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The Shear Modifier changes the distance of the mesh vertices perpendicular to a chosen axis (default: local z-axis) along another axis. The orientation of the shear axis and direction of the shear can be changed by changing the values in the Axis boxes. Choose a value of 1.0 to select a particular axis (setting the others to 0.0). Intermediate value result in an intermediate axis. A better way to set the reference axis is using the Widget. The Magnitude dialog allows you to define the squeeze amount as an Analytic Function of position along the reference axis. You can also use a Point graph where you can generate an arbitrary function by manually placing points and setting the spline interpolation. To do this, select Point from the Function drop-down list under the graph. The example graph on the right shows the way it was done for the example mesh displayed below. Modifiers: Shear

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.

Quick links Modules: Overview Downloads Modifiers: ​ Boost Bump Density Displacement GeoRotation ​ ​ Image Displacement Image Texture PA/Inc Rotation Pressure Projection ​ ​ Random Rotation Shear Shell Size Spiral ​ ​ Squeeze Squish Stretch Taper Temperature Texture Displacem. ​ ​ Translation Twist Universal Velocity Warp Key sub-systems: Overview

Shape The interactive 3-D astrophysical laboratory Images inspire us. Images lead to ideas. Shape was made as a tool to test astrophysical inspiration. Play True or False. By finding out whether an idea works or not, either way, we deliver new insight into nature for ourselves and others. That is why with Shape we make 3-D images of the universe...and more... ​ Shape responds to your scientific creativity for morpho-kinematic modeling or spectral radiation transfer calculations. Create schematic educational visualizations or even photo-realistic images of astronomical objects. ​ Our Introduction and Overview gives you more information about what you can do with Shape. ​ UPDATE REQUIRED (January 21, 2022) Due to a bug in some renders after camera rotation, an update is needed. Please go to the DOWNLOADS for a link to the patch and instructions. SBa Galaxy This 3-D volumetric galaxy model was created in ShapeX based on a detailed analysis of an actual galaxy image. The Orion Nebula This volumetric 3-D model of the Orion Nebula was created using pure polygon mesh and path objects with radiation transfer computation for the scattering and absorption by the dust from the central illuminating stars. Proto-planetary disk with jet. The dusty disk of this proto-planetary object has an enriched structure using noise-textures added to a relatively low-resolution hydrodynamic simulation from the Hydro Module. The disk and jet were then separated using filters and assigned different emission (jet) and dust scattering (disk) properties. Ring Nebula For the creation of this planetary nebula the application of image texture mapping along the line of sight allowed to include details of the dusty globules at precisely the right projected positions in the nebula. The environment of Eta Carinae This is the complex mesh structure that Mehner et al. (2016) used to model the fast expanding gaseous environment of the massive Eta Carinae stellar binary system. Eta Carinae Homunculus model This simple bipolar model of the dusty Homunculus around Eta Carinae demonstrates the multi-wavelength modeling capabilities with ShapeX. From left to right the wavelength range of the rendering moves from the optical to the infrared. About Shape was created by Wolfgang Steffen and Nico Koning. Shape is free software supported by the Institute of Astronomy, UNAM. Legal and Privacy Information Home: Homepage_about User Guide Index Introduction Learn about the possibilities and limitations of astrophysical modeling and visualization in Shape. What types of physical models can be done. Whether you pursue research or outreach, find out what you can do and what you need to learn to successfully apply Shape in your field. Overview A quick tour is given through the integrated modules of Shape is given. We briefly describe how they work individually and how the general workflow brings everything together via interactive input but no need for a single line of coding from the user. Modules The modular design of Shape allows the user to concentrate on the job at hand. The desktop and the main toolbar are the hubs to get you around. In this section we describe the functionality of each of the modules, so you can quickly decide which one will be needed for your project. Goto Introduction Goto Overview Goto Modules Data Preparation Images, spatially resolved spectra and other data can be displayed as direct background references to build your models. Such data images need to be prepared carefully and correctly imported into Shape. In this section we describe how such data images can be prepared and set up in Shape. Goto Data Preparation Coordinate Systems Detailed knowledge of the various coordinate systems is necessary to correctly modeling in Shape. This is particularly true when kinematic are to be modeled. Here is a description of the coordinate systems in different contexts of the available tools. Goto Coordinate Systems Radiation Transfer Mathematical and physical details about the radiation transfer on the Cartesian grid in Shape are described. The physics and approximations for the calculations of scattering on dust particles are also layed out. Radiation Transfer Home: Service Home: Contact

