Projection on Curved Surface: Distortion and Fixes
Key takeaways
- Concave surfaces stretch the outer columns of the image while convex surfaces compress them, so the required warp direction flips between the two.
- Edge stretch can be estimated from the arc-to-chord ratio: a 4 m radius, 5 m wide screen yields about 8% stretch and a 0.25 m sagitta.
- If the sagitta stays under roughly 2% of throw distance, warp and blend correction can usually hide edge stretch and focus falloff.
- Placement and lens choice fix keystone error for free, but only per-pixel warping in the media server removes residual edge stretch on concave surfaces.
- Use longer throw ratios rather than short-throw lenses on curves, because a wider depth of field holds focus across the surface's depth range.
A projection on curved surface stretches or compresses parts of your image depending on whether the surface bows toward or away from the projector: concave screens stretch the outer columns, convex screens squeeze them, and both shift your focus plane. This guide derives those effects geometrically, with worked numbers, so you can compensate with placement, lens choice, and warp maps before load-in.
What happens to image geometry when you project onto a curved surface?
A projector assumes a flat target. Its output is a rectangle defined by throw ratio and lens shift, both measured to a planar screen. Put a curve in front of the lens and that rectangle lands as a distorted shape: pixels near the beam centre hit the surface at a different angle and distance than pixels at the edges.
The flat image plane versus the curved screen plane
On a concave surface, the sides of the screen sit closer to the lens than the centre, so the image compresses horizontally at the edges. On a convex surface, the sides sit farther away, so the image stretches. The same projector, the same lens, opposite failure.
Why the corners and edges move first
The centre of the beam travels along the surface normal; the corners hit obliquely and across the curve. That is why keystone error and edge stretch show up at the frame boundary before anywhere else, and why a flat-surface spreadsheet calculation will not predict them. We break down the math for estimating that stretch in our simulation notes.
How does distortion differ between concave and convex projection surfaces?
On a curved surface, every projector pixel lands at a different distance from the lens. That distance variation is the whole story of curved-surface distortion: concave surfaces stretch edges, convex surfaces compress them.
Concave: the centre is closer, so edges stretch
A concave surface (dome interior, curved video wall facing the projector) curves toward the lens at its centre. The centre of the image hits the surface at throw distance D, but the edges travel farther, roughly D + (w²/2R) for surface width w and radius of curvature R. Because image height on the surface grows with distance, the edges of the frame appear taller and wider than the centre. Content looks pin-cushioned: straight horizontal lines bow outward.
Convex: the centre bulges, so edges compress
A convex surface (exterior cylinder, curved architectural column) bulges toward the projector. The centre is closer than the edges, so edge content shrinks vertically. Lines bow inward instead.
Why the warp direction flips between the two
| Concave | Convex | |
|---|---|---|
| Nearest point | Centre | Edges |
| Edge image | Stretched | Compressed |
| Pre-warp | Squeeze edges | Stretch edges |
The warp you apply is the inverse of the stretch, so it flips sign. Modelling both cases in THROXEL before load-in shows which direction and magnitude you need per projector.
How do you calculate or estimate edge stretch and keystone error on a curved screen?
The chord-versus-arc error
On a curved screen, the image path along the surface (the arc) is longer than the straight chord the projector "sees", so pixels near the edges of a flat-mapped image land stretched across more physical surface. The ratio between arc length and chord width, computed per projector, gives you a first-order estimate of edge stretch. Keystone error compounds it: on a concave screen, the corners sit closer to the lens than the centre, so the corners magnify and the centre compresses.
