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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

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.

Filamentary texture generator in Shape 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.

Top of Page Basic Workflow Overview 3-D view ports Menu Bar Primitives Objects, Tools & Lights tabs Transform tools 3-D Module Basic Workflow 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. Overview of the 3D Module : The purpose of the 3D Module is to set up your model interactively. This module is divided in several sections, the interactive 3-D view ports , the Menu Bar at the top, Objects, Tools & Lights tabs on the right and Transform Tools on the left. 3-D view ports: By default there are four view ports that can simultaneously show you the same number of different views of your mesh model. Several of these camera views are aligned with the coordinate axes (initial defaults: Front, Right). The Free-Form view can be changed arbitrarily using mouse input after selecting the Camera > Orbit tool from the Transform Tools to the left of the 3-D view ports (see Transform Tools for details). A special view port is the Render view, since it represents the view that will be used for rendering in the Render Module. This view can be controlled interactively with the Mouse in the same way as the Free-Form view, but also numerically with Image and Camera parameters in the Render Module. Right-click menu: When you right-click on the area of a 3-D viewport, a menu opens that allows you to set a number of properties of this particular view. Camera: Select a different camera view for this viewport. Save Image: Save the mesh images of the viewports. It saves the image of all viewports in one image. If you want to save only a single view, then use the Maximize command from the right-click menu to open a single view in the 3-D view space (to go back to the four viewports, right-click again and select Restore). Make sure to provide a filename with a valid image extension. Most common image formats are supported, such as .png (recommended), .jpg, .gif, etc. (example: image1.png). The Save Image function is the same as that of the Save button in the 3-D Module´s top menu bar. Saving your viewport images with this function does not include the colored coordinate axes or the viewport labels. To saves these you can make screenshots of these areas. Properties: In this dialog you can set a few parameters for the individual view port. Scene alpha: This parameter changes the transparency of the whole polygon object scene, so a comparison with observations or the rendered scene may be easier with lower alpha values. Background: This setting selects the background image of the scene between None, Observed and Rendered, which enables you to compared the corresponding images with the mesh. Including the Observed data is useful to place and shape mesh objects according to the observations. Note that a direct comparison with observed data makes only sense for the Render image. Sometimes, comparing the observed images with other views might be helpful when checking for symmetry properties. Maximize: For more detailed inspection, this command fills the space of the four viewports with a single one. Restore the four views using the Restore command in the right-click menu. 3-D view ports Overview Menu Bar Menu bar: The Menu Bar of the 3-D Module provides quick access to a number of commands (left section) and the creation of Primitive mesh objects (right section). Save: Save the mesh images of the viewports. It saves the image of all viewports in one image. If you want to save only a single view, then use the Maximize command from the right-click menu to open a single view in the 3-D view space (to go back to the four viewports, right-click again and select Restore). Make sure to provide a filename with a valid image extension. Most common image formats are supported, such as .png (recommended), .jpg, .gif, etc. (example: image1.png). Saving your viewport images with this function does not include the colored coordinate axes or the viewport labels. To saves these you can make screenshots of these areas. Import: This command allows you to import objects from a different project. A file selection dialog opens to select the project from which to import objects. Then a second dialog allows your to select one or more objects (shift-click for selecting multiple objects). Note that it is divided into tabs for different types of objects which have to be imported separately. Options: The Options dialog contains settings for viewing coordinate grids in the 3-D viewports and other options that might be helpful during modeling and for publication of model meshes. Undo: This command opens the Undo Stack utility. It shows recent commands that can be undone and redone. You can select which commands to undo or redo and set the maximum number of commands to be held in the stacks. Additional Undo options exist for example for the Path vertex objects which can be undone with Ctrl-z or redone with Ctrl-y. Primitives: The most important functionality of the menu bar in the 3-D Module is to provide quick access to the creation of various Primitives, i.e. basic geometric mesh objects that can be described with only a few parameters. Create a new primitive object by a first click on the corresponding icon, then click on one of the 3-D viewports and immediate drag the mouse to the right to increase the first parameter of the primitive. When the first size is adequate, click again and drag to the right to increase the second parameter (if necessary). One click and drag to the right for each parameter (sphere has one, cone and plane have two, “cube” has three) of the primitive object and then one more click to finish. Your object appears in the Systems folder of the Objects tab located to the right of the 3-D viewports. By default the names of the objects is PS_#, where # is the number in order of creation. This name can and should be changed to something more descriptive in the General parameters menu of the drop-down list to the right of the Objects folder tree. The detailed properties of the individual objects can be changed after selecting it by clicking on the objects name in the Objects stack, where it will be highlighted and in the 3-D viewports the corresponding mesh will turn white, if the Show status flag in the General properties is activated (this is the default). The Object Properties drop-down list contains five different parameter sections: General, Particles, Modifiers, Primitive and Fields. Click on Object Properties for a link to a more detailed description of its content. Primitives Objects, Tool and Lights tabs: The parameters of objects and different tools can be set in the Parameter Tabs on the right side of the 3-D Module. There are three tabs available for the parameters. Objects: handles the parameters of the objects in the 3-D viewports. Tools: allows access to the parameters of tools such as the Draw Tool or Erase Tool for particles accessed in the corresponding tab on the left of the 3-D Module). The parameters in the Tools tab appear once the tool has been activated. Lights: change the lighting properties of the 3-D viewports by changing the properties of the default Ambient Light or adding, deleting and changing the positions and parameters of other types of light. A more elaborate lighting scheme is often useful to create schematic illustrations using the mesh objects. Objects, Tools & Lights tabs Transform tools: On the left side of the 3-D Module there is a set of tabs with a variety of tools, most of which interactively change the positions and orientations of various types of helper objects: Cameras: change the view points of Render or Free-Form view ports interactively. Systems: change the transform properties of individual objects (Systems) of the scene. Widgets: change the local coordinate system of the selected tool or modifier. Vertices: with these tools individual or a group of vertices of meshes are manipulated for very detailed local changes of the meshes. Particles: draw and erase Particles on and around meshes that serve as supports. This allows very detailed structures to be added to an object than can not be easily generated with meshes or procedural filament tools. The parameters of the Draw and Erase particles tools are set in the Tools tab on the right of the 3-D Module. Transform tools Objects Tree: The objects tree is a hierarchical list of the current objects in the scene. They can be collected in folders and sub-folder. With the tick boxes to the left of each object an object can be switched on or off. Similarly switching on or off a folder does the same for all objects in a folder. New objects are placed in the default "Systems" folder. New folders are created using the "Add new folder" button at the bottom left. Copy objects with the copy-button. The copy is then placed at the bottom of the list in the same folder. Move objects and folders around within the object tree by dragging and dropping. Delete objects and folder with the delete button at the bottom of the panel. The color of the symbol to the left of the object name is the same as the mesh color and helps to identify the object in the 3-D views. If the object is not enabled, the color of the symbol is grey.

