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Animation Module Overview Most parameters in Shape can be animated over time. This can be used to generate time variation of the models either for scientific modeling of time varying phenomena or for visualization purposes. A simple example application is the simulation of the lightcurve of an exoplanet or of eclipsing binary stars. ​ An application that aims more at purely visualization could be rotating the virtual camera around an object go generate a movie that shows the structure as seen from many points of view. ​ Since animation implies the generation of a large number of individual images that can be joined together in the Movie Module, care needs to be taken in preparation in order for the rendering process to not take an unacceptably large amount of time. The key question is which type of rendering do you need : Camera motion: If you animation will consist of camera motion only and the spatial resolution that you need is small enough to allow you to use the grid renderer, then you can save a lot of time. In this case the steps before the final ray casting to determine the image pixel values can then be precalculated and saved. Then they do not need to be repeated for every frame. ​ Another option to get a camera animation is to use the interactive iluvia software from ilumbra.com . Using the Export Module in Shape you can quickly output your model in a format suitable for iluvia and inspect your model interactively or very quickly set up and capture animations. Varying model parameters: If parameters of the model itself need to be changed over time, then the precomputed grid changes and a full render is needed for every frame. For complex models and high resolutions, this may take a lot of time to compute, depending on your computing equipment. ​ Once you decided which type of animation and spatial resolution you need, you can time the rendering and estimate the total time it will take to render the necessary number of frames. For each rendering, come basic stats are output in the Info Module that include the time it took to render. This information can be used to estimate the total time necessary to render out the full animation.​ ​ General workflow: ​ 1. Set up the timing and output parameters in the Parameters Panel on the right. 2. Select variables to be animated from the Parameter Tree. They appear in the Animation Parameter Stack. 3. Select each animated parameter in the Animation Parameter Stack and set up its animation graph as a function of time 4. Render the animation Animation Module UI: The Animation Module is divided into five main sections. A control bar is at the top and the parameter tree and the animation parameter stack are on the left. In the middle you find the animation graph for the animated parameters. At the bottom is the time line . Finally, the General and Output parameters are in the panels on the right. Control Bar: Animate: Starts the rendering of an animation. After each rendered image it advances one frame and renders again. ​ Refresh: Updates the Parameter Tree after new renderable parameters have been added somewhere in Shape. This does not happen automatically, so make sure to click on this button to see any new parameters. Up & Down: In the Animation Parameter Stack move selected parameters up or down. This has no effect on the result but is helpful to keep order in the stack when a large number of parameters is animated. ​ Remove: Removes selected parameters from the Animation Parameter Stack. ​ Copy & Paste: Copy the animation graph from a selected animation variable in the Animation Variable Stack and paste it to another that you select after copying the previously selected graph. Parameter Tree: The parameter tree is a hierarchical list of all animatable parameters. The parameters may be from the UI, general project parameters or from particular objects. Additionally global parameters that have been defined in the Math module will also show at the bottom of the parameter tree. To select a parameter for animation, open the parent branches in which it is located. Once the parameter appears, double click on the tick box to the left of the parameter name. When the tick mark is on, the parameter appears in the Animated Parameter Stack, where the time variation of the parameter is set up (see below). Note that newly created parameters or objects do not automatically show in the parameter tree. To have them appear click on the Refresh button in the menu bar at the top of the Animation Module. Animated Parameter Stack: The Animated Parameter Stack is the list of parameters that are selected from the Parameter Tree to be changed, i.e. animated over time. ​ The first column shows the Parent branch in the Parameter Tree, the second is the name of the parameter. The third column contains the value of the parameter at the current time of the animation time line. ​ To select a parameter click on the row for that parameter. Automatically its animation graph will be shown. Animation Graph (not shown): In the Animation Graph you set up how the parameter selected in the Animation Parameter Stack changes over time. Note that in this graph the x axis is in units of time as defined in the Parameter Panel on the right (see below), whereas the Time Line at the bottom is in terms of the frame number. ​ The graph is not shown here . It work the same way as other graphs in Shape. For more information on how to set up a graph see the manual page on Graphs . Parameter Panel (right side) ​ General: Timing and frame numbers are set up in this tab. Name: The base name of for the output frames of the animation Start Frame: The frame number at which to beginn the animation. It