# 3D Visualization and Volume Rendering¶

yt has the ability to create 3D visualizations using a process known as volume rendering (oftentimes abbreviated VR). This volume rendering code differs from the standard yt infrastructure for generating Slices & Projections in that it evaluates the radiative transfer equations through the volume with user-defined transfer functions for each ray. Thus it can accommodate both opaque and transparent structures appropriately. Currently all of the rendering capabilities are implemented in software, requiring no specialized hardware. Optimized versions implemented with OpenGL and utilizing graphics processors are being actively developed.

Note

There is a Jupyter notebook containing a volume rendering tutorial available at Volume Rendering Tutorial.

## Volume Rendering Introduction¶

Constructing a 3D visualization is a process of describing the “scene” that will be rendered. This includes the location of the viewing point (i.e., where the “camera” is placed), the method by which a system would be viewed (i.e., the “lens,” which may be orthographic, perspective, fisheye, spherical, and so on) and the components that will be rendered (render “sources,” such as volume elements, lines, annotations, and opaque surfaces). The 3D plotting infrastructure then develops a resultant image from this scene, which can be saved to a file or viewed inline.

By constructing the scene in this programmatic way, full control can be had over each component in the scene as well as the method by which the scene is rendered; this can be used to prototype visualizations, inject annotation such as grid or continent lines, and then to render a production-quality visualization. By changing the “lens” used, a single camera path can output images suitable for planetarium domes, immersive and head tracking systems (such as the Oculus Rift or recent 360-degree/virtual reality movie viewers such as the mobile YouTube app), as well as standard screens.

## Volume Rendering Components¶

The Scene class and its subcomponents are organized as follows. Indented objects hang off of their parent object.

• Scene - container object describing a volume and its contents
• Sources - objects to be rendered
• VolumeSource - simulation volume tied to a dataset
• TransferFunction - mapping of simulation field values to color, brightness, and transparency

• OpaqueSource - Opaque structures like lines, dots, etc.

• Annotations - Annotated structures like grid cells, simulation boundaries, etc.

• Camera - object for rendering; consists of a location, focus, orientation, and resolution
• Lens - object describing method for distributing rays through Sources

### Scene¶

The Scene is the container class which encompasses the whole of the volume rendering interface. At its base level, it describes an infinite volume, with a series of RenderSource objects hanging off of it that describe the contents of that volume. It also contains a Camera for rendering that volume.. All of its classes can be accessed and modified as properties hanging off of the scene. The scene’s most important functions are render() for casting rays through the scene and save() for saving the resulting rendered image to disk.

The easiest way to create a scene with sensible defaults is to use the functions: create_scene() (creates the scene) or volume_render() (creates the scene and then triggers ray tracing to produce an image). See the Annotated Examples for details.

### RenderSources¶

RenderSource objects comprise the contents of what is actually rendered. One can add several different RenderSources to a Scene and the ray-tracing step will pass rays through all of them to produce the final rendered image.

#### VolumeSources¶

VolumeSource objects are 3D Geometric Objects of individual datasets placed into the scene for rendering. Each VolumeSource requires a TransferFunction to describe how the fields in the VolumeSource dataset produce different colors and brightnesses in the resulting image.

#### OpaqueSources¶

In addition to semi-transparent objects, fully opaque structures can be added to a scene as OpaqueSource objects including LineSource objects and PointSource objects. These are useful if you want to annotate locations or particles in an image, or if you want to draw lines connecting different regions or vertices. For instance, lines can be used to draw outlines of regions or continents.

Worked examples of using the LineSource and PointSource are available at Volume Rendering with Points and Volume Rendering with Lines.

#### Annotations¶

Similar to OpaqueSources, annotations enable the user to highlight certain information with opaque structures. Examples include BoxSource, GridSource, and CoordinateVectorSource. These annotations will operate in data space and can draw boxes, grid information, and also provide a vector orientation within the image.

For example scripts using these features, see Volume Rendering with Bounding Box and Overlaid Grids.

### Transfer Functions¶

A transfer function describes how rays that pass through the domain of a VolumeSource are mapped from simulation field values to color, brightness, and opacity in the resulting rendered image. A transfer function consists of an array over the x and y dimensions. The x dimension typically represents field values in your underlying dataset to which you want your rendering to be sensitive (e.g. density from 1e20 to 1e23). The y dimension consists of 4 channels for red, green, blue, and alpha (opacity). A transfer function starts with all zeros for its y dimension values, implying that rays traversing the VolumeSource will not show up at all in the final image. However, you can add features to the transfer function that will highlight certain field values in your rendering.