A worked example: 4 m radius, 5 m wide screen
Take a screen with a 4 m radius and a 5 m chord. Half-chord is 2.5 m, so the half-angle is asin(2.5/4) ≈ 38.7°. Arc length is 2 × 4 × 0.675 rad ≈ 5.40 m, about 8% longer than the 5 m chord, and the sagitta (centre depth) is 4 − √(16 − 6.25) = 0.25 m. If one projector covers that screen from a 10 m throw, the pixel density at the centre runs roughly 8% higher than at the edges, which is the number you would compensate with warp maps. You can replicate all three figures in a spreadsheet with asin, sqrt, and the arc formula, then scale by projector overlap: for a three-projector array with 15% edge blending, each projector's chord shrinks and the per-projector arc-to-chord ratio drops with it, and tools like VIOSO ProjectionTools automate this same geometry per projector so you can pre-build the warp maps in THROXEL before the media server ever sees the surface.
When the error is small enough to ignore
As a rule of thumb, if the sagitta is under roughly 2% of throw distance, edge stretch stays below what warp and blend correction handles invisibly. Beyond that, plan placement and lens shift around the curve rather than fixing it entirely in software.
How does the focus plane and depth of field change across a curved surface?
A projector focuses on a single plane. A curved surface puts parts of the image closer to and further from that plane, so depth of field, not throw distance alone, decides whether the whole curve is sharp.
Concave surfaces pull the edges out of focus
On a concave surface, the centre of the curve sits furthest from the lens and the edges curve back toward it. If you focus on the centre, the edges can fall outside depth of field and soften, especially with short-throw lenses at wide apertures. Focus slightly behind the centre to split the error across the surface.
Convex surfaces pull the centre out of focus
A convex surface bows toward the projector, so the centre is closest and the edges sit further away. Focus on the centre and the edges drift soft; focus on the edges and the centre blurs. The steeper the curve, the wider the depth range you are asking one lens to hold.
Choosing throw ratio and lens to cover the depth range
Longer throw ratios give you more depth of field, so step back and narrow the lens rather than stacking short-throw units close to the curve. Calculate the total depth range of the surface, compare it against the lens's depth of field at your sensor size and aperture, and check the numbers before you commit. THROXEL lets you simulate the geometry and lens choice in 3D, so you can confirm focus coverage across the curve before showtime instead of discovering falloff on site.
When should you use warping software versus physical projector placement on a curve?
Placement and lens choice are free. Get the throw distance right, keep the projector square to the surface where the geometry allows it, and use lens shift instead of keystone to frame the image. On a gentle convex wall, correct distance and a lens with the right throw ratio can eliminate most keystone error before any warp is applied.
What placement cannot fix is residual edge stretch. On a concave surface or a dome, the edges of every projector's footprint are physically farther from the lens than the center, and no amount of rotation or lens shift removes that. This is genuine warp territory: you need per-pixel geometry correction in the media server, and the blend overlap must be warped too or the seam will bow. Simulation tools model this warp and blend in advance so you know the correction budget before load-in.
Getting the split wrong costs site hours: discovering mid-load-in that a projector needed a different lens, or that the dome warp exceeds what your media server handles comfortably, means re-rigging while the clock runs toward showtime.
How do you blend multiple projectors across a curved surface without visible seams?
On a curve, a blend zone is never uniform. Projectors at different angles to the surface hit the overlap at different obliquities, so the same pixel width maps to a wider strip of screen on one side of the seam than the other. The result is a blend that looks correct in software but reads as a soft or hard band on site, because luminance and geometry drift across the overlap instead of staying constant.
Sizing the overlap on a curved seam
Size the overlap wider than you would on a flat wall. A common flat-screen starting point is 15-25% of one projector's width; on a concave surface, add margin because the projected footprints converge and the effective overlap shrinks toward the centre of the curve. On convex surfaces the footprints diverge, so measure the actual overlap at the seam line, not at the projector plane. Verify the numbers with a throw-distance and coverage plan before committing to lens choice.
Gamma and luminance matching across the blend
Blend ramps assume both projectors output identical luminance at every level. On a curve, one unit often sits closer to the surface, so its centre brightness is higher even at matched settings. Match black levels first, then gamma, then run a grey ramp across the seam and adjust each unit's output curve until the ramp reads flat.
