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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

Render Module Overview This module takes care of the rendering of image and position-velocity diagrams. The output of 3-D volume data is also controlled from here. ​ ​ Overall the Render module consist of the render area where images and position-velocity (P-V) diagrams are displayed on the left side. On the right side you have the render Properties panel . It can be hidden by clicking on the Properties pane on the right. By default the General rendering parameter panel is open. From the drop-down list at the top of the panel several other sub-panels can be opened that deal with the settings for the virtual Camera , the Spectrum , the 3-D Output , Units and those of the Selected Window . We will deal with each of these in their respective sections below. ​ ​ In the default configuration only one image is rendered. If more images and P-V diagrams are to be show, those can be added and configured in the Windows drop-down menu above the render window. In the example above two columns have been set and three P-V windows have been added to the default image window. The slits for each P-V window is represented on the image window. ​ In order to delete a window click on the X icon in the top-right corner of the window. Note that this icon may be hidden if the overall Shape interface has been reduced in size. If so, then resize the user interface until the X icon appears and then click to delete the corresponding window. ​ ​ The Image Render Window As the name suggests the Image Render Window displays the output images from the rendered model. ​ To keep order when you have several windows, they can be named individuall y to remind you of the expected content. Just replace the text "Window 1", etc., in the text field of the menu above the window. ​ In the same window several types of images can be displayed by selecting one of the five colorful icons above the image. By hovering over an icon a tool-tip gives a brief hint to what the corresponding image displays. ​ By default a grey-scale image is displayed that represents the brightness variations that have been integrated along the line of sight. ​ The selected type of image is marked by a blue border around the icon. The "Color Image" displays the each sub-object with the color that was assigned to its mesh in the 3-D Module. This allows to clearly distinguish and identify them for diagnostic or visualization purposes. Importantly, in the P-V diagrams it helps distinguishing the contributions by different parts of the model. The "Red/blue Image" displays the model in terms of its red and blue shifted regions. Volume cells with a velocity vector that points more towards the observer is colored blue and those with a line of sight component that points away are red. Regions were line-of-sight integration has a mixture of red and blue contributions will appear in a mixed color tending towards white. The "Rainbow Image" is similar to the red/blue image in that it color codes the velocity field along the line of sight. The difference is that a continuous color coding is used that follows the spectral rainbow colors. The range of velocities to be color coded can be set up in a right-click menu. The "Spectrum Image" uses the physical spectrum as set up in the Spectrum section of the Properties Panel on the right of the Render Module. Again the color coding follows the rainbow colors that are distributed through the range of the physical spectrum. Now the rendered color will depend on the full physical setup of the model. Therefore this image type is used to render physical and photo-realistic models. The "Image Modifiers" handles the operators (modifiers) that process the rendered image in terms of brightness scaling, contours, inversion, etc. The "Move Slit" icon activates the interactive changing of the slit parameters such as position and width. When active the slit width is change using the mouse wheel. The horizontal position is changed by pressing and dragging the left mouse button. Vertical size and position are change the same way while keeping the "y" key pressed during the operation. The "Zoom Image" button activates zooming in and out of the image using the mouse wheel. The "Pan Image" button activates moving the image left, right, up and down by dragging it with the left mouse button pressed. The "Render Window" button allows you to drag out with the left mouse button a rectangular window on the image. Combined with the HD renderer and the "Use window" option in the General tab of the Render Module only this region will be rendered. This can greatly reduce rendering times if you need high resolution, but only need to see a small region for testing. The "Image Transparency" button allows you to change the transparency of the rendered image to be able to compare with the background reference image. Close and Remove the Window by clicking on this button and confirm in the pop-up window. Properties Panel ​ The Properties Panel on the right side of the Render Module has several section that can be accessed from the drop-down menu at the top. We will deal with each of them in the order they appear in the menu. ​ General The general project properties are set up in this panel, such as spatial resolution, type of renderer, memory management, autorender, etc. Camera Camera orientation angles are set. The parameters include position angle, inclination, and angles with respect to the axes of the global coordinate system Spectrum The spectral range for the physical radiation calculations is provided here in various possible units. Output Ouput of the full 3-D cube to file in different forms. Selected Window Key parameters of the currently selected image or P-V window can be set in this panel. General Camera Spectrum Output Selected Window