may be necessary to start from a position different from 0 or 1 when an animation was interrupted or if several will be concatenated. ​ # Frames: The total number of frames for the duration of the animation from the Start Time to the End Time . ​ Start Time & End Time: in terms of time units (see below) when is the animation meant to start and end. ​ Time Units: Select the desired time unit from the drop-down list. The default is Years. Make sure the unit in the Variable tab is the same or consistent with the needs for this model. The animated variable that is selected and displayed in the graph uses the units from the Variable tab . Occasionally these units need to be different from each other. ​ Fields: Include the calculation of field lines, magnetic or velocity. ​ Distribute: Recompute the distribution of particles for each frame. ​ Render: Do a full render at each time step. Camera animation with "Autorender" on in the Render Module does not require this, since the model grid does not change and is calculated either before the animation is started or with the first frame. After that autorender is used if the Render flag in the Animation Module is off. Variable Some control parameters for the animated paramater that is currently selected in the Animated Parameters Stack . ​ Time Units: The time units to be used for this variable. Make sure it is the same as the Time Unit in the General tab or you are certain of the animation graph in this context of a different general time unit. Enabled: Enable the animation of this variable. If for some reason you disabled this variable, then later you might wonder why it doesn´t change in an animation. It may well be that you forgot that you disabled it. So, if something in your animation doesn´t change as expected, make sure all the variables that you need change are actually enabled for animation. ​ Stamp: The total number of frames for the duration of the animation from the Start Time to the End Time . ​ Stamp Format: The number format for the numerical stamp. ​ ​ Output: Here you define the output format and what you wish to output and where on disk it is to be placed. ​ Directory: Set the output directory for the individual animation frames. Note that the name of the files is set in the General Tab. Image Type: Specify the image type by writing the standard extension for the image. For instance, if you wish to output PNG format images, then write ".png". ​ 3D Mesh: Output and image of the 3D Mesh. Note that it is not the mesh itself that is output, but rather an image of the view in the 3-D Module. ​ Hydro: Output the full data from the hydrodynamics module at each time step. Note that, depending on the resolution, this might lead to a large amount of data to be output. ​ Plots (Images): Output images of any graphs that the animation might generate in the Graph Module. You can adjust the image resolution for these outputs. ​ Plots (Ascii): Output the ASCII values of any graphs that the animation might generate in the Graph Module. ​ Math Variable: Output any math variables that change over time during the animation. ​ Stereo: Output stereo images. ​ dStereo (deg): The parallax anglee. This is the difference between the horizontal camera angles for the two stereo images. ​ ​

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

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

Math Module Overview The ​Math module is a tool to centralize parameter values that are used in more than one place in Shape. In a way similar to a spreadsheet it allows to compute variables from other variables that have already been defined further up. This makes it possible to set up a complex mathematical model of physical processes that can then be harnessed throughout the rest of Shape. Global Variables: Since the variables defined in the Math Module can be used throughout Shape, they are called Global Variables. Whenever you wish to use variables from the Math Module in other modules, make sure to enable the flag "Use global variables" where applicable. Workflow ​ The basic workflow consists first in adding new slots for new variables in the order of dependency, if any. Then provide a meaningful name for and defining their relationships and values. They can then be used in a variety of contexts throughout Shape. ​ Variable Names: While Shape automatically assigns a letter as a name for new variables, it is very highly recommended to change them with meaningful and descriptive names, such that they can easily be understood wherever they might appear in Shape. The name can be changed by double-clicking on the name field of the variable. Column Functionalities ​ Variable: This column contains the name of the global variables. In order to use a variable in some other module of Shape, the name needs to match. Upper and lower case letters are not distinguished. When a new variable is added, it receives a default name in alphabetical order. Change the variable names to something descriptive of the meaning of its content. Expression: Variables get assign a value through a mathematical expression in this column. In most cases this will simply be a value. A value can be given in integer or floating point format as well as scientific format such as 1.09435e-7 for numbers that are much smaller than 1, or 3.2E15 those that are much larger than 1. In addition to numbers the field can contain more complex mathematical expression, including those combining one or more global variables that are further up in list. To avoid recursive dependencies, variables further down can not be included. Valid mathematical expression may include the basic symbolic operators +-*/ and ^, but also common textual operators which include