#### TransferFunctionHelper¶

Because good transfer functions can be difficult to generate, the TransferFunctionHelper exists in order to help create and modify transfer functions with smart defaults for your datasets.

To ease constructing transfer functions, each VolumeSource instance has a TransferFunctionHelper instance associated with it. This is the easiest way to construct and customize a ColorTransferFunction for a volume rendering.

In the following example, we make use of the TransferFunctionHelper associated with a scene’s VolumeSource to create an appealing transfer function between a physically motivated range of densities in a cosmological simulation:

import yt

sc = yt.create_scene(ds, lens_type='perspective')

# Get a reference to the VolumeSource associated with this scene
# It is the first source associated with the scene, so we can refer to it
# using index 0.
source = sc[0]

# Set the bounds of the transfer function
source.tfh.set_bounds((3e-31, 5e-27))

# set that the transfer function should be evaluated in log space
source.tfh.set_log(True)

# Make underdense regions appear opaque
source.tfh.grey_opacity = True

# Plot the transfer function, along with the CDF of the density field to
# see how the transfer function corresponds to structure in the CDF
source.tfh.plot('transfer_function.png', profile_field='density')

# save the image, flooring especially bright pixels for better contrast
sc.save('rendering.png', sigma_clip=6.0)


For fun, let’s make the same volume_rendering, but this time setting grey_opacity=False, which will make overdense regions stand out more:

import yt

sc = yt.create_scene(ds, lens_type='perspective')

source = sc[0]

# Set transfer function properties
source.tfh.set_bounds((3e-31, 5e-27))
source.tfh.set_log(True)
source.tfh.grey_opacity = False

source.tfh.plot('transfer_function.png', profile_field='density')

sc.save('rendering.png', sigma_clip=4.0)


To see a full example on how to use the TransferFunctionHelper interface, follow the annotated Transfer Function Helper Tutorial.

#### Color Transfer Functions¶

A ColorTransferFunction is the standard way to map dataset field values to colors, brightnesses, and opacities in the rendered rays. One can add discrete features to the transfer function, which will render isocontours in the field data and works well for visualizing nested structures in a simulation. Alternatively, one can also add continuous features to the transfer function.

See Volume Rendering with a Custom Transfer Function for an annotated, runnable tutorial explaining usage of the ColorTransferFunction.

There are several methods to create a ColorTransferFunction for a volume rendering. We will describe the low-level interface for constructing color transfer functions here, and provide examples for each option.

The easiest way to create a ColorTransferFunction is to use the add_layers() function, which will add evenly spaced isocontours along the transfer function, sampling a colormap to determine the colors of the layers.

import numpy as np
import yt

sc = yt.create_scene(ds, lens_type='perspective')

source = sc[0]

source.set_field('density')
source.set_log(True)

bounds = (3e-31, 5e-27)

# Since this rendering is done in log space, the transfer function needs
# to be specified in log space.
tf = yt.ColorTransferFunction(np.log10(bounds))

source.tfh.tf = tf
source.tfh.bounds = bounds

source.tfh.plot('transfer_function.png', profile_field='density')

sc.save('rendering.png', sigma_clip=6)


##### sample_colormap¶

To add a single gaussian layer with a color determined by a colormap value, use sample_colormap().

import numpy as np
import yt

sc = yt.create_scene(ds, lens_type='perspective')

source = sc[0]

source.set_field('density')
source.set_log(True)

bounds = (3e-31, 5e-27)

# Since this rendering is done in log space, the transfer function needs
# to be specified in log space.
tf = yt.ColorTransferFunction(np.log10(bounds))

tf.sample_colormap(np.log10(1e-30), w=.01, colormap='arbre')

source.tfh.tf = tf
source.tfh.bounds = bounds

source.tfh.plot('transfer_function.png', profile_field='density')

sc.save('rendering.png', sigma_clip=6)


If you would like to add a gaussian with a customized color or no color, use add_gaussian().

import numpy as np
import yt

sc = yt.create_scene(ds, lens_type='perspective')

source = sc[0]

source.set_field('density')
source.set_log(True)

bounds = (3e-31, 5e-27)

# Since this rendering is done in log space, the transfer function needs
# to be specified in log space.
tf = yt.ColorTransferFunction(np.log10(bounds))

tf.add_gaussian(np.log10(1e-29), width=.005, height=[0.753, 1.0, 0.933, 1.0])

source.tfh.tf = tf
source.tfh.bounds = bounds

source.tfh.plot('transfer_function.png', profile_field='density')

sc.save('rendering.png', sigma_clip=6)


