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Vector representation of the movement of a body or fluid
A hodograph is a diagram that gives a vectorial visual representation of the movement of a body or a fluid. It is the locus of one end of a variable vector
Hodograph
Type of spline curve
In mathematics, a Pythagorean hodograph curve or PH curve is a curve defined by a polynomial parametric equation for which the speed (the derivative of
Pythagorean_hodograph_curve
Vector used in astronomy
momentum hodograph in the relevant section above, B is readily seen to connect the origin of momenta with the center of the circular hodograph, and to
Laplace–Runge–Lenz_vector
Meteorological process associated with developing thunderstorms
amounts of ambient crosswise vorticity, as characterized by a straight hodograph, produces similarly strong left and right movers. Storm splits also occur
Splitting_storm
Airflow above and below the speed of sound
used to circumvent the nonlinearity of transonic flow models was the hodograph transformation. This concept was originally explored in 1923 by an Italian
Transonic
Curve used in computer graphics and related fields
a (scaled and translated) Tschirnhausen cubic. These are Pythagorean hodograph curves, curves whose arc length and offset curves have a rational parameterization
Bézier_curve
Thunderstorm composed of multiple storm cells
sometimes not following the path of the cells that compose it. The typical hodograph, plot of the wind versus altitude, associated with it shows a linear wind
Multicellular_thunderstorm
Number, approximately 3.14
or index of the curve. N is the winding number about the origin of the hodograph of the curve parametrized by arclength, a new curve lying on the unit
Pi
Relation between sides of a right triangle
circle Pythagoras in popular culture Pythagorean expectation Pythagorean hodograph curve – determined by polynomials that obey the Pythagorean theorem Pythagorean
Pythagorean_theorem
Difference in wind speed or direction over a short distance
Hodograph plot of wind vectors at various heights in the troposphere. Meteorologists can use this plot to evaluate vertical wind shear in weather forecasting
Wind_shear
Cubic plane curve
case of a sinusoidal spiral, of a pursuit curve, and of a Pythagorean hodograph curve. The original study of this curve, by Ehrenfried von Tschirnhaus
Tschirnhausen_cubic
Natural movement of air or other gases relative to a planet's surface
Hodograph plot of wind vectors at various heights in the troposphere, which is used to diagnose vertical wind shear
Wind
Generalization of the concept of parallel lines
parallel curve has to be solvable. Such curves are called Pythagorean hodograph curves and were investigated by R.T. Farouki. Not all implicit curves
Parallel_curve
2024 EF4 tornado in Iowa, U.S.
have to rise, in addition to powerful wind fields producing elongated hodographs, a measure indicative of a shift in wind speed with height that allows
Greenfield_tornado
Croatian seismologist and geophysicist
transversalnih valova potresa (undae primae et undae secundae)). Part 1. Hodographs" [Hodographs of the longitudinal and transversal earthquake waves (undae primae
Andrija_Mohorovičić
Irish mathematician and physicist (1805–1865)
on fluctuating functions in Fourier analysis, and the invention of the hodograph. Of his investigations into the solutions, especially by numerical approximation
William_Rowan_Hamilton
1925 tornado outbreak in the U.S. states of Missouri, Illinois, and Indiana
as winds veered with height, resulting in low-level curvature and long hodographs. Strong wind shear thus existed, with pronounced directional shear likely
1925 Tri-State tornado outbreak
1925_Tri-State_tornado_outbreak
United States tornado outbreak in May 2025
observed soundings indicated a strongly sheared environment, with enlarged hodographs near the warm front and low-level jet intensification expected during
Tornado outbreak of May 18–21, 2025
Tornado_outbreak_of_May_18–21,_2025
graphical representation of the Rankine–Hugoniot equations in either the hodograph plane or the pressure ratio-flow deflection angle plane. The polar itself
Shock_polar
American composer (1926–2002)
which could be interpreted with even greater flexibility. In 1959, with Hodograph I, Brown sketched the contour and character abstractly in what he called
Earle_Brown
1925 tornado in Missouri, Illinois and Indiana, U.S.
