Search

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

Key Sub-S ystem: Textures Many astronomical objects, especially nebulas have filaments with random structures. This can be simulated with procedural 3-D texture s. In Shape procedural textures can be applied to physical quantities such as density, temperature, velocity, etc . These textures are multiplied on top of the spatial variation given by the Magnitude of a quantity. Open the Texture Parameter Panel by clicking on the Edit button beside the Texture label in the parameter panel of a selected modifier. ​ Getting the right texture may require quite a bit of experimentation, often combining several basic textures. Texture Parameter Panel ​ The Texture Parameter Panel has several sections. At the top-left is the preview window, where a single slice from the x-y coordinate plane of the 3-D texture is shown. A list of combined basic textures is below the preview window and various types of parameters are at the top-right. Transformation modifiers can be added at the bottom-right. Basic Workflow ​ Initially the texture editor is blank. A new texture is added from a list of different types after clicking on the Add button to the right of the Textures List. The most commonly used type is the Space Convolution noise. Now a preview of the texture is generated using the default parameters. To get the texture that is needed change the parameters until a suitable result is obtained. More than one texture may be combined by adding further textures to the list. Note that the combination is done in the form of a multiplication of the texture values in the range (0-1). Therefore, the more textures you combine, locally the result becomes smaller and smaller. ​ In the modifiers area, rotation and translation modifiers can be applied that are similar to the corresponding image modifiers applied in the Render Module. This is not descussed in more detail in this section. Textures Panel ​ Add: Opens a dialog with a list of different types of procedural noise from which to choose. When you click on OK, the new texture is included in the list of already chosen textures. ​ Del: Deletes the selected texture from the list. ​ Up & Down : Move the selected texture up or down in the list. ​ Copy & Paste: Copy stores the selected texture in a buffer. Paste pastes the copied texture as a new texture to the list. ​ Note: As mentioned above, if there is more than one texture they are combined as a local product of their values, which range in the interval (1,0). Moving the textures up and down in the list does not change the result since multiplication is a commutative operation. However, if you explicitly name the textures, the sequence may help at keeping order General: Name: Set a name for this texture ​ Enable: Enable or disable this texture ​ Seamless : This parameter works together with the Distortion (see below). If a Distortion is applied that stretches the texture along the angle in a cylindrical coordinate system, a discontinuity appears at the 0 to 360 degrees transition. To prevent this enable the Seamless flag. An attempt is then made to generate a seamless texture by copying and rotating the same texture by 180 degrees and overlapping the two with a linear transition between the two that excludes the seam region. Currently, the result is a seamless texture that has a 180 degrees point symmetry. ​ Bias: Sets a minimum intensity for the texture. If b is the bias level, now the range for the texture is (b,1). Properties: ​ The detailed parameters for different types of textures vary. Here we discuss the example of Sparse Convolution Noise, which is the most suitable for most filamentary features in diverse nebular objects. Many of the parameters are common to all textures, others will differ. But a bit of experimentation will clarify the meaning of the differing parameters. ​ Sparse Convolution Noise: ​ Scale: The scale of the texture can be set separately in the three coordinate directions. By default they are looked together, i.e. when you change one of them, the other two automatically get the same value. They can be unlocked by unchecking the Lock flag. Then the values can be set independently. To asses the size of the features in the context of the model domain note that the preview window has the same size as the scene size in the Render Module. ​ X Y Z Offset: These parameters move the texture along the corresponding axis. The units are those of the Render Module. ​ Exponent : Controls the contrast between the highest and lowest levels of brightness. High values deemphasize initially lower values. ​ Freq: The levels of spatial frequencies to be included in the random noise generation. Higher values will include smaller features. ​ Type 2: This type generates a different look and overall smaller structures. Invert: inverts the greyscale, the interval (0,1) is linearly mapped to (1,0). Image Size: Sets the pixel size of the texture preview image. ​ Z slice : Selects the slice to be shown in the preview. Changing the value moves the preview through the cube of slices along the line of sight. Distortion: This button opens a dialog that controls the re-mapping of the noise as a function of position. Analytical expressions can be set up to remap the noise in different coordinate systems. This allows the user to stretch the noise pattern in radial or circular directions. There is an example for such a distorted texture on the right. The second image is the same texture after applying the Seamless flag (see above). ​ Below is the dialog that opens when you click on the Distortion button. It is similar to other Graphs . Make sure to set the correct coordinate system for the distortion to be applied. The example uses the Cylindrical Coordinate system and distorts the radial and the angular directions. Some experimentation with the analytic expression or point graph is likely needed to get the desired result.

