LogoLogo
WebsiteSupportDownloadsForumsQuick LinksContact Us
v3.1
v3.1
  • OptiTrack Documentation
  • WHAT'S NEW
    • What's New in Motive 3.1
  • QUICK START GUIDES
    • Quick Start Guide: Getting Started
    • Quick Start Guide: Prime Color Camera Setup
    • Quick Start Guide: Precision Capture
    • Quick Start Guide: Tutorial Videos
    • Quick Start Guide: Active Marker Tracking
    • Quick Start Guide: Outdoor Tracking Setup
  • HARDWARE
    • Cameras
      • Ethernet Cameras
        • PrimeX 120
        • PrimeX 41
        • PrimeX 22
        • PrimeX 13
        • PrimeX 13W
        • SlimX 13
        • Prime Color
      • USB Cameras
        • Slim 3U
        • Flex 13
        • Flex 3
        • Duo 3
        • Trio 3
        • Adjusting Global Origin for Tracking Bars
    • Prepare Setup Area
    • Camera Mount Structures
    • Camera Placement
    • Ethernet Camera Network Setup
      • General Overview and Specs
      • Windows 10 Network Settings
      • Cabling and Load Balancing
      • Switch Configuration for PrimeX 120
      • NETGEAR ProSafe GSM7228S: Disabling the Broadcast Storm Control
      • White/Blacklisting Cameras
    • USB Camera System Setup
      • USB Camera Network Overview and Specs
      • Duo 3 and Trio 3 Setup
      • Tracking Bar Coordinate System
        • Transforming Coordinate System: Global to Local
    • Aiming and Focusing
    • Camera Status Indicators
  • MOTIVE
    • Installation and License Activation
    • Motive Basics
    • Calibration
      • Continuous Calibration
      • Continuous Calibration (Info Pane)
      • Calibration Squares
    • Markers
    • Assets
      • Gizmo Tool: Translate, Rotate, and Scale
    • Rigid Body Tracking
      • Aligning Rigid Body Pivot Point with a Replicated 3D Model
    • Skeleton Tracking
    • Trained Markersets
    • IMU Sensor Fusion
    • Data Recording
      • Data Types
    • Labeling
    • Data Editing
    • Data Export
      • Data Export: BVH
      • Data Export: C3D
      • Data Export: CSV
      • Data Export: FBX
      • Data Export: TRC
    • Data Streaming
    • Camera Video Types
    • Audio Recording
    • Motive HotKeys
    • Measurement Probe Kit Guide
    • Motive Batch Processor
    • Reconstruction and 2D Mode
  • MOTIVE UI PANES
    • Settings
      • Settings: General
      • Settings: Assets
      • Settings: Live Pipeline
      • Settings: Streaming
      • Settings: Views
      • Settings: Mouse and Keyboard
      • Settings: Audio
    • Assets Pane
    • Builder Pane
    • Constraints Pane
      • Constraints XML Files
    • Calibration Pane
    • Data Pane
    • Devices Pane
    • Edit Tools Pane
    • Graph View Pane
    • Info Pane
    • Labels Pane
    • Log Pane
    • Probe Pane
    • Properties Pane
      • Properties Pane: Camera
      • Properties Pane: Force Plates
      • Properties Pane: NI-DAQ
      • Properties Pane: OptiHub2
      • Properties Pane: Rigid Body
      • Properties Pane: Skeleton
      • Properties Pane: Take
      • Properties Pane: Trained Markerset
      • Properties Pane: eSync2
    • Status Panel
    • Toolbar/Command Bar
    • Control Deck
    • Viewport
  • PLUGINS
    • OptiTrack Blender Plugin
      • OptiTrack Blender Plugin
    • OptiTrack Unreal Engine Plugin
      • Unreal Engine: OptiTrack Streaming Client Plugin
      • Unreal Engine: OptiTrack Live Link Plugin
        • Quick Start Guide: Real-Time Retargeting in Unreal Engine with Live Link Content
        • Unreal Editor for Fortnite (UEFN): OptiTrack Plugin for Live Link Hub
        • Unreal Engine: Live Link Camera Stream Setup
        • Live Link Content: Active Puck Static Meshes
      • Unreal Engine: MotionBuilder Workflow
      • Unreal Engine: HMD Setup
      • Unreal Engine VCS Inputs
    • OptiTrack Unity Plugin
      • Unity: HMD Setup
    • OptiTrack OpenVR Driver
    • Autodesk Maya
      • Autodesk Maya: OptiTrack Insight VCS Plugin
    • Autodesk MotionBuilder
      • Autodesk MotionBuilder Plugin
      • Autodesk MotionBuilder: OptiTrack Skeleton Plugin
      • Autodesk MotionBuilder: OptiTrack Optical Plugin
      • Autodesk MotionBuilder: OptiTrack Insight VCS Plugin
      • Autodesk MotionBuilder: Timecode Data
    • OptiTrack Peripheral API
    • External Plugins
      • Houdini 19 Integration
  • ACTIVE COMPONENTS
    • Active Components Hardware
      • Active Puck
      • CinePuck
      • BaseStation
      • Information for Assembling the Active Tags