as winds veered with height, resulting in low-level curvature and long hodographs. Strong wind shear thus existed, with pronounced directional shear likely
1925_Tri-State_tornado
Sum of directed areas in exterior algebra
ISBN 978-0-8218-0907-5. Farouki, Rida T. (2007). "Chapter 5: Quaternions". Pythagorean-hodograph curves: algebra and geometry inseparable. Springer. p. 60 ff. ISBN 978-3-540-73397-3
Bivector
diode, electrode, episode, ergodic, exodos, exodus, heptode, herpolhode, hodograph, hodology, hodometer, hodonym, hodophobia, hodoscope, hydathode, method
List of Greek and Latin roots in English/H–O
List_of_Greek_and_Latin_roots_in_English/H–O
Visual mathematical proofs
will describe the shape of the generating circle. Cavalieri's principle Hodograph – This is a related construct that maps the velocity of a point using
Visual_calculus
Region of rotation within a powerful thunderstorm
Retrieved 2006-12-07. A review for forecasters on the application of hodographs to forecasting severe thunderstorms. Charles A. Doswell III Appeared in
Mesocyclone
1995 Texas Panhandle tornado outbreak
supported supercells, and with a large amount of shear and curvature in the hodograph, supercell development was supported. These conditions lead to several
Tornado outbreak of June 8, 1995
Tornado_outbreak_of_June_8,_1995
Curve that winds around a central point
573–581. doi:10.1016/j.cagd.2006.03.004. Farouki, R.T., 1997. Pythagorean-hodograph quintic transition curves of monotone curvature. Computer-Aided Design
Spiral
Weather event in the United States
values exceeding 50 kn (58 mph; 93 km/h) and pronounced curvature in hodographs near the warm frontal zone. Low-level helicity was locally enhanced where
Tornado outbreak of February 13–14, 2000
Tornado_outbreak_of_February_13–14,_2000
2010 EF4 tornado in Mississippi, U.S
area depicted a 60–70 mph (95–115 km/h) low-level jet supporting large hodographs, which plot winds from soundings from Earth's atmosphere, and storm relative
2010_Yazoo_City_tornado
k=1,...,N.} The solution of this system can be given by the generalized hodograph method. Consider the one-dimensional Euler equations written in terms
Riemann_invariant
2023 EF3 tornado across Tennessee and Kentucky, USA
the possibility of a longer-lived tornado threat. Deep wind shear and hodographs were foreseen strengthening northward, with approximately 200-300 M/S2
2023_Clarksville_tornado
Pursuit of severe weather conditions
(1 February 2021). "Anticipating Deviant Tornado Motion Using a Simple Hodograph Technique". Weather and Forecasting. 36 (1): 219–235. doi:10.1175/WAF-D-20-0056
Storm_chasing
Tornado outbreak in the United States
CAPE-based instability, ranging from 1500 to 2500 J/kg, and elongated hodographs, forecasted to produce 400–500 m2/s2 storm-relative helicity in the first
Tornado outbreak of March 13–16, 2025
Tornado_outbreak_of_March_13–16,_2025
Common misconceptions about tornadoes
(February 1, 2021). "Anticipating Deviant Tornado Motion Using a Simple Hodograph Technique". Weather and Forecasting. 36 (1). American Meteorological Society:
Tornado_myths
Flow in region adjacent to constant-state region
waves are also defined by the behavior that all the characteristics under hodograph transformation collapses into a single curve. This means that the Jacobian
Simple_wave
beginning with the 2008–09 winter storm season. helicity high-pressure area hodograph A vectorial visual representation of the movement of a body or a fluid
Glossary_of_meteorology
Book by Richard Feynman
Kepler's first law. Feynman's geometric proof relies on the concept of a hodograph. Feynman reported that his motivation for presenting a proof different
Feynman's_Lost_Lecture
Automation technique for CNC machines
Farouki, Rida T (Jan 1999). "G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNC
Canned_cycle
Dutch physicist (1900–1985)
p. 1169. ISBN 978-0-387-77698-9. Rida T. Farouki (2008). Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Springer Science & Business
Cornelis_Zwikker
the derivation of Richards' equation. However, the derivation employs a hodograph transformation to produce an advection solution that does not include
Finite water-content vadose zone flow method
Finite_water-content_vadose_zone_flow_method
2022 Tornado outbreak in Russia and Ukraine
Severe wind gusts and tornadoes are the primary threats. More pronounced hodograph curvature is simulated further east towards the evening". Tomas Pucik
2022 Russia–Ukraine tornado outbreak
2022_Russia–Ukraine_tornado_outbreak
EF4 tornado in Mississippi, U.S.