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.

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 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: ​ 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. 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) . 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 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 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. 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.

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-S ystem: Graphs In Shape graphs are used to display functions. The functions are either analytical or set interactively by adding control points to a curve. The control points of an interactive curve can also be loaded from an external ascii file. ​ In modifiers the graphs are usually applied to set and display spatial variation of a quantity that is passed on to some quantity as a multiplier. In the modifiers the graphs may be single coordinate functions or they may depend on all three space coordinates in different types of coordinate systems (spherical by default, Cartesian or cylindrical). Generally the result is a single number, but in the case of the velocity field, for instance, the output can be a vector. ​ In the Physics Module graphs commonly are a function of wavelength. ​ The functionality and appearance of the graphs varies slightly depending on the particular context. ​ The image of the graph on the right is taken from the Squeeze Modifier, which controls the shape of a cylindrically symmetric mesh. The function display at the top shows a line of how the function f(x) changes with the independent variable (always x). In this modifier it is the position along the axis of the object. ​ At the bottom is a list of tabs to set a variety of f unction properties . ​ ​ Workflow: ​ Analytic: By default the function is set to Point , but can be changed to Analytic with the Function drop-down list. ​ In the analytic mode, the graph is controlled by a mathematical expression, that by default is the constant function f(x) = 1. ​ Templates: From the Templates drop-down list a few commonly used functions can be selected that are the inserted as mathematical expressions in the editor line for the function. These templates can then be edited as needed. In our example we have typed the function manually. In additional to several standard mathematical operators such as "exp" and "abs", it includes the variables "a" and "b". Variables can have alphanumerical names. Reserved variables include "n", "t" and "Pi", referring to density, temperature and the number p. ​ Variables: The numerical value of the variables is displayed in the Variables tab . Here the value can either be written manually or be assigned from the Math Module. If the variable was defined in the Math Module, then the flag labeled "Use global variables" needs to be set. If the flag is not set, the local manually set value is used (Local variable ). Global variables are then marked by a grey background. Global variables are accessible from any function throughout Shape. ​ Constraints: Frequently used functions such as the Gaussian vary over an infinite range. In many practical situations the function is required to smoothly reach zero or some other fixed value within a finite range. This can be achieved by setting constraints in the Constraints tab. Here the function can be made to smoothly Fade in and Fade out within the ranges set there. The value form and to which the function converges is the "Default" which can be changed by the user. In the graph the region that is covert by the Fade in is shaded in blue and the Fade out in red. ​ ​ Point Graph: ​ A point graph is set up using manually placed points. These point may also be loaded from a file (Load Ascii button). To obtain a continuous function the values between the points are interpolated. ​ There are two modes for interpolation . By default the interpolation is linear between the points. The second is a spline interpolation that is controlled manually with separate handle on each side of the points. ​ ​ ​ ​ ​ ​ The spline interpolation is activated by clicking on the following icon: A green color in these icons at the top of the graph indicates that they are activated. To move the points in the graph use the left-click and drag mouse functionality. To move the spline handles , use Crtl- left-click and drag . ​ Additional interactive functions to manipulate the points individually or collectively are available by activating some of the icons on the toolbar above the graph. ​ If you hover over a button or icon, a tool tip shows a short description of the functionality, which are very self-explanatory in this case. The hand tool is active by default and allows one to move points by left-clicking