Projection cylindrique à 360° : guide pratique de conception géométrique
Using 30% Deformation as a GeoBox Reference
For preliminary cylindrical projection design, 30% deformation can be used as a practical GeoBox geometry-correction reference. (Click here for Série GeoBox Edge blending et Warping)
It should not be treated as an absolute hard limit. Actual correction capability also depends on projector throw ratio, projection distance, lens characteristics and installation geometry.
The purpose of the 30% reference is to identify when a design is becoming geometrically demanding and should be verified before installation.
1. Converting Cylinder Curvature into a Percentage
For a circular surface:
- Chord (c) = straight-line distance between the two edges of the projected area
- Sagitta (h) = maximum depth between the chord and curved surface
The curvature ratio is: h/c
For a circular arc with coverage angle θ
h/c= 1/2 tan(θ/4)
This gives:
| Projector Coverage | Curvature Ratio |
|---|---|
| 90° | 20.7% |
| 100° | 23.3% |
| 110° | 26.0% |
| 120° | 28.9% |
| 124° | ~30% |
| 127° | ~31% |
A single projector covering approximately 120–125° of a cylinder is therefore already close to the 30% reference range.
2. Projector Count and Required Coverage
Without edge-blending overlap, the number of projectors is 360 degree divided by the nominal coverage per projector. However, adjacent projectors require overlap for edge blending. GeoBox documentation indicates that a typical overlap region is around 20–40% of the individual projector image, depending on the application.
Using 20% overlap as a preliminary design value:
θ= 360° / N(1-f)
where:
- N= number of projectors
- f= overlap ratio
This gives approximately:
| Projecteurs | Actual Coverage with 20% Overlap | Curvature Ratio |
|---|---|---|
| 3 | 150° | ~38% |
| 4 | 112.5° | ~27% |
| 5 | 90° | ~21% |
| 6 | 75° | ~17% |
This makes four projectors a practical starting point for many 360° cylindrical systems. Three projectors may already exceed the 30% reference once normal blending overlap is included.
3. More Projectors Are Not Always Better
Adding projectors reduces the coverage angle and therefore reduces geometric deformation.
However, it also reduces the physical image size produced by each projector.
For a cylinder: C=πD
and the approximate projected width per projector is: W= C/N(1-f)
Adding more projectors makes each image even smaller. At this point, the limitation may no longer be GeoBox geometry correction. It may become the projector minimum focus distance and minimum image size
This is why very small cylinders can become impractical even when more projectors are added.
In one previous project, a 50 cm diameter cylinder was therefore increased in size to create a more practical balance between curvature correction and projector optics.
4. Throw Ratio and Distortion
Throw ratio has a direct impact on cylindrical distortion.
A longer throw allows the projector to be positioned farther from the cylinder, making the light paths more parallel. This reduces distortion at the sides of the image and leaves more margin for geometry correction.
A shorter throw creates more divergent light paths, increasing edge distortion and the amount of correction required.
GeoBox documentation also notes that larger throw ratios produce less distortion on curved screens, while ultra-short-throw projectors are not recommended for this type of application.
5. Physical Test Result
A scaled cylindrical test was carried out using:
- GeoBox M810
- un projecteur
- approximately 1.0:1 throw ratio
- regular grid test pattern
- normal video content
The result was:
Around 110° coverage
Geometry correction remained within a comfortable range.
Around 120° coverage
Most of the cylindrical deformation could still be corrected. However, small residual distortion remained near the extreme edges, which can be viewed with a grid test pattern, though was difficult to notice during normal video playback.
Beyond 120°, the correction requirement increased quickly.
6. Practical SOP for 360° Cylindrical Projection
For new cylindrical projection projects, the following workflow can be used.
Step 1 — Calculate cylinder circumference
C=πD
This defines the total physical width of the 360° image.
Step 2 — Start with projector count
For full 360° projection:
- 3 projectors = theoretical minimum
- 4 projectors = practical starting point
- 5–6 projectors = lower geometry demand
Step 3 — Add overlap and confirm coverage
For a regular 360° system, 20–25% overlap is a practical starting point.
With four projectors, this normally keeps the single-projector coverage within the approximate 30% deformation reference.
A larger overlap may be useful when:
- more image height is required,
- a smoother blending transition is preferred,
- or additional geometry-adjustment flexibility is needed on the curved surface.
If the larger overlap pushes the actual coverage angle beyond the preferred correction range, consider increasing the number of projectors to reduce the coverage angle and overall deformation per projector.
Step 4 — Check physical image size
Calculate the approximate projected width per projector:
W= C/N(1-f)
Then confirm that the selected projector and lens can produce and focus that image size at the available installation distance.
Step 5 — Check throw ratio and distance
A longer throw and greater projection distance generally reduce cylindrical distortion. Avoid using projector with shorter than 1.0:1 throw ratio in cylinder projection.
Step 6 — Adjust the design if necessary
If the geometry is too aggressive, consider:
- increasing projection distance (using loner throw ratio lens projetors),
- increasing projector count,
- increasing cylinder diameter.
Conclusion
For 360° cylindrical projection, the first question should not be:
How much warping can the processor provide?
A better design sequence is:
Cylinder diameter → projector count → overlap → coverage angle → 30% deformation check → image size → throw ratio
The 30% deformation reference provides a useful first-stage feasibility check.
If the required correction approaches or exceeds this range, the preferred solution is usually to improve the optical geometry by increasing projection distance, increasing projector count or increasing cylinder diameter before asking the processor to compensate for more distortion.
Good cylindrical projection starts with manageable optical geometry. GeoBox then provides the precision needed for final warping, alignment and edge blending.