Why curved seams show colour shifts more than flat ones
Oblique projection changes the path length through the surface's gain response, and on curved surfaces that angle varies across the blend zone. A screen with directional gain amplifies the difference, so the seam shows a hue shift even when luminance matches. Test with a colour sweep across the overlap, not just white.
What surface materials and gain characteristics matter most for curved projection?
Gain and viewing angle on a curve
Gain is specified at a nominal viewing angle, usually on-axis to a flat sample. On a curved surface, every seat sees a different angle, so a 1.2-gain screen that looks even from centre falls off quickly toward the edges of a concave sweep. Check the manufacturer's gain-versus-angle curve, not just the headline number, and match it against your widest off-axis seat before committing to a spec.
Matte versus gain surfaces for domes and immersive rooms
For domes and immersive rooms, matte finishes near 1.0 gain are the default because brightness stays consistent across the warp and blend zones, and hotspots from overlapping projector arrays stay manageable. Higher-gain paints can help in long-throw architectural work where lumen budget is tight, but they amplify seam visibility at blend edges. Verify reflectance behaviour in a 3D previsualisation before ordering material; Disguise's Mapping Matter is built for exactly this kind of surface and material simulation ahead of showtime (Disguise Mapping Matter).
How do you validate a curved-surface projection plan before load-in?
Simulating the surface in 3D before showtime
Build the surface first: measure radius, chord, and height on site or from CAD, then model it as a mesh. Place each projector in software, set throw ratio, lens shift, and zoom, and check coverage, overlap, and blend zones against the curved geometry. A simulation shows where edge stretch and focus falloff will bite before the truck is loaded.
Tool options and where each falls short
VIOSO ProjectionTools and VIOSO Experience Designer are established for multi-projector simulation. Disguise Mapping Matter fits Disguise-centric workflows. Spreadsheets and manufacturer PDF calculators handle single-throw math but ignore curvature. THROXEL covers plan-to-3D simulation and geometry export at EUR 29/month or EUR 290/year with a 7-day trial, but it is Windows-only, machine-licensed, and has no public user reviews yet, so judge it on the trial.
Handing geometry to Disguise, PIXERA, or Resolume
Export the projector array, warp maps, and blend parameters so the media server starts from your simulated geometry instead of a blank canvas. On site you confirm placement, refine warp, and verify blend overlap against the plan, cutting setup time before showtime.
FAQ
Can I project onto a curved wall without a warping server?
Sometimes. A gentle convex wall with correct throw distance and lens shift can look acceptable with no warp at all. Concave surfaces are different: the edges of every projector footprint sit physically farther from the lens, so edge stretch cannot be removed by placement or lens choice. Past roughly 2% sagitta relative to throw, you need per-pixel warp correction.
How much projector overlap do I need on a dome or curved screen?
Start from the flat-screen baseline of 15-25% of one projector's width, then add margin. On a concave dome, projected footprints converge toward the centre of the curve, so the effective overlap shrinks below what you measured at the projector plane. On convex surfaces the footprints diverge, so measure the actual overlap at the seam line before committing.
Does a short-throw lens work better on curved surfaces?
No, usually worse. Short-throw lenses sit close to the curve, which magnifies the depth range across the surface and makes it harder for one focus setting to hold the whole image sharp. They also run wider apertures in practice, shrinking depth of field further. A longer throw ratio with a narrower lens splits focus error more evenly across the curve.
Why does my blend look bright in the middle on a curved screen?
Because one projector usually sits closer to the surface than the other, so its centre luminance is higher even at matched settings. Blend ramps assume identical output at every level. Fix it in order: match black levels first, then gamma, then run a grey ramp across the seam and adjust each unit's output curve until the ramp reads flat.
What screen radius is too tight for standard lenses?
There is no single cutoff radius; the deciding number is the depth range of the surface versus your lens's depth of field at your sensor size and aperture. A practical first check: if the sagitta exceeds roughly 2% of throw distance, edge stretch and focus falloff outgrow what warp and blend can hide invisibly. Model the geometry in simulation before choosing a lens.