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Everything about Point reflection
Geometric symmetry operation
In geometry, a point reflection is a geometric transformation of affine space in which every point is reflected across a designated inversion center, which remains fixed. In Euclidean or pseudo-Euclidean spaces, a point reflection is an isometry. In the Euclidean plane, a point reflection is the same as a half-turn rotation, while in three-dimensional Euclidean space a point reflection is an improper rotation which preserves distances but reverses orientation. A point reflection is an involution: applying it twice is the identity transformation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Point reflectionA 5-minute orientation
- Skim a recent paper: A Reflection Coefficient Estimation Method for Power Cable Defects Based on Three-Point Interpolated FFTInfluential work since 2022
- Pick up a classic book: Wave PhenomenaThe most-reprinted book on the subject
- Read the landmark paper: Common reflection point horizontal data stacking techniquesCited 273 times
- Go sideways: Euclidean groupA closely related topic
- Go sideways: Improper rotationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Common reflection point horizontal data stacking techniques
High-resolution common-depth-point seismic reflection profiling; instrumentation
Polarization structure transition of C-point singularities upon reflection
From Single-Point to Multi-Point Reflection Modeling: Robust Vital Signs Monitoring via mmWave Sensing
Conductance features in point contact Andreev reflection spectra
Common-reflection-point stacking in laterally inhomogeneous media
On point to point reflection of harmonic functions across real-analytic hypersurfaces in ℝ n
Two‐point boundary value problems involving reflection of the argument
🆕 Influential since 2022
A Reflection Coefficient Estimation Method for Power Cable Defects Based on Three-Point Interpolated FFT
Fast THz-TDS Reflection Imaging with ECOPS—Point-by-Point versus Line-by-Line Scanning
Andreev reflection of quantum Hall states through a quantum point contact
Prediction of triple point trajectory on two-dimensional unsteady shock reflection over single surfaces
Learning-Based Reflection-Aware Virtual Point Removal for Large-Scale 3D Point Clouds
📚 Books worth reading
Wave PhenomenaDudley H. Towne · 1967- 📕Discretized energy minimization in a waveguide with point sourcesG. Probst · 1994
- 📕Topics in Hyperplane ArrangementsMarcelo Aguiar, Swapneel Mahajan · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Euclidean group In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space 𝔼n; that is, the transformations of that space that preserve…
- Improper rotation In geometry, an improper rotation (also called rotation-reflection, rotoreflection, rotary reflection, or rotoinversion) is an isometry in Euclidean space…
- Reflection (mathematics) In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of…
- Symmetry (geometry) In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/objec…
- Affine involution In Euclidean geometry, an affine involution is an involution which is a linear or affine transformation over the Euclidean space ℝn. Such involutions…
- Rotation (mathematics) Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe…
- Symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group…
- Point groups in three dimensions In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group…