the distance of the camera. X Y Z rot: Set the rotation angles of the camera per axis in degrees. The X & Y rotation can also be changed interactively by dragging the mouse over the preview window with the left button pressed. If the resolution of the simulation is small enough for your system, the preview responds interactively at a reasonable framerate. The interactive preview is rendered on the CPU and is therefore efficient only for relatively small resolutions. Render Slice In the Camera Tab you can scroll down to find the Render Slice controls. They allow you to display slices of the full simulation domain to closely inspect particular regions. The slices go along the coordinate axes. The initial position in terms of cell number are set with the sliders labeled X0, Y0, Z0, while the width of the slices are dX, dY, dZ. If you click on the slider handle a number field hopes that allows you to numerically set the value. It is convenient to set the Z width of the slices to 1 and the position to the middle. Then by enabling and disabling the Render Slice with the Enable flag, one can quickly change to a visualization that allows one to read off particular values in the preview window. As mentioned above the local value is only displayed in the preview window, if the width of the slice is set to 1. Otherwise the value shown for the cursor position is the integrated value along the line of sight, where each cell counts with a distance step of 1. For instance, if the integrated value along z is 200 and the domain resolution is 100, then the average local value is 2 along the line of sight at the position of the cursor. Output In the Camera Tab you can scroll down to find the Output section. When enabled it will output the full state of the simulation every dSteps timesteps. Choose a location on the filesystem afer opening the Directory selection dialog by clicking on the folder button. Make sure it is a location with sufficient disk space to accommodate the amount of data that will be saved. Status At the bottom of the Parameters Panel on the right there are three values updated at every timestep of a simulation. They help to judge the current status and rate of progress of the simulation. It show the current total Time in seconds, the current timestep dTime and the number of Step s computed so far. Considering the ratio between the total time and the timestep is very large, then the simulation will be progressing very slowly. This could be a hint to regionally problematic physical values.

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.

They are a key functionality in ShapeX the usage of which should be mastered in order to create the most realistic models. Modifiers determine the properties of the objects as a function of position in space, hence it is important to know as much as possible about coordinate systems in general (Spherical, Cartesian & Cylindrical) and how they are used in ShapeX. See Coordinate Systems for more information on this topic. Modifiers are assigned to an object in the form of a list or Modifier Stack . This list of operators is executed on the object from the top to the bottom. For many of the modifiers the order in which they are executed does not matter. However, some operators, e.g. those that globally or locally involve some form of rotation, need to be stacked in the right order to produce the desired result. It is therefore important to know whether they order can be reversed or not. Knowledge about commutative properties of operators, or sufficient experimentation, is useful here. Modifiers Overview Modifiers are a operators in the 3-D module that allow you to add or change, i.e. modify properties of an object in the scene. There are different types of modifiers, some change the geometry of the mesh objects, others assign scalar or vector type physical properties such as density or velocity, respectively. After adding or selecting a particular modifiers, its Properties are displayed under the Modifier Stack . These can then be edited either by changing parameter value fields or after opening additional dialogs or graphs. Adding or deleting modifiers is done using the blue + and the red x sign, respectively. When you select a modifier you can move it up and down in the stack with the green arrows. More than one modifier of the same type can be applied with different coordinate systems. In some cases you might have to change the Operation setting from Replace to either Add or Scale , otherwise the last modifier of this type replaces all previous ones. Using combinations of the same type of modifiers allows a larger variety of structures to be build. Modifiers can also be copied and pasted with the corresponding buttons. When you use the paste button, a small dialog will open that asks you to decide whether the modifier should be a copy or and instance of the original modifier. When you choose copy then the new modifier will be completely independent from the other. However, and instanced modifier will always change together with its original and vice versa. Instanced modifiers are a great tool to provide the same parameters for more than one object, while only needing to change a single one of them. Types of Modifiers Physical Modifiers Physical modifiers add or change physical properties as a function of position. They include the Density , Temperature , Pressure , Image Texture , Taper , Velocity, GField and BField . The Boost modifier is a helper modifier to the scalar physical modifiers and is used to change those quantities, but depending on the geometry of another mesh object. This is useful, for instance, to reduce or cut out part of the density of one object using another. Geometry Modifiers Geometry modifiers change the structure of the polygon mesh. They include Bump, Curvature, Displacement, Image Displacement , Projection, Random, Sculpt, Shear, Shell, Size, Spiral, Squeeze, Squish, Stretch, Texture Displacement, Twist, Universal, and Warp . The geometry modifiers move the vertices of a polygon mesh within the local coordinate system of an object. If you move or rotate the local coordinate system with a Rotation or Translate modifier, then the geometry modifiers act in the transformed coordinate system. Note that the Displacement modifier is a geometry modifier and moves only the vertices, but not the origin of the local coordinate system is does the Translate modifier. This is useful when you want to move a complete object, such as a small sphere within a fixed coordinate system and apply, for instance, the Velocity or Density modifiers in the original coordinate system. Modifier Parameter Panel: Common Parameters The parameters that modifiers take vary considerably. They are described in the sections for individual modifiers. What they have in common are the Name field and the Enabled flag . In the Name field you can set a name for this particular modifier, which is strongly recommended, since it allows one to easily identify a modifier, which becomes more and more important once the number of modifiers increases for a particular object or for the project itself. It is especially important once the Modifier Module is used to manage a large number of modifiers. As the name implies, the Enabled flag allows one to enable or disable a particular modifier. Modifier Module: The Modifier Module becomes important once a model contains a large number of objects and modifiers. Often different objects have similar basically the same modifiers that have at least some parameters in common. If they are not instances of each other or have their parameters organized as global variables, the Modifier Module allows you to select a number of modifiers and change their parameters in a single operation. It also provides a good way to get an overview of which modifiers are used by which objects as well as the possibility to sort them by type. For more details on the Modifier Module go to its more detailed description in its own section of this manual.

