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Bo Li, Xin Zhao and Hong Qin Four-Dimensional Geometry Lens: A Novel Volumetric Magnification Approach Computer Graphics Forum 32

Article first published online: 22 AUG 2013 | DOI: 10.1111/cgf.12166

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We present a novel methodology that utilizes 4-Dimensional (4D) space deformation to simulate a magnification lens on versatile volume datasets and textured solid models. Compared with other magnification methods (e.g., geometric optics, mesh editing), 4D differential geometry theory and its practices are much more flexible and powerful for preserving shape features (i.e., minimizing angle distortion), and easier to adapt to versatile solid models. The primary advantage of 4D space lies at the following fact: we can now easily magnify the volume of regions of interest (ROIs) from the additional dimension, while keeping the rest region unchanged. To achieve this primary goal, we first embed a 3D volumetric input into 4D space and magnify ROIs in the 4th dimension. Then we flatten the 4D shape back into 3D space to accommodate other typical applications in the real 3D world.

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