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Graphs

Description​

The Quest Graph Visualizer is a sophisticated VR application designed to render interactive 3D graphs, offering a dynamic and immersive way to explore mathematical functions and partial derivatives. This app is particularly useful for users interested in visualizing complex mathematical landscapes.

Image: Screenshot of the Graphs Quest app

The app presents a menu from which users can select predefined 3D functions, ranging from simple sinusoidal wave functions to more complex shapes like a torus or a hyperbolic surface. Users can select a function using the controllers. Once a menu entry is selected, the mesh of the 3D function is calculated and visualized in front of the user. Users can change the visualization mode, for example, switching from a solid surface to a wireframe mode, or toggling normals on and off (by clicking the controller buttons). Additionally, after setting the controllers aside, users can visualize a Gradient Descent path at arbitrary locations using simple hand interactions: the left hand points with the index finger to select the intersection point on the surface, while the right hand projects the fingertips onto the function's surface.

Adding a new 3D function for visualization is straightforward — simply provide the function pointer to the new function to be visualized. The app utilizes Ocean's AutomaticDifferentiation functionality to automatically calculate the function values and their partial derivatives.

Furthermore, a custom scale and visualization boundary can be defined for each graph to ensure that only a specific part of the function is visualized. This demo serves as an excellent introduction to Ocean's mathematical capabilities and demonstrates how to customize and adjust 3D meshes for rendering.

Building​

The following instructions are for macOS but can be easily converted to other host operating systems. First, ensure that the

have been completed. And that the third-party libraries have been built according to these instructions.

Then run the following steps:

# Define environment variables required for Android and Quest apps as per setup instructions above:
# ANDROID_HOME, ANDROID_NDK, ANDROID_NDK_VERSION, JAVA_HOME, and OVRPlatformSDK_ROOT

# Adjust this to your location of the third-party libraries
export OCEAN_THIRDPARTY_PATH="${HOME}/install_ocean_thirdparty"

cd ${OCEAN_DEVELOPMENT_PATH}/build/gradle/application/ocean/demo/platform/meta/quest/openxr/graphs/quest

./gradlew assemble

# Install debug build of the app
adb install app/build/outputs/apk/debug/app-debug.apk

# Install release build of the app
adb install app/build/outputs/apk/release/app-release.apk

Features​

  • 3D Graph Rendering: Displays mathematical functions in 3D.
  • Visualization Options: Switch between solid, wireframe, and normals views.
  • Hand-Gesture Interaction: Explore Gradient Descent paths with hand movements.
  • Automatic Differentiation: Computes values and derivatives automatically.

Educational and Immersive​

  • Hands-On Learning: Direct interaction with mathematical concepts.
  • Visualizing Complex Concepts: Makes abstract math tangible and visual.