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Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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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 has...
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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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Gauss's Law01:07

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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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Gauss's Law: Problem-Solving01:10

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Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
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Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
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3D Gaussian Splatting Texture Editing via Single Modified Image.

Hanul Baek, Dohae Lee, Kyumin Kim

    IEEE Transactions on Visualization and Computer Graphics
    |April 20, 2026
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new framework for editing 3D Gaussian Splatting (3DGS) using a single image. The method enables precise, view-consistent texture modifications for 3D scene reconstruction.

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    Area of Science:

    • Computer Vision
    • Computer Graphics
    • 3D Reconstruction

    Background:

    • 3D Gaussian Splatting (3DGS) offers high-quality 3D scene reconstruction but lacks intuitive editing capabilities.
    • Existing 3DGS editing methods, often text-driven, limit direct user control over visual appearance.
    • Mesh-based editing is more established, but 3DGS requires specialized techniques due to its implicit geometry.

    Purpose of the Study:

    • To develop a novel texture editing framework for 3D Gaussian Splatting (3DGS).
    • To enable precise and view-consistent 3DGS editing using only a single user-modified image.
    • To provide direct control over visual appearance and lighting adjustments in edited 3D scenes.

    Main Methods:

    • Proposed a texture editing framework for 3DGS leveraging a single user-modified image.
    • Introduced aligned edit propagation to transfer edits across multiple views.
    • Implemented mask-based filtering and opacity-based selection to refine edits and target influential Gaussians.

    Main Results:

    • Demonstrated precise and spatially controllable 3DGS editing.
    • Achieved view-consistent updates and accounted for lighting adjustments in edited regions.
    • Outperformed existing techniques in both qualitative and quantitative evaluations on synthetic and real-world data.

    Conclusions:

    • The proposed framework offers a more intuitive approach to 3DGS editing.
    • The techniques facilitate precise control over texture modifications in 3D scenes.
    • This work lays the groundwork for future advancements in 3D Gaussian Splatting editing pipelines.