Introduction Why Shape? Images inspire us. Images lead to ideas. We made Shape as a tool to test inspirations. Play True or False. By finding out whether an idea works or not, either way, with Shape you can find new insight into nature for yourself and others. 3-D visualizations of astrophysical objects and phenomena in science and the media are often made with non-scientific software or the result is too abstract most of the time. Shape combines both worlds, putting as much computational astrophysics as possible to the service of research and outreach. Whether you are looking for profound scientific insight or photorealistic volumetric visualizations of what is going in the universe around us. the odds are you are in the right place. What makes Shape different? We want Shape to be easy to handle and fast to learn, so you can quickly play with the results and change things, before an inspiration evaporates. Shape is different from other astrophysical modeling tools, since it is based on modern interactive 3-D modeling technology similar to the one used for special effects, video games and architectural visualization. We combined this technology with custom made rendering, visualization and plotting techniques drawn from numerical astrophysics. Shape allows you to build astrophysical structures and processes in a controlled way from very simple structures to highly complex environments. They can either be static or variable and are build either from polygon meshes, hydrodynamic simulations or a combination of both. The combination of hydrodynamic models with polygon mesh objects in astrophysics is a unique feature of Shape. Shape continuously evolves, following the users' ideas and needs. It is interactive and the physics is highly customizable through the interface and, make sure to note: all this without the need for programming by the user .

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.

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 .

Render Module Properties Panel: General Properties Panel: General The initial panel contains the General properties of the 3-D volume that is going to be generated and the type of rendering algorithm that is going to be employed. Resolution: The number of volume elements (voxels) that the computing domain is to have in each direction. The total number will the N^3. Note that the rendering time required therefore increases very quickly with this number and your system may run out of memory. Make sure Shape is run with sufficient memory allocated for the process at startup. 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. Renderer: Choose the type of renderer from this drop-down list: either the High-Definition (HD) render (default) or the Standard renderer (SD). The HD renderer 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. Grid: When the HD render mode is switched on and scattering or photo-ionization processes are to be calculated, you can activate the Grid flag to use a grid for the scattering and ionization calculations. This speeds up the computation, but may be less accurate and uses more memory, which may limit the resolution on systems with insufficient RAM. For the most accurate calculation make the grid the same size as the Resolution parameter. Smaller sizes are best set smaller by factors of 2. They speed up the computation, but are less accurate. Grid Size: When the Grid flag for the HD renderer is set, then you can choose the size of the grid with this parameter. Make sure it is not larger than the Resolution parameters. Step Size: The ray casting and ray tracing step size in units of the cell size of the domain. Setting it smaller than 1 can in some cases yield somewhat better accuracy. It does, however, take more computing time. Jitter: As an anti-aliasing method you can randomly displace the rays from the center of the image pixels. This is in units of the pixels size. # samples: The number of samples, i.e. rays to be cast, for each pixels. The position of the rays in a pixels are random. This may be used to increase accuracy slightly or as a measure to reduce aliasing. 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.