They are a key functionality in ShapeX the usage of which should be mastered in order to create the most realistic models. ​ Modifiers determine the properties of the objects as a function of position in space, hence it is important to know as much as possible about coordinate systems in general (Spherical, Cartesian & Cylindrical) and how they are used in ShapeX. See Coordinate Systems for more information on this topic. Modifiers are assigned to an object in the form of a list or Modifier Stack . This list of operators is executed on the object from the top to the bottom. For many of the modifiers the order in which they are executed does not matter. However, some operators, e.g. those that globally or locally involve some form of rotation, need to be stacked in the right order to produce the desired result. It is therefore important to know whether they order can be reversed or not. Knowledge about commutative properties of operators, or sufficient experimentation, is useful here. Modifiers Overview Modifiers are a operators in the 3-D module that allow you to add or change, i.e. modify properties of an object in the scene. There are different types of modifiers, some change the geometry of the mesh objects, others assign scalar or vector type physical properties such as density or velocity, respectively. After adding or selecting a particular modifiers, its Properties are displayed under the Modifier Stack . These can then be edited either by changing parameter value fields or after opening additional dialogs or graphs. ​ Adding or deleting modifiers is done using the blue + and the red x sign, respectively. When you select a modifier you can move it up and down in the stack with the green arrows. More than one modifier of the same type can be applied with different coordinate systems. In some cases you might have to change the Operation setting from Replace to either Add or Scale , otherwise the last modifier of this type replaces all previous ones. Using combinations of the same type of modifiers allows a larger variety of structures to be build. ​ Modifiers can also be copied and pasted with the corresponding buttons. When you use the paste button, a small dialog will open that asks you to decide whether the modifier should be a copy or and instance of the original modifier. When you choose copy then the new modifier will be completely independent from the other. However, and instanced modifier will always change together with its original and vice versa. Instanced modifiers are a great tool to provide the same parameters for more than one object, while only needing to change a single one of them. Types of Modifiers Physical Modifiers ​ Physical modifiers add or change physical properties as a function of position. They include the Density , Temperature , Pressure , Image Texture , Taper , Velocity, GField and BField . The Boost modifier is a helper modifier to the scalar physical modifiers and is used to change those quantities, but depending on the geometry of another mesh object. This is useful, for instance, to reduce or cut out part of the density of one object using another. Geometry Modifiers ​ Geometry modifiers change the structure of the polygon mesh. They include Bump, Curvature, Displacement, Image Displacement , Projection, Random, Sculpt, Shear, Shell, Size, Spiral, Squeeze, Squish, Stretch, Texture Displacement, Twist, Universal, and Warp . ​ The geometry modifiers move the vertices of a polygon mesh within the local coordinate system of an object. If you move or rotate the local coordinate system with a Rotation or Translate modifier, then the geometry modifiers act in the transformed coordinate system. Note that the Displacement modifier is a geometry modifier and moves only the vertices, but not the origin of the local coordinate system is does the Translate modifier. This is useful when you want to move a complete object, such as a small sphere within a fixed coordinate system and apply, for instance, the Velocity or Density modifiers in the original coordinate system. ​ Modifier Parameter Panel: Common Parameters ​ The parameters that modifiers take vary considerably. They are described in the sections for individual modifiers. ​ What they have in common are the Name field and the Enabled flag . In the Name field you can set a name for this particular modifier, which is strongly recommended, since it allows one to easily identify a modifier, which becomes more and more important once the number of modifiers increases for a particular object or for the project itself. It is especially important once the Modifier Module is used to manage a large number of modifiers. ​ As the name implies, the Enabled flag allows one to enable or disable a particular modifier. ​ Modifier Module: The Modifier Module becomes important once a model contains a large number of objects and modifiers. Often different objects have similar basically the same modifiers that have at least some parameters in common. If they are not instances of each other or have their parameters organized as global variables, the Modifier Module allows you to select a number of modifiers and change their parameters in a single operation. It also provides a good way to get an overview of which modifiers are used by which objects as well as the possibility to sort them by type. For more details on the Modifier Module go to its more detailed description in its own section of this manual.

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.