##### map_to_colormap¶

Finally, to map a colormap directly to a range in densities use map_to_colormap(). This makes it possible to map a segment of the transfer function space to a colormap at a single alpha value. Where the above options produced layered volume renderings, this allows all of the density values in a dataset to contribute to the volume rendering.

import numpy as np
import yt

sc = yt.create_scene(ds, lens_type='perspective')

source = sc[0]

source.set_field('density')
source.set_log(True)

bounds = (3e-31, 5e-27)

# Since this rendering is done in log space, the transfer function needs
# to be specified in log space.
tf = yt.ColorTransferFunction(np.log10(bounds))

def linramp(vals, minval, maxval):
return (vals - vals.min())/(vals.max() - vals.min())

tf.map_to_colormap(np.log10(3e-31), np.log10(5e-27), colormap='arbre',
scale_func=linramp)

source.tfh.tf = tf
source.tfh.bounds = bounds

source.tfh.plot('transfer_function.png', profile_field='density')

sc.save('rendering.png', sigma_clip=6)


#### Projection Transfer Function¶

This is designed to allow you to generate projections like what you obtain from the standard Projection Plots, and it forms the basis of Off Axis Projection Plots. See Off-Axis Projection (an alternate method) for a simple example. Note that the integration here is scaled to a width of 1.0; this means that if you want to apply a colorbar, you will have to multiply by the integration width (specified when you initialize the volume renderer) in whatever units are appropriate.

#### Planck Transfer Function¶

This transfer function is designed to apply a semi-realistic color field based on temperature, emission weighted by density, and approximate scattering based on the density. This class is currently under-documented, and it may be best to examine the source code to use it.

#### More Complicated Transfer Functions¶

For more complicated transfer functions, you can use the MultiVariateTransferFunction object. This allows for a set of weightings, linkages and so on. All of the information about how all transfer functions are used and values are extracted is contained in the sourcefile utilities/lib/grid_traversal.pyx. For more information on how the transfer function is actually applied, look over the source code there.

### Camera¶

The Camera object is what it sounds like, a camera within the Scene. It possesses the quantities:

#### Moving and Orienting the Camera¶

There are multiple ways to manipulate the camera viewpoint and orientation. One can set the properties listed above explicitly, or one can use the Camera helper methods. In either case, any change triggers an update of all of the other properties. Note that the camera exists in a right-handed coordinate system centered on the camera.

Rotation-related methods

For the rotation methods, the camera pivots around the rot_center rotation center. By default, this is the camera position, which means that the camera doesn’t change its position at all, it just changes its orientation.

Zoom-related methods

Perhaps counterintuitively, the camera does not get closer to the focus during a zoom; it simply reduces the width of the field of view.

Translation-related methods

The iterative methods provide iteration over a series of changes in the position or orientation of the camera. These can be used within a loop. For an example on how to use all of these camera movement functions, see Moving a Volume Rendering Camera.

### Camera Lenses¶

Cameras possess Lens objects, which control the geometric path in which rays travel to the camera. These lenses can be swapped in and out of an existing camera to produce different views of the same Scene. For a full demonstration of a Scene object rendered with different lenses, see Various Lens Types for Volume Rendering.

#### Plane Parallel¶

The PlaneParallelLens is the standard lens type used for orthographic projections. All rays emerge parallel to each other, arranged along a plane.

#### Perspective and Stereo Perspective¶

The PerspectiveLens adjusts for an opening view angle, so that the scene will have an element of perspective to it. StereoPerspectiveLens is identical to PerspectiveLens, but it produces two images from nearby camera positions for use in 3D viewing. How 3D the image appears at viewing will depend upon the value of disparity, which is half the maximum distance between two corresponding points in the left and right images. By default, it is set to 3 pixels.

#### Fisheye or Dome¶

The FisheyeLens is appropriate for viewing an arbitrary field of view. Fisheye images are typically used for dome-based presentations; the Hayden planetarium for instance has a field of view of 194.6. The images returned by this camera will be flat pixel images that can and should be reshaped to the resolution.

#### Spherical and Stereo Spherical¶

The SphericalLens produces a cylindrical-spherical projection. Movies rendered in this way can be displayed as YouTube 360-degree videos (for more information see the YouTube help: Upload 360-degree videos). StereoSphericalLens is identical to SphericalLens but it produces two images from nearby camera positions for virtual reality movies, which can be displayed in head-tracking devices (e.g. Oculus Rift) or in mobile YouTube app with Google Cardboard (for more information see the YouTube help: Upload virtual reality videos). This virtual reality video on YouTube is an example produced with StereoSphericalLens. As in the case of StereoPerspectiveLens, the difference between the two images can be controlled by changing the value of disparity (See above).

