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Modifiers The Boost Modifier is basically an enhanced version of a Boolean object or modifier. The idea is to use one mesh to regionally change the properties of another. However, instead of completely cutting out or adding to a mesh, it scales the properties by some factor that may vary spatially either through a function of space or a texture. In the example below a sphere contains a complex mesh structure which has a Boost Modifier that is linked to the spherical mesh. In the first rendering below, the boosting factor was set to zero, such the sphere is hollow in the region of the boosting mesh. In the second examples, the boosting factor for the density was set to 2, enhancing the density by that factor. The Boost Modifier is applied to the mesh to is meant to change another, in this case the inner mesh. Note that more than one boosting mesh can be applied to the main mesh. Parameters: Name: If multiple Boost Modifiers are used, make sure to name them adequately for ease of identification. Enabled: When deselected, the modifier will not be applied. Boost: This is the boosting factor that is applied to the main mesh. It can be a mathematical expression and function of the main variables such as n (density), T (temperature) or P (pressure). Note that these are the properties of the boosting mesh object, i.e. they relate to the modifiers within the boosting object itself. To make the hollow structure above, this factor was set to zero (0) and 2 for the enhancement of the structure. If set to "n" as shown, the factor is taken from the Density modifier in the boosting object. This may be a function of position, including the texture. This allows for a complex manipulation of the region covered by the boosting object. Variable: From this drop-down list select the variable upon which the boosting shall act on in the main object. Note that this is different from the variables in the Boost factor. Operation: Select the operation that the Boost Modifier shall perform on the main object. You can select from Scale, Add and Replace. Applied Object: From the drop-down list select the objects on which the Boost modifier shall act on. Several objects may be chosen. Hide itself: Generally the boosting object is used only to act upon other meshes, but is not rendered itself. This may, however, not always be the case. So, if the boosting object is a rendered object in itself, disable this flag, such that the boosting mesh itself is rendered, too. Modifiers: Boost

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.

The Warp Modifier rotates the mesh vertices as a function of distance around an axis. To actually be a warped surface, the axis of the Widget for the Warp Modifier needs to be at an angle to a reference plane such as a flat disk. Name: Set a name that allows you to identify this modifier easily. Enabled: When this flag is turned off, the Warp Modifier is switched off. Deg: If set, the the rotation as a function of distance in the Magnitude Graph is given in degrees per unit distance. When switched off, then it will be radians per unit distance. Magnitude: Opens the function graph to set how the rotation angle is as a function of distance from the local coordinate system set by the Widget. Widget: The Widget opens the Widget Dialog. It allows you to change the direction of the Warp Modifier. The turquoise arrow indicates the direction around which the rotation will be performed. In the example it was rotated around the original x-axis by 30 degrees. Modifiers: Warp

Math module of the Shape software. 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.

Filamentary texture generator in Shape 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.

Modules In this section we give an overview of the functionality of the different modules and provide links to more detailed information on how to use them and their subsystems. Click on the Module Icon to the left of the description for more information and access to video tutorials on the module. 3-D Module In the 3-D Module the geometric and most other properties of a model are set up interactively. Description Render Module This module takes care of the rendering of image and position-velocity diagrams and a number of settings for other render options. Description Physics Module Radiation transport properties such as emissivity, absorption or scattering are set up as materials (species) in the Physics Module. Description Desktop Module The Desktop Module is your hub to all the other modules, project files, ShapeX configuration and more. Description Video Tutorial Math Module The Math Module allows you to set up variables and relations between them that can then be used throughout Shape as "global variables". Description Modifier Module The Modifier Module lists all modifier that are currently in use and allows you to change parameters of a selection of modifiers simultaneously. Description Maps Module The Maps Module displays channels maps of the 3-D model. The number and velocity range between the first and last channel can be set up. Description Animation Module 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. Description Filter Module Filters for various physical quantities can be defined here. They can then be applied to objects in the 3-D Module. Description Movie Module In the Movie Module one or more animation sequences can be concatenated to a movie and exported for viewing with an external movie player. Description Export Module The Export Module exports the 3-D model into various output formats that can then be used as data for external use. Description Hydrodynamics Module Shape is the first astrophysical tool to introduce an interactive mesh-based setup for such simulations without the need of programming or scripting by the user. Description

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.

The Squish Modifier changes the distance of a vertex perpendicular to a plane (default: local xz-plane), The action is similar to the Squeeze Modifier , except that it´s planar, not radial around an axis. The Magnitude dialog allows you to define the squish amount as an Analytic Function of position along the reference axis. You can also use a Point graph where you can generate an arbitrary function by manually placing points and setting the spline interpolation. To do this, select Point from the Function drop-down list under the graph. The example graph on the right shows the way it was done for the example mesh displayed below. Widget: The Widget opens the Widget Dialog. It allows you to change the direction of the Squish Modifier. The purple arrow will indicate the direction of its action. Modifiers: Squish

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.

The Bump Modifier is designed to add individual bumpy extrusions to a mesh. Position, orientation and detailed shape of the bump can be controlled. To add a Bump Modifier to the Modifier Stack, click on the Add Modifier button (the + sign under the Modifier Stack) and select Bump. The modifier appears at the end of the stack. It is important to note that the detailed effect of the modifier may depend on the position within the stack. Therefore experiment how it interacts with other modifiers before or after in the list. Different properties of the Bump Modifier is controlled in different places. The Control Panel under the Modifier Stack has several check marks: Enable: Enable or disable the Bump Modifier Symmetric: By default the bump will be cylindrically symmetric around its direction axis that can be seen when the Widget is on. Then the check mark is on. When the Symmetric flag is off, then the bump will be infinite in one direction and controllable in the other. Radial: When the Radial flag is checked, then the bump will be applied radially from the coordinate center of the Widget. Otherwise it is parallel to the directional axis (pink) of the the Widget starting in the plane that contains its coordinate center. Widget: Posititon & Orientation The position and orientation are controlled with the Widget. The numerical control panel for the Widget can be opened by clicking on the Widget button in the Control Panel. Alternatively, use the interactive Widget controls on the left side of the 3-D views. As usual, during interactive control use the x, y and z keys to restrict moving and rotating actions to a particular axis. Magnitude: Shape & Size The shape and size of the bump are controlled from the Magnitude Graph that is accessed in the Control Panel under the Modifier Stack. The Magnitude Graph works the same way as other graphs in Shape. For details see the user manual entry for Graphs . The shape of the bump is set using an Analytic function or a Point graph, where the "x" is the distance from the local coordinate system (widget axis) is cylindrical coordinates. For the "symmetric", i.e. cylindrically symmetric case, the values at negative x are ignored. By default the shape of the bump is set to a Gaussian function. The overall size of the bump can additionally be controlled using the f0 parameter in the top left corner. Magnitude: Change the bump structure The detailed shape of the bump can be arbitrarily complex. This can be achieved by changing the Analytic function as shown in the examples on the right. Alternatively, for even more arbitrary complexity use the Point function by clicking on the Function drop-down list. Edit the Point function following the instructions in on the Graphs page . Mesh resolution: Note that the application of the Bump Modifier may lead to poor mesh resolution in the bump. Currently the mesh resolution can not be improved locally. Therefore, if necessary, the overall mesh resolution can be increased by increasing the number of Segments in the Primitive tab of the object. Modifiers: Bump