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

Physics Module Overview In the Physics Module you define the radiative properties of gas and dust components. Materials or "species" are set up which then are assigned to the objects from the 3D Module . This section covers how to access and use the interface functionality. For a more detailed account of the underlying physical and numerical procedures and assumptions, please refer to the Theory section of the manual or to the PDF document "Radiative Transfer in Shape" . ​ In general, we have tried to keep the physical calculations in line with the general philosophy of Shape, i.e. keep it simple and fast, but good enough to capture the most important phenomenology to allow qualitative and first order quantitative analysis. ​ Units: Note that contrary to most of the astrophysics literature, in Shape we use Standard International (SI) units, i.e. MKS units based on meter, kilogram and seconds. For example, astronomers used to thinking in terms of particles per ccm should multiply all the densities by 1e6 before they put them into the density modifier. If needed, unit conversions can be done easily on a number of websites, e.g. at UnitConversion. ​ Workflow ​ The basic procedure is to define material species in the Physics Module where you specify the radiative properties. The species are then assigned to a selected object in the 3-D Module using the Species drop-down list in the General tab. ​ By default, i.e if you do not specify a species, an objects has purely emitting species that is proportional to the density squared (n^2) ​ To change that default species you first select a basic species from the Species list that opens by clicking on the blue "+"-button on the toolbar at the top. Select the species in the species list and edit its properties. ​ ​ ​ ​ ​ ​ Selected species can be removed from the list by clicking on the Remove button on the main menu. Copy ing is a good why to use an existing species as a basis for a new one by just modifying some of its properties. The Sort button sorts the species in alphabetical order. ​ Selected species can be saved to disk individually or in groups using the Save button . This allows one to create a library of repeatedly used species. They can be loaded into any other project using the Open button. ​ ​ ​ Custom Species: The most likely and general species that you can choose is the Custom species. It allows to define all its properties manually. We discuss this species in some detail. ​ On the right there is a screenshot with the general options . ​ Name your species in a descriptive way that makes it easy to identify. This becomes important in complex projects with many different species. ​ Enable tick box: Species can be disable by switching off the Enable tick box . If more than one object use this species, they will all be switched off. ​ n scale: The n scale parameter allows you to multiply the density n of all objects that use this species by this factor. The resulting density will be used only for this species. Other species that an object may also use will not be affected by this factor. This allows to use different scales for the density depending on the species but specifying a single object mesh and density distribution. ​ Emitter boost: If the scattering and/or ionization options are used, then for this species only, the local brightness of the received emission from the emitter is multiplied by this factor. This is useful, for instance, when you need to brighten the objects scattered light without changing the emitter itself or the intervening absorption. ​ Color: In the color rendering mode by default an object is rendered with the color assigned to the mesh in the 3D Module. However, the rendered color can be changed easily without changing the mesh color by clicking on the color swatch (white rectangle) and selecting a different color. For this to take effect switch on the Override Color tick box. When selected, the color swatch above the flag determines the color of the object and overrides the color resulting from the physics setup. NOTE: There are many other ways to change the rendered color of an object using the spectral settings for the emission. They are explained below in their respective parameter settings. ​ Contribution : In the Contribution section different contributions to the radiation transfer can be enabled or disabled. They include the Emission (on by default), Absorption, Scattering, Ionization. We can also specify whether for ionization. If you do not wish to define the Absorption explicitly, then it can be calculated using Local Thermal Equilibrium (LTE) conditions. For that switch on the Absorption, LTE and Calculate K(j) flags. ​ You define the emissivity, absorption and scattering coefficients as a function of wavelength. First activate one of these coefficients in the Contribution area (there may be more than one active). Then Edit their wavelength dependence by setting up the panel that pops up in a separate window after clicking on the corresponding Edit button. ​ Coefficient: The pop-up panel for each coefficient mainly consists of an analytic function f(x) that is set up in the Function tab at the bottom, A display and control panel of such functions in the middle and the graph of the functions at the top. ​ In the graph, when using an analytical function, the reserved variables n and t give direct access to the density (by number) and temperature fields, respectively, as provided by the corresponding modifiers in the 3D Module. ​ The x variable in this graph refers to the wavelength in meters. Remember that the meaning of x varies by context throughout Shape. ​ Spectral distributions from external data can be used, too. To do this remove the default function first by selecting