Coordinate Systems
What is a Coordinate System?
Every 3D scene — including the reconstructions you create in HemoVision — exists within a three-dimensional coordinate system. This system is defined by three axes: X, Y, and Z.
How these axes are arranged relative to one another depends on two things:
- Which axis represents the vertical direction
- The rotational direction of the system, defined by its handedness
Y-up vs Z-up
In a 3D Cartesian coordinate system, the three axes are orthogonal (perpendicular) to one another. The difference between Y-up and Z-up coordinate systems lies in which axis represents the vertical direction.
In a Y-up system:
- The Y-axis represents the vertical direction.
- The X-axis and Z-axis lie in the horizontal plane.
In a Z-up system:
- The Z-axis represents the vertical direction.
- The X-axis and Y-axis define the horizontal plane.
The figure below demonstrates the difference between Y-up and Z-up.
Left-handed vs Right-handed
The concept of handedness defines the orientation of the axes relative to one another.
When two axes of a 3D coordinate system are defined, they determine the line along which the third axis must lie (perpendicular to the plane formed by the first two). However, this line has two possible orientations. These two possibilities result in either a right-handed or a left-handed coordinate system.
The distinction between right-handed and left-handed systems is commonly illustrated using the hand rule. In a right-handed system, if the thumb, index finger, and middle finger of the right hand are positioned at right angles to one another, they represent the positive directions of the X-, Y-, and Z-axes respectively. Performing the same configuration with the left hand produces a left-handed coordinate system.
The difference between the two systems lies solely in the orientation of the axes relative to one another. Comparing the two coordinate systems in the image below, we can see that the Z-axes point in opposite directions.
Warning
Mixing data from different coordinate systems without proper conversion may result in mirrored geometry.
Practical implications in HemoVision
HemoVision allows you to use both left-handed and right-handed systems, as well as Y-up and Z-up systems. This means that HemoVision support the following four coordinate systems:
- Y-up, left-handed
- Y-up, right handed
- Z-up, left handed
- Z-up, right-handed
A graphical comparison of these coordinate systems is shown in the image below.
When you create a new project in HemoVision, you specify the coordinate system you will be working in (see the screenshot below). Once the project has been created, all coordinates, models, reconstructions, etc. will be expressed within the selected coordinate system.
Warning
Once you have created a project, you cannot change the coordinate system.
Info
When importing external 3D models or point clouds, you can specify the coordinate system in which the model was created so that the geometry of these models is properly converted. This enables you to import any data you may have, regardless of the coordinate system that was used to create it.
Summary
HemoVision supports:
- Two vertical axis conventions (Y-up and Z-up)
- Two handedness conventions (left-handed and right-handed)
These options ensure compatibility across different technical environments while maintaining consistent reconstruction mathematics.
Understanding your coordinate system ensures accurate interpretation, correct imports, and defensible exports.
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