Overview ​ The mesh objects serve as containers of density and limit the volume where the density of an object is placed in space. The density modifier controls the density distribution within the volume fixed by the mesh container. ​ Several other modifiers work in exactly the same way as the density modifier and are therefore not treated separately. These include the temperature and the pressure modifiers . ​ In addition to the common parameters for naming and enabling modifiers, the density modifier has the following parameters: ​ f0: factor that scales the density that is otherwise controlled by the 3-D distribution defined in the Magnitude graph (see below). It is actually part of the Magnitude graph, but because of its frequency of use it is also exposed at this level of the panel. ​ Sigma: currently not in use ​ Operation : This is a drop-down list with the options: Replace, Add and Scale . These are the operations that will be used to determine how this density modifier affects a possibly existing sequence of density modifiers further up in the modifier stack. Replace mode: The first density modifier should be used in Replace mode . If there is a density modifier further down in the stack in Replace mode, then all previous density modifiers have no effect and only this one and those further down in the stack are used. ​ Add mode: the density of this modifier is added to whatever is the result of the previous density modifiers in the stack. ​ Scale mode: the density of this modifier is added to whatever is the result of the previous density modifiers in the stack. ​ In the example on the right there are three renderings of the same geometrical object with density modifiers as shown in the stack above the rendered images. The first image has a density with a point graph that changes as a function of the z-coordinate in cylindrical coordinates. See the graph below the rendered images and note that the Coordinates have been set to Cylindrical. This density modifier is label Ladder Strungs. It is located at the top of the modifier stack and is in Replace mode . ​ The second density modifier is labeled Global Decay and is in Scale mode retaining the default Spherical Coordinate system (see the second modifier graph under the rendered images). It scales the density that results from the first modifier with a normalized Gaussian as a function of distance. ​ In the final example, a Texture was included in the first density modifier. The texture scales this modifiers with the three-dimensional procedural texture of which a slice is shown below. How textures work in more detail is explained in the corresponding section of this manual on Textures. Modifiers: Density (Temperature, Pressure)

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

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

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

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

Modifiers The Image Displacement Modifier ​uses an grey-scale image to move vertices as a function of the image pixel intensity. This allows one to use actual images to influence the model structure. As shown in the example mesh on the right, a potential application is in the modelling of spiral galaxies. An external drawing device can be used to design structures almost interactively with the automatic update functionality. ​ For this example the image of a spiral galaxy was smoothed and a flipped copy of it generated. The flipped version is needed for the top-bottom symmetry of the galaxy structure. The image on the right is the rendered image. The Image Displacement Modifier (IDM) works in a similar way as the Bump Modifier with the basic difference of using an image as data source instead of a simple function. The handling of the Gizmo for placement is similar. One difference is that the Gizmo of the IDM include a preview of the image to help with the precise placement and scaling. ​ In this example of a spiral galaxy two IDM are required, one for each side, as shown in the example modifier stack on the right. Parameters: ​ Name: If multiple Modifiers are used, make sure to name them adequately for ease of identification. ​ Enabled: When deselected, the modifier will not be applied. ​ Filename: Click on the button on the right to open the file selection dialog to open the image file to be used to the IDM. The filename will be displayed in the text field. ​ Width & Height: The full size of the image in the 3-D Module in local x & y directions. ​ Radial: Select this option if you wish the displacement to be radial from the origin of the Local Coordinate System of the mesh. ​ Auto Update: If you change the image texture using an external software such as Gimp or Photoshop, then you can enable the automatic loading of the image by clicking on Start. Make sure to Stop it again after you finish. Since the image is read from disk, you need to save it after every change you want to be updated in Shape. ​ Interval (ms): The the interval between Updates of the image from disk. Magnitude: Set up the how the mesh displacement shall be as a function of the pixel brightness of the image assuming that it has an interval from x=(0-1) for greyscale values of (0-255). You can use an analytic function of x (the pixel value between 0 and 1) or a corresponding point function. Widget: Opens the Widget panel shown on the right and enables the preview of the displacement image that helps to place it correctly. To see the preview image, the Display has to be enabled and the object needs to be selected in the object tree. The not only the Widget arrows are show, but also the preview image as shown below the Widget panel on the right. ​ Note on Rendering IDM objects: Below are a few renderings of the example galaxy object. The first one shows the rendering at an intermediate viewing of the disk. At the center the bulge is seen as a vertical uniformly lit structure. This is typical for the applications of the IDM, especially with small-scale features. These turn out to look like little vertical "sticks". ​ There are a number of measures that one can take to remedy that depending on the feature and the application of the IDM. For the smooth structure of the galaxy, for instance, one can use the Taper Modifier to taper off the emission towards the surface of the mesh. This is shown below where the galaxy has been rendered edge-on. The upper image is without and the lower one has a Taper Modifier applied. ​ In addition to the IDM to strengthen the spiral features in the galaxy an Image Texture Modifier was applied with the same image. Modifiers: Image Displacement

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

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

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

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