Pre-distorting Rectangular Images for Curved Dome Projection
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Solution Overview
Problem
Curved projection screens, such as those in planetariums, distort rectangular images due to their non-planar surfaces, making it difficult to display conventional movie screen images without significant distortion, and existing solutions like fisheye lenses require specialized equipment and fail to adequately compensate for the curvature.
Innovation Solution
A virtual surface is defined using 3-D modeling to represent the curved screen, allowing for the angular distribution of vertices and polygons, which enables the minimization of distortion when projecting rectangular images by mapping them onto this virtual surface using UV mapping techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Area of stationary object
If a rectangular image is projected onto a curved surface, then the image covers the curved surface area, but the image becomes distorted with the center appearing disproportionately large and outer edges appearing compacted
Solution Approach 1:
The patent applies preliminary action by pre-distorting the rectangular image in the opposite direction of the expected curvature distortion before projection. The image is pre-wrapped around a virtual cylinder that matches the curvature of the projection surface, so that when projected onto the curved screen, the pre-applied distortion counteracts the curvature-induced distortion, resulting in a visually undistorted image on the curved surface.
2Manufacturing precision
If fisheye lens projectors are used to display rectangular images on curved screens, then image distortion is reduced, but specialized equipment is required for both capturing and projecting images
Solution Approach 1:
The patent uses copying by creating a virtual cylindrical model that replicates the geometry of the actual curved projection surface. Instead of using specialized fisheye lens hardware, the invention copies the curvature characteristics into a virtual environment where standard rectangular images can be pre-distorted and mapped onto the virtual cylinder, then projected using conventional projectors onto the physical curved screen without requiring specialized optical equipment.
3Adaptability or versatility
If video compositing software is used to distort rectangular images for curved projection, then images can be displayed on curved screens, but the distorted images must remain relatively small (less than one quarter of the dome)
Solution Approach 1:
The patent applies dimensionality change by transitioning from a two-dimensional flat image plane to a three-dimensional virtual cylindrical surface. By wrapping the rectangular image around the virtual cylinder before projection, the solution accommodates the three-dimensional curvature of the projection environment, enabling full-dome or large-area curved screen projection without the size limitations of traditional video compositing software that operates only on flat 2D planes.
Data Source
AI summary
An image display system for displaying a planar image on a curved viewing surface, such as a theater dome, with minimized image distortion. In order to display the image, a virtual surface, which is a representation of the curved viewing surface, is textured with the image using an angular distribution to thereby form a textured virtual image. The textured virtual image is then displayed onto the curved viewing surface.