Filters for physical quantities in Shape can be defined here. 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.

Export Module Overview The Export Module exports the 3-D model into various output formats that can then be used as data for external use. It was mainly designed to prepare models for export to the iluvia software for external interactive visualization. The Export Module uses data from an intermediate output of Shape that contains all the radiation information within a cubic grid with uniform voxels. The name and disk folder in which this intermediate file is located are set in the Output tab of the Render Module . Exporting Shape models into new formats for external visualization may be a challenge. This is due to the fact that in Shape you may can use a variety of physical radiation effects, some of which can not be directly mapped to the simpler treatment of emission and opacity in interactive graphics software that rely on ARGB color coding or similar. General Workflow: In the Output tab of the Render Module, make sure there is a valid filename and path provided. The output will be with the extension .ilv . This file is loaded into the Export Module. Then a previsualization is generated by adjusting the parameters on the left and right side of the preview image in the middle. The parameters on the left adjust the behavior on the level of the voxels of the input grid. Those on the left adjust the visualization on the image plane after the preview rendering. The preview attempts to recreate the view of a GPU rendering by simulating a similar shader. It also allows you relatively quick interactive inspection. For low resolution you can interactive rotate the object for inspection. Parameter Panels: Volume: The parameters on the left side of the preview control the values of voxel data cube before it is previewed and converted to a different data format. Note that scaling and clamping these values in the presence of opacity maybe result in non-linear behavior that sometimes is not intuitiv. In combination with the parameters on the output side (Preview parameters), it may require some trial and error to obtain the expected result. Filename: Select the .ilv input file to be used for exporting to an external file format. Click on the icon on to the right of the text box to open the file system dialog and choose a file from disk. Reload: If the content of the input file has been updated and the filename remains the same, use the Reload Button to load the new content. Size: Shows the width of the cube by the number of voxels along one side. Downsample: If the original .ilv file is too large, it can be downsampled x2 in terms of side length by clicking on this button. Intensity range: The range of voxel intensities. Histogram: The histogram of the voxel intensity values opens when this button is clicked. Opacity range: The range of opacity values is shown. Histogram: Shows the histogram of the voxel opacity values when this button is clicked. Intensity scale: Scale all voxel intensities by this factor. Opacity scale: Scale all voxel opacity values by this factor. Max Intensity: Set the value of the maximum intensity. All higher values of voxel intensity are clamped to this value. If the default value of -1 is set, then the maximum value of all voxels is automatically used. Max Opacity: Set the value of the maximum opacity. All higher values of voxel opacity are clamped to this value. If the default value of -1 is set, then the maximum value of all voxels is automatically used.} Show stars: This flag switches on any stars that might be saved in a file that has the same base name as the .ilv file. Show volume: Shows the volume save in the .ilv file. Show cube: Show a line cube that delineates the space domain of the .ilv file. Preview: The Preview parameters to the right side of the preview image window control the preview in the output format. It allows you relatively quick interactive inspection. For low resolution you can interactive rotate the object for inspection. Image size: The preview image resolution in pixels. Lower resolution allows for a faster and more interactive preview. I factor: Intensity factor to be applied to the preview at the image level. Star factor: A scaling factor for the brightness of the stars. A factor: A scaling factor for the opacity. Camera: X, Y, Z rot: The rotation angles of the preview camera around the cartesian coordinate axes (in degrees). X, Y, Z pos: The shifted position of the preview camera around the cartesian coordinate axes in units of the width of the domain (0-1). Zoom: Camera distance from the center in units of the width of the domain. Reset Camera: Set the camera values back to the defaults. Statistics: Shows the Maximum value of the preview image. It is convenient to adjust this to values near 1. Export: Format: Various output formats can be chosen. Most importantly, the DDS format is a standard format that encapsulates slices of the data cube in ABGR image format, that can then be imported in external volume visualization software. This is also the format for the iluvia software that is developed by ilumbra.com where you can fully interactively view your models. The Volume option, is a .ilv file with properties that correspond to the transformation that the Export Module made to the original. The PNG option outputs a sequence of slices of the volume in standard PNG image format including absorption. The slices are in the XY plane and change along the Z-axis of the World Coordinate System. Directory: Select the directory on disk where to output the exported file. Omit empty: When selected, the slices where the emission and opacity are both zero will be omitted from the output. This may save data and may reduce the load on the visualization system that will process the output data. Crop: . When activated, the output will be cropped to a size of Crop size. This is useful for models in which for some reason the domain is significantly larger than the content. Export: Start the export process.

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