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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Gauss's Law: Spherical Symmetry01:26

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
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The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
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Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Depth perception is the ability to perceive objects three-dimensionally. It relies on two types of cues: binocular and monocular. Binocular cues depend on the combination of images from both eyes and how the eyes work together. Since the eyes are in slightly different positions, each eye captures a slightly different image. This disparity between images, known as binocular disparity, helps the brain interpret depth. When the brain compares these images, it determines the distance to an object.
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A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
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Photorealistic Learned Landscapes for Augmented Reality
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Spherical Patch Generative Adversarial Net for Unconditional Panoramic Image Generation.

Mai Xu, Xiancheng Sun, Shengxi Li

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |June 16, 2025
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new method for generating panoramic images directly in spherical format, overcoming limitations of current techniques. The developed Spherical Patch Generative Adversarial Network (SP-GAN) ensures accurate representation of panoramic deformation and continuity.

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    Area of Science:

    • Computer Vision
    • Computer Graphics
    • Artificial Intelligence

    Background:

    • Advancements in virtual reality (VR) and augmented reality (AR) drive demand for immersive panoramic content.
    • Existing methods generate planar images from panoramic sources, failing to address spherical deformation and continuity issues, resulting in pseudo-panoramic content.
    • The need for unconditional panoramic image generation that accurately represents 360° format is critical.

    Purpose of the Study:

    • To develop a novel method for unconditional panoramic image generation that directly creates spherical content.
    • To address the limitations of existing methods in handling panoramic deformation and closed-loop characteristics.
    • To generate high-quality, continuous panoramic images with proper accommodation of spherical distortion.

    Main Methods:

    • Proposal of a novel spherical patch convolution (SPConv) operating on local spherical patches to handle panoramic content deformation.
    • Introduction of a spherical patch generative adversarial network (SP-GAN) incorporating spherical local embedding (SLE) and spherical content synthesiser (SCS) modules.
    • Patch-by-patch generation of spherical content ensuring continuity and accurate deformation accommodation.

    Main Results:

    • The proposed SP-GAN successfully accommodates spherical distortion for closed-loop panoramic image generation in a patch-by-patch manner.
    • Experimental results demonstrate superior performance in generation quality, computational memory efficiency, and generalization across various resolutions.
    • Human-rated evaluations confirm the consistently superior performance of the proposed method.

    Conclusions:

    • The SP-GAN offers a significant advancement in unconditional panoramic image generation by directly producing spherical content.
    • The method effectively addresses deformation and continuity issues, providing a more accurate and immersive visual experience.
    • The approach is computationally friendly and generalizes well, offering a robust solution for panoramic content creation.