the following reserved functions and variable names: POWER, SIN, COS, TAN, COT, RAND, CSC, ARCSIN, ARCCOS, ARCTAN, EXP, LN, LOG10, LOG2, ABS, SQRT, ROUND, ARCTANH, UNARYMINUS, LT, GT, and the irrational numbers "e" and "pi"; ​ As mentioned above, these functions can also be written with lower-case letters. Menu bar ​ The buttons on the top menu bar of the Math Module control the overall content of the Math Module. ​ Calculate : The Calculate button executes all calculations that may in standby, e.g. for iterative computations. Direct calculations of variables that depend on variables further up are executed on confirming the variable name with the Enter key. Variable : The Variable button adds a new variable to the end of the list. The variables sequentially get names of single letters in alphabetical order. As mentioned above, it is recommended to change these names to something descriptive of its meaning. The variable name is changed by double-clicking on the text field. Separator : Separators are used to keep different sections of the list of variables clearly distinct. They can also function as headings if you add some descriptive text to their text fields. The separators are colored in dark blue. Constants : This button adds a set of variables that contain the most important natural constants in SI units. If you only need a subset of them, simply select the unwanted ones and delete them with the Remove button. Remove : To remove variables from the Math Module, select them and click the Remove button. You can select several variable together with Shift-Click and remove them in one operation. A confirmation dialog helps to make sure that you do not delete variables by accident.. Up & Down : To move a variable in position in the list, select the variable and click on the Up or Down button to move it by one position. Repeat the operation until the variable is in the desired position. Defaults : Use these buttons to restore the default values that variables may have in the Default field. Note that this button restores the defaults of ALL variables at once . Individual or a subset of defaults have to be reset manually. Save & Load : In order to keep sets of variable interchangeable between different projects that have similar setups, one can save the content of the Math Module in a file with the Save button. To open a saved set of variables use the Load button.

Render Module Properties Panel: Camera Properties Panel: Camera ​ The Camera parameters include various rotation angles in different coordinate systems. The are either observer oriented, such as position angle (PA) or inclination. Or, they are rotations around the Cartesian world coordinate axes. ​ One can change from Orthogonal camera projection (on by default) to perspective camera. Furthermore various filters or "modifiers" can be applied to the data prior to the final render or after the render. These modifiers are discussed in more details below. Scene size: The width of the computing domain in terms of physical units, which by default is meters (m). This number corresponds to half the voxel size assigned to the Resolution parameter above. The physical domain runs from -(scene size):+(scene size). Scene center: The center of the cubic computational domain may be shifted in the physical scene that might be larger than the rendering domain. Setting a smaller domain with a shifted center may be useful for testing purposes or for achieving higher resolution outputs for certain regions. HD: The high-definition (HD) render is activated with this flag. It does not use a predefined cubic voxel grid and works similar to a ray-tracing engine that integrates to the pixel plane. If there are computations that depend on light sources, such as dust scattering, it is computed along the way. This may require more time, but is much less memory intensive. Therefore higher resolutions can be achieved. Fast renders, e.g. for camera animation movies, is not possible, however, since the some information is not stored for quick rendering from the precomputed voxel grid. Scatter Grid Size: When the HD render mode is switched on and scattering or photo-ionization processes are to be calculated, a sub-grid needs to be set that comfortably fits into RAM, but is as large as practical to avoid potential artifacts at grid limits. Recommendable is about half of the size that you can fit, if HD is off. Save grid: The grid data used for the final render step are retained in memory. This allows the Autorender (see below) to work. It requires more memory though and hence limit the achievable resolution smaller than with this option off. So, if you are doing quick tests or plan on rendering camera animations, then this option is convenient to be on. Auto render: If the HD is off or the Save grid flag is on, then data of the full grid have been saved and can be used to quickly render the scene for different camera views and animations. When you change the parameters of the camera the rendering updates automatically. The effect is not "real time" and may take a few seconds, depending on the resolution. Use window: For quick render in HD mode that require only a small portion of the image to be rendered, you can set a window using the Window Button above the image. Click on the icon with the square and then drag out a rectangle with the left mouse-button pressed. If the Use window flag is on, only this region will be rendered. This reduces the rendering times during model development when it is sufficient to see only part of the model. Overlay: Occasionally it is convenient to retain the previous image or images and add progressive images together. This is useful for diagnostics or simply as a nice "special effect.