## Annotated Examples¶

Warning

3D visualizations can be fun but frustrating! Tuning the parameters to both look nice and convey useful scientific information can be hard. We’ve provided information about best practices and tried to make the interface easy to develop nice visualizations, but getting them just right is often time-consuming. It’s usually best to start out simple and expand and tweak as needed.

The scene interface provides a modular interface for creating renderings of arbitrary data sources. As such, manual composition of a scene can require a bit more work, but we will also provide several helper functions that attempt to create satisfactory default volume renderings.

When the volume_render() function is called, first an empty Scene object is created. Next, a VolumeSource object is created, which decomposes the volume elements into a tree structure to provide back-to-front rendering of fixed-resolution blocks of data. (If the volume elements are grids, this uses a AMRKDTree object.) When the VolumeSource object is created, by default it will create a transfer function based on the extrema of the field that you are rendering. The transfer function describes how rays that pass through the domain are “transferred” and thus how brightness and color correlates to the field values. Modifying and adjusting the transfer function is the primary way to modify the appearance of an image based on volumes.

Once the basic set of objects to be rendered is constructed (e.g. Scene, RenderSource, and VolumeSource objects) , a Camera is created and added to the scene. By default the creation of a camera also creates a plane-parallel Lens object. The analog to a real camera is intentional – a camera can take a picture of a scene from a particular point in time and space, but different lenses can be swapped in and out. For example, this might include a fisheye lens, a spherical lens, or some other method of describing the direction and origin of rays for rendering. Once the camera is added to the scene object, we call the main methods of the Scene class, render() and save(). When rendered, the scene will loop through all of the RenderSource objects that have been added and integrate the radiative transfer equations through the volume. Finally, the image and scene object is returned to the user. An example script the uses the high-level volume_render() function to quickly set up defaults is:

import yt

# volume render the 'density' field, and save the resulting image
im, sc = yt.volume_render(ds, 'density', fname='rendering.png')

# im is the image array generated. it is also saved to 'rendering.png'.
# sc is an instance of a Scene object, which allows you to further refine
# your renderings and later save them.

# Let's zoom in and take a closer look
sc.camera.width = (300, 'kpc')
sc.camera.switch_orientation()

# Save the zoomed in rendering
sc.save('zoomed_rendering.png')


Alternatively, if you don’t want to immediately generate an image of your volume rendering, and you just want access to the default scene object, you can skip the expensive operation of rendering by just running the create_scene() function in lieu of the volume_render() function. Example:

import numpy as np
import yt

sc = yt.create_scene(ds, 'density')

source = sc[0]

source.transfer_function = yt.ColorTransferFunction(
np.log10((1e-30, 1e-23)), grey_opacity=True)

def linramp(vals, minval, maxval):
return (vals - vals.min())/(vals.max() - vals.min())

source.transfer_function.map_to_colormap(
np.log10(1e-25), np.log10(8e-24), colormap='arbre', scale_func=linramp)

# For this low resolution dataset it's very important to use interpolated
# vertex centered data to avoid artifacts. For high resolution data this
# setting may cause a substantial slowdown for marginal visual improvement.
source.set_use_ghost_zones(True)

cam = sc.camera

cam.width = 15*yt.units.kpc
cam.focus = ds.domain_center
cam.normal_vector = [-0.3, -0.3, 1]
cam.switch_orientation()

sc.save('rendering.png')


For an in-depth tutorial on how to create a Scene and modify its contents, see this annotated Volume Rendering Tutorial.

## Volume Rendering Method¶

Direct ray casting through a volume enables the generation of new types of visualizations and images describing a simulation. yt has the facility to generate volume renderings by a direct ray casting method. However, the ability to create volume renderings informed by analysis by other mechanisms – for instance, halo location, angular momentum, spectral energy distributions – is useful.

The volume rendering in yt follows a relatively straightforward approach.

1. Create a set of transfer functions governing the emission and absorption as a function of one or more variables. ($$f(v) \rightarrow (r,g,b,a)$$) These can be functions of any field variable, weighted by independent fields, and even weighted by other evaluated transfer functions. (See transfer_functions.)

2. Partition all chunks into non-overlapping, fully domain-tiling “bricks.” Each of these “bricks” contains the finest available data at any location.

3. Generate vertex-centered data for all grids in the volume rendered domain.

4. Order the bricks from front-to-back.

5. Construct plane of rays parallel to the image plane, with initial values set to zero and located at the back of the region to be rendered.

6. For every brick, identify which rays intersect. These are then each ‘cast’ through the brick.

1. Every cell a ray intersects is sampled 5 times (adjustable by parameter), and data values at each sampling point are trilinearly interpolated from the vertex-centered data.