on and dragging them. The magnifying glass: zoom in and out in the graph The next icon allows you to pan left-right and up-down in the graph. The box with a pencil is for selecting multiple points by dragging a rectangle around them, while the cursor symbols with the arrows activates moving the selected points together. ​ Selected point are deleted by clicking on the cross icon . Note that unselected individual points can be added and removed from the right-click menu (see below). ​ The range of the graph is adjust ed to the points in them by clicking on the icon with the two curvy arrows . As mentioned above the next icon activates the spline interpolation with two handles on each point. The wrench icon opens a pop-up windows that gives access to detailed options for the appearance of the graph . These should be largely self-explanatory. Right-click menu: The right-click menu give quick access to additional functionality for graphs. In particular there are four functions for point graphs at the top of the list. ​ Add Point add a point to the curve where the curser is currently located. Remove Point removes a point over which the cursor is hovering. Set Point opens a small pop-up window where the exact x and y values of a point can be set. Mirror Point is a very useful function when a perfectly symmetric setting is required. When clicked while you hover over a point with coordinates (x,y) a copy of the point is added to the graph at (-x,y). ​ The second set of functions toggle on and off various functions, which are self-explanatory. ​ The Save Ascii function will open a dialog that allows you to save the point values of the graph in a file in ascii format. The Save Image function saves an image of the graph. In the file dialog that opens, the filename has to be give a suitable file extension for the image to be correctly saved. The extension can be one of typical file formats, such as .png or .jpg, etc. ​ Finally, the Properties functions opens a dialog where the graph´s appearance may be customized in more detail by changing colors, tick-mark spacing, coordinate grids, etc. ​ ​ Special variants of graphs: ​ Some contexts in Shape have specific features in addition to the basic functionality described above. These are explained in their specific contexts, such as the graph for the velocity modifier, which has a number of special functions. ​ There is one common feature of the extended graphs that depend on more than one variable, which we describe here. Most function graphs have as output a single number that controls a modifier or displays some property. An exception is the velocity modifier, which has a vector as output. ​ The basic graph that has been described above depends on a single variable. Many modifiers do, however, depend on more than one spatial dimension. Those have a separate graph that describes the spatial dependence of the output on each spatial coordinate. They are accessible through tabs at the top of the graph. The active coordinate is marked in grey. ​ Using the default Custom Mode one can select from three different types of coordinate system in the Coordinates drop-down list: Spherical (default), Cartesian and Cylindrical. The labels of the access tabs for the graphs change their labels accordingly. ​ Note that for the spherical coordinates the label convention is that of the North America, with q being longitude and f the latitude. ​ SEPARABILITY: an important property of the default behavior of these graph is that the resulting function F(u,v,w) is separable in their component functions: F(u,v,w) = f0 * f(u) * f(v) * f(w) ​ where f0 is a constant parameter set by the user under the Coordinates drop-down list. ​ Non-separable functions: a non-separable analytic function can be set up when enabling the Analytic mode from the the Mode drop-down list. This feature requires an analytic description of the function and a point-graph can not be used. ​ As before, one chooses the type of coordinate system from the Coordinates drop-down list. Then in the function editor a formula is types as a function of the general coordinates (u,v,w) as shown in the example on the right. The coordinates have to be in terms of the letters u,v and w, no matter which type of coordinates is chosen. Their meaning changes automatically to (x,y,z), (r, q,f) or (r, q, z ) for Cartesian, spherical or cylindrical coordinates, respectively. The image on the right shows a rendering of the density that was described by the analytic function above it. It illustrates the how the wavelength of the sinusoidal pattern can be continuously changed by mixing the coordinates appropriately. ​ ​ ​

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 . ​

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

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.