Key Sub-S ystem: Coordinate Systems There are several coordinate systems defined in Shape. First of all in most contexts the coordinates may be defined in Cartesian, Spherical or Cylindrical coordinates. ​ Note that for the spherical coordinates the label convention is that of the North America, with q being longitude and f the latitude. ​ Hierarchy of coordinate systems: ​ In addition to the types of coordinate system, there is a hierarchy that determines the origin and orientation of the coordinates. ​ First there is the global "world" coordinate system that is fixed and everything else is embedded in this system. ​ The orientation of the world coordinate system is show by the colored coordinate axes in the lower left corner of the 3D views in the 3D Module (see images on the right). Note that it is not centered on the center of the coordinate system and only provides a visual cue of the orientation. The colors of the xyz axes follow the common order of the color channels rgb (red, green, blue), respectively. ​ Every object has its own "local" coordinate system , that may move around in the world coordinate system depending on the types of modifier that are applied. ​ As an illustration compare the two images on the right. In the first one the spherical mesh and the density distribution are centered on the world coordinate system. No changes have been made to any positions. In the second example a Translation Modifier has been applied. It moves the mesh away from the World Origin. Not only the mesh is moved but the density distribution goes along. Similarly, the Rotation Modifier will rotate the density structures along with the mesh, since thee local coordinate system changes . ​ The translation, rotation and scale operations can be interactively handled using the corresponding Move, Rotate and Size tools in the System tab that is located to the left of teh 3-D views. It is important to note that, contrary to the Translation and Rotation modifiers, the Size tool and Modifier does NOT change the scaling of the local coordinate system. This would cause too many practical problem during modeling. It only changes the mesh. This is similar to the Displacement modifier which only moves the mesh, not the coordinate system. For rotating only the mesh, operators such as the Twist modifier can be applied. ​ In third place there is the "widget" coordinate system that is applied to some modifiers. They often need to be centered at different positions within an object, which can be achieved by moving and rotating the coordinate system of the modifier using the Widget tool or Widget dialog . Different modifiers have independent widget coordinate systems. By default modifiers follow the local coordinate system , meaning that their widget coordinates are coincident with the local system until the widgets themselves are changed. ​ ​ ​ ​ But the coordinate center that a modifier refers to can be changed by changing the widget either interactively with the Widget tool or numerically by opening the Widget dialog from within the modifier panel. To open the Widget dialog click on the Widget Edit button at the bottom of the modifier panel. ​ ​ In the image on the right under the widget dialog the object mesh remains at the world origin, while the density distribution is off-center at the position of the widget . The widget itself is represented by arrows. Each modifier may have independent widget, i.e. local coordinate system positions. ​ In the following image shows the application of the Displacement modifier , which moves only the mesh , not the coordinate system. The mesh container changed position, but the density distribution remained centered on the world coordinates. ​ ​ An additional fourth coordinate system is that of the observer or camera . These are the coordinates seen in the "shape view port" of the 3D Module and the rendered image in the Rendering Module . ​ ​ OPERATOR ORDER MATTERS! In the modifier stack several rotations, translations and other operators can be applied one after the other. The result of such combined operations, in general, strongly depends on the order in which they are executed. Therefore the order of the operator in the modifier stack is very important. For instance, translation can be combined in any order (they are commutative ), rotations among themselves and rotations together with translations can not. ​ ​ Coordinate Display Options Dialog: ​ The Options Dialog that opens by clicking on the wrench icon on the menu bar of the 3D Module allows you to customize the display of a Cartesian coordinate mesh within the 3D views. It can helps as a reference during the modeling process. An example is show in the bottom image in the column on the right. A little experimentation should clarify the meaning and effect of the various parameters. ​

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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