2. Each transfer function is evaluated at each sample point. This gives us, for each channel, both emission ($$j$$) and absorption ($$\alpha$$) values.

3. The value for the pixel corresponding to the current ray is updated with new values calculated by rectangular integration over the path length:

$$v^{n+1}_{i} = j_{i}\Delta s + (1 - \alpha_{i}\Delta s )v^{n}_{i}$$

where $$n$$ and $$n+1$$ represent the pixel before and after passing through a sample, $$i$$ is the color (red, green, blue) and $$\Delta s$$ is the path length between samples.

4. Determine if any addition integrate will change the sample value; if not, terminate integration. (This reduces integration time when rendering front-to-back.)

7. The image is returned to the user:

## Parallelism¶

yt can utilize both MPI and OpenMP parallelism for volume rendering. Both, and their combination, are described below.

### MPI Parallelization¶

Currently the volume renderer is parallelized using MPI to decompose the volume by attempting to split up the AMRKDTree in a balanced way. This has two advantages:

1. The AMRKDTree construction is parallelized since each MPI task only needs to know about the part of the tree it will traverse.

2. Each MPI task will only read data for portion of the volume that it has assigned.

Once the AMRKDTree has been constructed, each MPI task begins the rendering phase until all of its bricks are completed. At that point, each MPI task has a full image plane which we then use a tree reduction to construct the final image, using alpha blending to add the images together at each reduction phase.

Caveats:

1. At this time, the AMRKDTree can only be decomposed by a power of 2 MPI tasks. If a number of tasks not equal to a power of 2 are used, the largest power of 2 below that number is used, and the remaining cores will be idle. This issue is being actively addressed by current development.

2. Each MPI task, currently, holds the entire image plane. Therefore when image plane sizes get large (>2048^2), the memory usage can also get large, limiting the number of MPI tasks you can use. This is also being addressed in current development by using image plane decomposition.

### OpenMP Parallelization¶

The volume rendering also parallelized using the OpenMP interface in Cython. While the MPI parallelization is done using domain decomposition, the OpenMP threading parallelizes the rays intersecting a given brick of data. As the average brick size relative to the image plane increases, the parallel efficiency increases.

By default, the volume renderer will use the total number of cores available on the symmetric multiprocessing (SMP) compute platform. For example, if you have a shiny new laptop with 8 cores, you’ll by default launch 8 OpenMP threads. The number of threads can be controlled with the num_threads keyword in snapshot(). You may also restrict the number of OpenMP threads used by default by modifying the environment variable OMP_NUM_THREADS.

### Running in Hybrid MPI + OpenMP¶

The two methods for volume rendering parallelization can be used together to leverage large supercomputing resources. When choosing how to balance the number of MPI tasks vs OpenMP threads, there are a few things to keep in mind. For these examples, we will assume you are using Nmpi MPI tasks, and Nmp OpenMP tasks, on a total of P cores. We will assume that the machine has a Nnode SMP nodes, each with cores_per_node cores per node.

1. For each MPI task, num_threads (or OMP_NUM_THREADS) OpenMP threads will be used. Therefore you should usually make sure that Nmpi*Nmp = P.

2. For simulations with many grids/AMRKDTree bricks, you generally want to increase Nmpi.

3. For simulations with large image planes (>2048^2), you generally want to decrease Nmpi and increase Nmp. This is because, currently, each MPI task stores the entire image plane, and doing so can approach the memory limits of a given SMP node.

4. Please make sure you understand the (super)computer topology in terms of the numbers of cores per socket, node, etc when making these decisions.

5. For many cases when rendering using your laptop/desktop, OpenMP will provide a good enough speedup by default that it is preferable to launching the MPI tasks.

There are currently two models for opacity when rendering a volume, which are controlled in the ColorTransferFunction with the keyword grey_opacity=False or True (the default). The first will act such for each of the red, green, and blue channels, each channel is only opaque to itself. This means that if a ray that has some amount of red then encounters material that emits blue, the red will still exist and in the end that pixel will be a combination of blue and red. However, if the ColorTransferFunction is set up with grey_opacity=True, then blue will be opaque to red, and only the blue emission will remain.
If your images appear to be too dark, you can try using the sigma_clip keyword in the save() or volume_render() functions. Because the brightness range in an image is scaled to match the range of emissivity values of underlying rendering, if you have a few really high-emissivity points, they will scale the rest of your image to be quite dark. sigma_clip = N can address this by removing values that are more than N standard deviations brighter than the mean of your image. Typically, a choice of 4 to 6 will help dramatically with your resulting image. See the cookbook recipe Volume Rendering with Sigma Clipping for a demonstration.