      • Manus Glove Setup
    • Configuration
      • Active Batch Programmer
      • Active Hardware Configuration: PuTTY
      • Active Component Firmware Compatibility
    • Active Marker Tracking
      • Active Finger Marker Set
  • SYNCHRONIZATION
    • Synchronization Hardware
      • External Device Sync Guide: eSync 2
      • External Device Sync Guide: OptiHub2
    • Synchronization Setup
    • OptiTrack Timecode
  • VIRTUAL PRODUCTION
    • Unreal Engine: OptiTrack InCamera VFX
    • Entertainment Marker Sets
    • PrimeX 41
  • MOVEMENT SCIENCES
    • Movement Sciences Hardware
      • General Motive Force Plate Setup
      • AMTI Force Plate Setup
      • Bertec Force Plate Setup
      • Kistler Force Plate Setup
      • Delsys EMG Setup
      • NI-DAQ Setup
      • Multiple Device Setup
    • Movement Sciences Marker Sets
      • Biomechanics Marker Sets
      • Biomech (57)
      • Rizzoli Marker Sets
    • For Visual3D Users
    • Prime Color Camera Setup
      • Prime Color Setup: Required Components
      • Prime Color Setup: Hardware Setup
      • Prime Color Camera Setup: Camera Settings
      • Prime Color Camera Setup: Prime Color FS Calibration
      • Prime Color Setup: Data Recording / Export
      • Prime Color Camera Setup: FAQ / Troubleshooting
      • Prime Color Camera Setup: Windows Network Settings
  • VIRTUAL REALITY
    • VR Plugins
      • VR Unreal Engine
        • OptiTrack Unreal Engine Plugin
        • Unreal Engine: OptiTrack Live Link Plugin
          • UE5.1 Live Link Retarget External Workaround
        • Unreal Engine: Using the OptiTrack Streaming Client Plugin
        • Unreal Engine VCS Inputs
      • VR Unity
        • OptiTrack Unity Plugin
      • VR OpenVR
        • OptiTrack OpenVR Driver
    • VR HMD Setup
      • Unreal Engine: HMD Setup
      • Unity: HMD Setup
      • Manually Calibrating the HMD Pivot Point
      • Sync Configuration with an HTC Vive System
    • SlimX 13
    • Active Marker Tracking
      • Active Finger Marker Set
    • Synchronization Hardware
      • External Device Sync Guide: eSync 2
      • External Device Sync Guide: OptiHub2
  • ANIMATION
    • Autodesk Maya
      • Autodesk Maya: OptiTrack Insight VCS Plugin
    • Autodesk MotionBuilder
      • Autodesk MotionBuilder Plugin
      • Autodesk MotionBuilder: OptiTrack Skeleton Plugin
      • Autodesk MotionBuilder: OptiTrack Optical Plugin
      • Autodesk MotionBuilder: OptiTrack Insight VCS Plugin
      • Autodesk MotionBuilder: Timecode Data
  • ROBOTICS
    • MoCap4ROS2 Setup
    • OptiTrack Robot Applications
    • Outdoor Tracking Setup
  • DEVELOPER TOOLS
    • Developer Tools Overview
    • Camera SDK
      • Class: cCameraModule
      • Class: cUID
    • Motive API
      • Motive API: Quick Start Guide
      • Motive API Overview
      • Motive API: Function Reference
      • Motive API Camera Calibration
    • NatNet SDK
      • NatNet 4.1
      • NatNet: Class/Function Reference
      • NatNet: Creating a Managed (C sharp) Client Application
      • NatNet: Creating a Native (C++) Client Application
      • NatNet: Data Types
      • NatNet: Matlab Wrapper
      • NatNet: Migration to NatNet 3.0 libraries
      • NatNet: Remote Requests/Commands
      • NatNet: Sample Projects
      • NatNet: Unicast Data Subscription Commands
      • Latency Measurements
    • Peripheral API: Glove Devices
  • SKELETON MARKER SETS
    • Full Body
      • Baseline (41)
      • Core (50)
      • Biomech (57)
      • Conventional (39)
    • Full Body + Fingers
      • Baseline + Passive Fingers (49)
      • Baseline + Active Fingers (57)
      • Core + Passive Fingers (54)
      • Core + Active Fingers (62)
    • Upper
      • Baseline Upper (25)
      • Conventional Upper (27)
    • Lower
      • Baseline Lower (20)
      • Helen Hayes Lower (19)
      • Conventional Lower (16)
    • Hand and Fingers
      • Left/Right Hand (4) Active
      • Left/Right Hand (10) Active + Passive
      • Active Finger Marker Set
    • Glove Device Setup
      • Manus Glove Setup
      • StretchSense Glove Setup
    • Rizzoli Marker Sets
    • Entertainment Marker Sets
    • Rigid Body Skeleton Marker Set
  • GENERAL TROUBLESHOOTING
    • Licensing Troubleshooting
    • Windows 11 Optimization for Realtime Applications
    • Network Troubleshooting
    • Troubleshooting Q&A
    • Running Motive on High DPI Displays
    • Firewall Settings
Powered by GitBook
On this page

