Image warping for projection onto a cylinder

(Including stereoscopic)

Written by Paul Bourke
December 2004

Introduction

In general, given a cylindrical surface and an arbitrary projector position and orientation angle, the projected image as it appears on the cylindrical surface will look distorted, see figure 1 and 2. In addition there may be parts of the image plane that do not lie on the cylindrical surface (shown in grey below) and it may be necessary to tile the images and therefore edge blend between adjacent images (shown in blue below).

Figure 1: Projecting standard mesh (View 1).
Blue is edge blend region.
Grey is outside the screen area.

Figure 2: Projecting standard mesh (View 2).

It is possible to warp the projected image so that the image as it appears on the cylindrical surface looks undistorted to an observer at the center of the cylinder. Figure 3 and 4 show a warped grid and the correct result on the cylindrical surface. With current graphics hardware this warping can be performed in real time, in this case the input to the warping stage is a cylindrical panoramic image. The exact warping function can be calculated by simulating the physical system and tracing rays from the projector, taking into account the lens, and finding where that ray hits the cylindrical surface. Given that information, the coordinates of the panoramic image that should be at that point on the cylinder can be calculated. While the warping for some projector/lens/screen arrangements can be calculated analytically, this simulation approach is most appropriate for dealing with arbitrary arrangements.

Figure 3: Projecting corrected mesh (View 1).

Figure 4: Projecting corrected mesh (View 2).

Example

The following is an example using a rendered panoramic from a computer model of the Royal Exhibition Building in Melbourne, Australia. In figure 6 the warped image can be seen on the projection plane and figure 5 shows the undistorted image as it would appear on the cylindrical surface. In this environment the full cylinder will be illuminated with 4 projectors, each edge blended for a continuous cylindrical panoramic image.

Figure 5: Projecting corrected mesh (View 2).
Royal Exhibition Building, Melbourne.

Figure 6: Projecting corrected mesh (View 2).
Royal Exhibition Building, Melbourne.

Screen dumps from single computer, a stereoscopic pair

Warping mesh and texture coordinates

Stereo pairs (left and right eye) mapped onto textured mesh

Edge blend zones

Gamma corrected edge blend

Final image with edge blend zones

Example: 360 degree stereoscopic display

The following is one of 4 computers, each computer presents the left and right eye, edge blended pair.

Each display is connected to a single projector, stereo is achieved using passive polaroid filters on the projectors that match the filters in the polaroid glasses.

In total, 4 projectors for 360 degree coverage, 2 projectors per eye.....8 projectors in total.