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

LEGAL AND PRIVACY INFORMATION ​ Impressum ​ Wolfgang Steffen Contact: e-mail: wsteffen@astro.unam.mx Responsible for the content: Wolfgang Steffen Instituto de Astronomía UNAM Carr. Tijuana-Ensenada km 107 22860 Ensenada, Baja California México ​ ​ Copyright ​ 2021 Owners: Nico Koning (Calgary, Canada), Wolfgang Steffen (IA-UNAM, Mexico) ​ Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal use the Software without restriction, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. THE SOFTWARE MAY BE USED AND DISTRIBUTED IN COMPILED FORM. NO PORTION OF THE ORIGINAL CODE MAY BE USED, CHANGED OR DISTRIBUTED WITHOUT EXPRESS PERMISSION IN WRITING BY THE COPYRIGHT OWNERS. ​ Disclaimer of liability: Liability for the Shape software and the manual contents ​ The Shape software is provided as is and no guarantee is given for its fitness for a particular purpose. We can not be made responsible for any incorrect scientific results or other that may or may not appear in publications of any kind. ​ The contents of the Shape manual may not correspond to the version of the Shape software that user is applying and may therefore or for other reasons deviate from the actual functionality of the software. Liability for general contents The contents of our pages were created with the greatest care. However, we cannot guarantee that the contents are correct, complete and up-to-date. As a service provider, we are responsible for our own content on these pages in accordance with § 7 para.1 TMG (German Telemedia Act) and general laws. According to §§ 8 to 10 TMG we are not obliged to monitor transmitted or stored information from third parties or to investigate circumstances that indicate illegal activity. Obligations to remove or block the use of information according to general laws remain unaffected by this. However, liability in this respect is only possible from the time of knowledge of a concrete infringement. If we become aware of any such legal infringements, we will remove the content in question immediately. Liability for links Our offer contains links to external websites of third parties, on whose contents we have no influence. Therefore we cannot assume any liability for these external contents. The respective provider or operator of the sites is always responsible for the contents of the linked sites. The linked pages were checked for possible legal violations at the time of linking. Illegal contents were not identified at the time of linking. However, a permanent control of the contents of the linked pages is not reasonable without concrete evidence of a violation of the law. If we become aware of any infringements, we will remove such links immediately. Copyright The contents and works on these pages created by the site operators are subject to German copyright law. The reproduction, editing, distribution and any kind of use outside the limits of copyright law require the written consent of the respective author or creator. Downloads and copies of these pages are only permitted for private, non-commercial use. Insofar as the content on this site was not created by the operator, the copyrights of third parties are observed. In particular, third-party content is identified as such. Should you nevertheless become aware of a copyright infringement, please inform us accordingly. If we become aware of any infringements, we will remove such contents immediately. Data protection The use of our website is usually possible without providing personal data. As far as personal data (e.g. name, address or e-mail addresses) is collected on our website, e.g. for access to the forum or to contact us, this is always done on a voluntary basis, as far as possible. This data will not be passed on to third parties without your express consent. We would like to point out that data transmission over the Internet (e.g. communication by e-mail) can have security gaps. A complete protection of data against access by third parties is not possible. The use by third parties of contact data published within the framework of the imprint obligation for the purpose of sending advertising and information material not expressly requested is hereby expressly prohibited. The operators of the pages expressly reserve the right to take legal action in the event of the unsolicited sending of advertising information, for example through spam mails. Google Analytics This website uses Google Analytics, a web analysis service of Alphabet Inc. ("Google"). Google Analytics uses "cookies", which are text files placed on your computer, to help the website analyze how users use the site. The information generated by the cookie about your use of this website (including your IP address) is transferred to a Google server in the USA and stored there. Google will use this information for the purpose of evaluating your use of the website, compiling reports on website activity for website operators and providing other services relating to website activity and internet usage. Google may also transfer this information to third parties where required to do so by law, or where such third parties process the information on Google's behalf. Google will not associate your IP address with any other data held by Google. You may refuse the use of cookies by selecting the appropriate settings on your browser, however please note that if you do this you may not be able to use the full functionality of this website. By using this website, you agree to the processing of the data collected about you by Google in the manner and for the purpose described above. ​ Support ​ The design of the Shape software was partially supported by the "Universidad Nacional Autónoma de México" (UNAM-DGAPA, UNAM-PASPA).

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

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