Was this helpful?

Export as PDF
  1. HARDWARE
  2. USB Camera System Setup
  3. Tracking Bar Coordinate System

Transforming Coordinate System: Global to Local

PreviousTracking Bar Coordinate SystemNextAiming and Focusing

Last updated 1 year ago

Was this helpful?

The API reports "world-space" values for markers and rigid body objects at each frame. It is often desirable to convert the coordinates of points reported by the API from the world-space (or global) coordinates into the local space of the rigid body. This is useful, for example, if you have a rigid body that defines the world space that you want to track markers within.

Rotation values are reported as both quaternions, and as roll, pitch, and yaw angles (in degrees). Quaternions are a four-dimensional rotation representation that provide greater mathematical robustness by avoiding "gimbal" points that may be encountered when using roll, pitch, and yaw (also known as Euler angles). However, quaternions are also more mathematically complex and are more difficult to visualize, which is why many still prefer to use Euler angles.

There are many potential combinations of Euler angles so it is important to understand the order in which rotations are applied, the handedness of the coordinate system, and the axis (positive or negative) that each rotation is applied about.

These are the conventions used in the API for Euler angles:

  • Rotation order: XYZ

  • All coordinates are *right-handed*

To create a transform matrix that converts from world coordinates into the local coordinate system of your chosen rigid body, you will first want to compose the local-to-world transform matrix of the rigid body, then invert it to create a world-to-local transform matrix.

To compose the rigid body local-to-world transform matrix from values reported by the API, you can first compose a rotation matrix from the quaternion rotation value or from the yaw, pitch, and roll angles, then inject the rigid body translation values. Transform matrices can be defined as either "column-major" or "row-major". In a column-major transform matrix, the translation values appear in the right-most column of the 4x4 transform matrix. For purposes of this article, column-major transform matrices will be used. It is beyond the scope of this article, but it is just as feasible to use row-major matrices by transposing matrices.

In general, given a world transform matrix of the form: M = [ [ ] Tx ] [ [ R ] Ty ] [ [ ] Tz ] [ 0 0 0 1 ]

where Tx, Tz, Tz are the world-space position of the origin (of the rigid body, as reported from the API), and R is a 3x3 rotation matrix composed as: R = [ Rx (Pitch) ] * [ Ry (Yaw) ] * [ Rz (Roll) ]

where Rx, Ry, and Rz are 3x3 rotation matrices composed according to:

A handy trick to know about local-to-world transform matrices is that once the matrix is composed, it can be validated by examining each column in the matrix. The first three rows of Column 1 are the (normalized) XYZ direction vector of the world-space X axis, column 2 holds the Y axis, and column 3 is the Z axis. Column 4, as noted previously, is the location of the world-space origin. To convert a point from world coordinates (coordinates reported by the API for a 3D point anywhere in space), you need a matrix that converts from world space to local space. We have a local-to-world matrix (where the local coordinates are defined as the coordinate system of the rigid body used to compose the transform matrix), so inverting that matrix will yield a world-to-local transformation matrix. Inversion of a general 4x4 matrix can be slightly complex and may result in singularities, however we are dealing with a special transform matrix that only contains rotations and a translation. Because of that, we can take advantage of the method shown here to easily invert the matrix:

Once the world matrix is converted, multiplying it by the coordinates of a world-space point will yield a point in the local space of the rigid body. Any number of points can be multiplied by this inverted matrix to transform them from world (API) coordinates to local (rigid body) coordinates.

The API includes a sample (markers.sln/markers.cpp) that demonstrates this exact usage.

http://stackoverflow.com/questions/2624422/efficient-4x4-matrix-inverse-affine-transform