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Everything about Parallel curve
Generalization of the concept of parallel lines
A parallel curve of a given (progenitor) curve is the envelope of a family of congruent (equal-radius) circles centered on the curve. It generalises the concept of parallel (straight) lines. It can also be defined as a curve whose points are at a constant normal distance from a given curve. These two definitions are not entirely equivalent as the latter assumes smoothness, whereas the former does not. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Parallel curveA 5-minute orientation
- Skim a recent paper: Time-Optimal Pick-and-Throw S-Curve Trajectories for Fast Parallel RobotsInfluential work since 2022
- Pick up a classic book: Smoothing Techniques for Curve EstimationThe most-reprinted book on the subject
- Read the landmark paper: Investigation of Mediational Processes Using Parallel Process Latent Growth Curve ModelingCited 358 times
- Go sideways: Parametric surfaceA closely related topic
- Go sideways: CurvatureA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Investigation of Mediational Processes Using Parallel Process Latent Growth Curve Modeling
Surface Reconstruction From Non‐parallel Curve Networks
A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton
Parallel transport along a space curve and related phases
Wheel curve generation error of aspheric microgrinding in parallel grinding method
RNS-Based Elliptic Curve Point Multiplication for Massive Parallel Architectures
A fast parallel implementation of elliptic curve point multiplication over GF(2m)
Non-Parallel Yield Curve Shifts and Immunization
🆕 Influential since 2022
Time-Optimal Pick-and-Throw S-Curve Trajectories for Fast Parallel Robots
Childhood experiences of threat and deprivation predict distinct depressive symptoms: A parallel latent growth curve model
Tribological effects of different scaled chevron-shaped microstructures on the Stribeck curve of parallel contacts under unidirectional friction
Parallel Parking Path Planning in Narrow Space Based on a Three-Stage Curve Interpolation Method
High‐speed parallel reconfigurable Fp multipliers for elliptic curve cryptography applications
📚 Books worth reading
Smoothing Techniques for Curve EstimationGasser · 1979- 📕De curvis aequedistantibusAbraham Gotthelf Kaestner · 1795
- 📕Zur Theorie der ParallelcurvenWilhelm Wolkenhauer · 1874
- 📕Einladungs-Programm zu der öffentlichen Prüfung der Schüler des Gymnasiums zu Hildburghausen am 2., 3. und 4. ... · 1841
- 📕Einladungs-Programm zu der ©œffentlichen Pr©ơfung der Sch©ơler des Gymnasiums zu Hildburghausen am 2., 3. und 4. ...B©ơchner · 1841
- 📕Do paralelismo das curvas torsasPedro José da Cunha · 1935
- 📕Sur les courbes parallèles à l'ellipseFrancisco Gomes Teixeira · 1898
- 📕Sobre o paralelismo de curvas e superfíciesPedro José da Cunha · 1936
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Parametric surface A parametric surface is a surface in the Euclidean space ℝ3 which is defined by a parametric equation with two parameters 𝐫:ℝ2→ℝ3. Parametric representation…
- Curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being…
- Evolute In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature…
- Normal (geometry) In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve…
- Differential geometry of surfaces In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most…
- Surface (mathematics) In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be…
- Osculating circle An osculating circle is a circle that best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has…
- Principal curvature In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by…