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

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

The Stretch Modifier changes the mesh vertices along a chosen axis (default: local z-axis) as a function of distance from the axis. There are two different Modes: Scale and Absolute . When you switch on Absolute, the values in the Magnitude graph are the distance from the axis in units of the current project instead of a scaling factor based on the original shape of the mesh. The Magnitude dialog allows you to define the stretch amount as an Analytic Function of position along the reference axis. You can also use a Point graph where you can generate an arbitrary function by manually placing points and setting the spline interpolation. To do this, select Point from the Function drop-down list under the graph. The example graph on the lower right shows the way it was done for the example mesh displayed below. It scales a spherical primitive mesh to a disk with a hump around a certain distance. This modifier is ideal to set up a disk with a complex structure. Modifiers: Stretch

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

Filters for physical quantities in Shape can be defined here. Movie Module Overview In the Movie Module you concatenate individual animation frames into a movie. It can be reproduced in the integrated movie player and saved to disk for viewing in an external movie player. Several movie can be displayed side by side. These can then be saved into a single movie file. This is useful when comparing different visualizations of the same object simultaneously. Menu Bar: Create: Once you loaded the animation sequence of images, click on the Create Button to render the movie in a single file for viewing in external movie players. Add: Add a second or more movie panel to the right of the current one. Several frames can be rendered side by side into a single movie. Delete: Remove the currently selected movie panel. Select by clicking on the panel with the left mouse-button. Load: Load a sequence of animation frame into the currently selected movie panel. When you click on the Load button, a file dialog open. Select the first of the frames. Then go to the last one of the sequence and Shift-Left-Click it to select all the frames from the first to the last. Click "Open" to load them into the frame buffer of the selected movie panel. Options: Name: Set a descriptive name for the filter. This name appears in the Filter selection drop-down list in objects in the 3-D Module. Enable: The check box activates or disactivates this filter for all objects that use it. Mode: Here to can chose the Mode of the filter, which refers to whether the range between the Min and Max values is to be included or excluded. Clamp: If checked then all values above the Max values are set to the Max values. If unchecked, then the value is set to zero. Min & Max: The minimum and maximum of the filter range.

Render Module Overview This module takes care of the rendering of image and position-velocity diagrams. The output of 3-D volume data is also controlled from here. Overall the Render module consist of the render area where images and position-velocity (P-V) diagrams are displayed on the left side. On the right side you have the render Properties panel . It can be hidden by clicking on the Properties pane on the right. By default the General rendering parameter panel is open. From the drop-down list at the top of the panel several other sub-panels can be opened that deal with the settings for the virtual Camera , the Spectrum , the 3-D Output , Units and those of the Selected Window . We will deal with each of these in their respective sections below. In the default configuration only one image is rendered. If more images and P-V diagrams are to be show, those can be added and configured in the Windows drop-down menu above the render window. In the example above two columns have been set and three P-V windows have been added to the default image window. The slits for each P-V window is represented on the image window. In order to delete a window click on the X icon in the top-right corner of the window. Note that this icon may be hidden if the overall Shape interface has been reduced in size. If so, then resize the user interface until the X icon appears and then click to delete the corresponding window. The Image Render Window As the name suggests the Image Render Window displays the output images from the rendered model. To keep order when you have several windows, they can be named individuall y to remind you of the expected content. Just replace the text "Window 1", etc., in the text field of the menu above the window. In the same window several types of images can be displayed by selecting one of the five colorful icons above the image. By hovering over an icon a tool-tip gives a brief hint to what the corresponding image displays. By default a grey-scale image is displayed that represents the brightness variations that have been integrated along the line of sight. The selected type of image is marked by a blue border around the icon. The "Color Image" displays the each sub-object with the color that was assigned to its mesh in the 3-D Module. This allows to clearly distinguish and identify them for diagnostic or visualization purposes. Importantly, in the P-V diagrams it helps distinguishing the contributions by different parts of the model. The "Red/blue Image" displays the model in terms of its red and blue shifted regions. Volume cells with a velocity vector that points more towards the observer is colored blue and those with a line of sight component that points away are red. Regions were line-of-sight integration has a mixture of red and blue contributions will appear in a mixed color tending towards white. The "Rainbow Image" is similar to the red/blue image in that it color codes the velocity field along the line of sight. The difference is that a continuous color coding is used that follows the spectral rainbow colors. The range of velocities to be color coded can be set up in a right-click menu. The "Spectrum Image" uses the physical spectrum as set up in the Spectrum section of the Properties Panel on the right of the Render Module. Again the color coding follows the rainbow colors that are distributed through the range of the physical spectrum. Now the rendered color will depend on the full physical setup of the model. Therefore this image type is used to render physical and photo-realistic models. The "Image Modifiers" handles the operators (modifiers) that process the rendered image in terms of brightness scaling, contours, inversion, etc. The "Move Slit" icon activates the interactive changing of the slit parameters such as position and width. When active the slit width is change using the mouse wheel. The horizontal position is changed by pressing and dragging the left mouse button. Vertical size and position are change the same way while keeping the "y" key pressed during the operation. The "Zoom Image" button activates zooming in and out of the image using the mouse wheel. The "Pan Image" button activates moving the image left, right, up and down by dragging it with the left mouse button pressed. The "Render Window" button allows you to drag out with the left mouse button a rectangular window on the image. Combined with the HD renderer and the "Use window" option in the General tab of the Render Module only this region will be rendered. This can greatly reduce rendering times if you need high resolution, but only need to see a small region for testing. The "Image Transparency" button allows you to change the transparency of the rendered image to be able to compare with the background reference image. Close and Remove the Window by clicking on this button and confirm in the pop-up window. Properties Panel The Properties Panel on the right side of the Render Module has several section that can be accessed from the drop-down menu at the top. We will deal with each of them in the order they appear in the menu. General The general project properties are set up in this panel, such as spatial resolution, type of renderer, memory management, autorender, etc. Camera Camera orientation angles are set. The parameters include position angle, inclination, and angles with respect to the axes of the global coordinate system Spectrum The spectral range for the physical radiation calculations is provided here in various possible units. Output Ouput of the full 3-D cube to file in different forms. Selected Window Key parameters of the currently selected image or P-V window can be set in this panel. General Camera Spectrum Output Selected Window

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.

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