it in the center section of the panel and clicking on the Remove button. Now click on Add and from the pop-up menu select Point-Function. Now you can load the external data file by clicking on the Load button. The data format is ASCII in vertical column with the wavelength in meters in the first column and intensity in the second column. ​ For the Scattering and (Photo-) Ionization coefficients the same setup is required as a function of wavelength as for the emission coefficient. ​ For scattering, in addition, a scattering function as a function of angle may be defined via the Phase Function . In this context the variable x is the angle in units of radian. By default there is a Henyey-Greenstein with the coefficient g=0 (isotropic scattering) applied. The coefficient g can be set in the Variables tab (or in the Math Module vía a Global Variable). ​ Note that for scattering to work, you need at least one emitter objects in the 3D Module. ​ ​ ​ Dust Species: The dust species has the options to contribute by Emission , Absorption and Scattering . ​ The grain attributes include the range of radii (assuming a power-law distribution with parameters a, a_min, a_max, q), the index of refraction with the real part n and the complex part k. k controls the absorption. Both, n and k can be set as a function of wavelength, by editing the corresponding graph (click on the Edit button). ​ The default option Custom in the Type drop-down menu has a simple default setup, which can be changed as required. There are a few additional options from the Type drop-down list approximating different types of grains. Here the index of refraction n and the absorption coefficients are based on data. A graph of these can be seen by clicking on the corresponding Edit button . To fully appreciate you might have to adjust the settings of the graph (right-click) ​ The Scattering currently is single scattering. Dust scattering calculations have the option to include a scattering phase function. To see and edit the function click on the Edit button to the right of the label Phase Function . The preset is the Henyey-Greenstein function . The single parameter g of this function can be changed in the variables tab of the graph. The user can change this function. Note that in this context the variable x stands for the angle in units of radians . For scattering calculations remember that you need at least one Emitter object in the 3D Module. The properties of the Emitter can be set after you select Emitters from the Object Type drop-down menu at the top-right of the 3D Module. ​ The default dust model is an approximation to the Mie model. For a the full Mie computer enable the corresponding flag. For more details on the approximate Mie calculation see the document "Physics in Shape" . ​ ​ Atomic Species: ​ The atomic species allows to calculate the emission properties based on the atomic transition coefficients and the physical conditions like density and temperature in the object. ​ NOTE: Usage of atomic species for the calculation of emission and absorption requires detailed knowledge of the underlying physics. We recommend the application of this option only for users that are experienced in this area. Testing of the atomic calculations in Shape has been limited so far. It is advised you solve your own test problems comparing the results either with analytical calculations. ​ You have the choice from two databases for the atomic coefficients: Kurucz and Chianti . To apply one or the other database select the Database at the bottom of the Species Panel. ​ Now select the Ionization State of the species in the Misc panel of the Options. For hydrogen the ionization state has to be set to "0", because lines only occur for neutral hydrogen, even thought they might come from a recombination. Processes that involve free electrons, i.e. Bound-Free (BF), take the next higher ionization state into account automatically. Now select the Database for this particular species from the drop-down menu. Click on the Reload button to read the lines. If the background of the Element label changes from red to green, then you successfully read the lines. If it is still red, one or more of the settings are incorrect. ​ To see a listing of the lines and their atomic properties click on the View Lines button. It opens a table of the atomic properties in the database. If you want to see only the lines in a certain wavelength interval, you can set Constraints for a minimum and maximum wavelength, as well as for the minimum and maximum Einstein coefficients (e.g. to select for allowed or forbidden lines). ​ The Contributions area allows you to select from various radiative process to be included in the calculations. The label B stands for Bound and F for Free. Note that not all processes are available for all the atoms, except for hydrogen. ​ The numerical factor the right of the contributions is a scaling factor. By default it is set to 1. The toolbar of the Physics Module

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

Coordinate Systems ​ The hierarchy and types of coordinate systems is key to the flexibility of the modeling of structures and velocity fields. Video Tutorial The Modifier Stack ​ Graphical representations of functions are a fundamental tool to control parameters that vary in space, time or wavelength. Video Tutorial Graphs ​ Graphical representations of functions are a fundamental tool to control parameters that vary in space, time or wavelength. Video Tutorial Textures ​ Textures are either random procedural 3-D structures or external images that determine structures of density, temperature or others. Video Tutorial Particles Particles are used to generate complex specific structures by spraying them interactively on surfaces and into volumes. Video Tutorial