levels of instability, ranging from 1500 to 2500 J/kg, and elongated hodographs, forecasted to produce 400–500 m2/s2 storm-relative helicity in the first
2025_Kentwood–Carson_tornado
Curve which could be used to trisect an angle with compass and straightedge
excerpt, p. 12, at Google Books Farouki, Rida T. (2008), Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Geometry and Computing, vol
Trisectrix
All Latin and Greek roots beginning with H
diode, electrode, episode, ergodic, exodos, exodus, heptode, herpolhode, hodograph, hodology, hodometer, hodonym, hodophobia, hodoscope, hydathode, method
List of Greek and Latin roots in English/H
List_of_Greek_and_Latin_roots_in_English/H
2017 severe weather in central US
and sustain themselves in the moisture-rich environment with a sizable hodograph were probable to pose a tornadic threat. As the mid-level wave turned
Tornado outbreak and floods of April 28 – May 1, 2017
Tornado_outbreak_and_floods_of_April_28_–_May_1,_2017
Velocity field as the gradient of a scalar function
γ + 1 ) / 2 {\displaystyle \alpha _{*}=\alpha =(\gamma +1)/2} . Under hodograph transformation, the transonic equation in two-dimensions becomes the Euler–Tricomi
Potential_flow
Rida T. Farouki (2007), "Variation-diminishing Property", Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Springer, p. 298, ISBN 9783540733973
Variation diminishing property
Variation_diminishing_property
European tornado outbreak in October 2022
while low-level shear (0–1 km) reached 15–20 m/s, producing long, curved hodographs. Storm-relative helicity values in the lowest kilometer locally exceeded
October 2022 European tornado outbreak
October_2022_European_tornado_outbreak
upper 70s Fahrenheit, along with strong low-level winds and favorable hodographs, would be conducive to the development of tornadoes. On July 7, multiple
Hurricane Beryl tornado outbreak
Hurricane_Beryl_tornado_outbreak
German geophysicist and meteorologist
with altitude. In 1888 he demonstrated using time-distance plots (or hodographs), that earthquake waves did not move in straight lines. In 883 he developed
Carl_August_von_Schmidt
Angular velocity vector of the Frenet frame of a space curve
Sons, p. 62, ISBN 9781118165478. Farouki, Rida T. (2008), Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Geometry and Computing, vol
Darboux_vector
rotation; magnitude and speed of rotation of the magnetic induction vector hodograph, which in real devices is an ellipse with eccentricity increasing when
Electromagnetic vortex intensifier with ferromagnetic particles
Electromagnetic_vortex_intensifier_with_ferromagnetic_particles
Tornado Outbreak in April 2002
a moist and unstable environment materialized, but long and straight hodographs—plots showing the change in wind with height—favored a predominant large
Tornado outbreak of April 27–28, 2002
Tornado_outbreak_of_April_27–28,_2002
2024 EF3 tornado in Ohio, U.S.
mid-level, lapse-rate plume, along with substantial deep-layer shear and hodograph enlargement, led to the increase in the 5% tornado risk. At 7:27 p.m.
2024 Lakeview–Russells Point tornado
2024_Lakeview–Russells_Point_tornado
2017 tornado outbreak in Texas, USA
and cold front later in the afternoon. Strong vertical shear and large hodographs would be present in the warm sector, but initiation was expected to remain
2017_East_Texas_tornadoes
2008 tornado in Alabama, U.S.
that "storms may intensify during the day as they advance EWD with large hodographs and strong deep shear supportive of bows and supercells". The Day 2 convective
2008 Prattville–Millbrook tornado
2008_Prattville–Millbrook_tornado
and organ Oliver Cromwell, for unison voices and piano Earle Brown – Hodograph I, for flute, piano + celesta, and percussion Alan Bush – Dorian Passacaglia
1959_in_music
1016/S0923-5965(00)00047-3. "The Bernstein Basis" (PDF). Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Geometry and Computing. Vol
Biorthogonal nearly coiflet basis
Biorthogonal_nearly_coiflet_basis
2019 Tornado event in Alabama and Georgia, United States
tornado went over. The SPC cited that several radars had strong, curved hodographs with little weakness in them; indicative for this strong tornado potential
2019_Beauregard_tornado
Early-season tornado outbreak in Southern United States
500–3,000 J/kg, favorable wind shear was present, and elongated, curved hodograph values were expected, allowing any mature supercell to rotate. During
Tornado outbreak of March 13–15, 2024
Tornado_outbreak_of_March_13–15,_2024
Weather event in the United States
speed shear and adequate directional shear (noted by curved low-level hodographs) led to 0–3 km storm relative helicities of 300–500 m2/s2, favorable for
Tornado outbreak of January 21–23, 1999
Tornado_outbreak_of_January_21–23,_1999
American engineer
Dr. Weinig. This led to a thesis on mapping the phreatic line in dams (hodograph). This thesis was judged very well and even led to a publication. Because
Albert_F._Shields
Floods in Montreal, Canada in 1987
showed a very strong convective available potential energy (CAPE) and the hodograph had a strong wind shear in the first 4 kilometres (13,000 ft) above ground
Montreal_flood_of_1987
2023 EF2 tornado across the Nashville, Tennessee metro, USA
the possibility of a longer-lived tornado threat. Deep wind shear and hodographs were foreseen strengthening northward, with approximately 200-300 M/S2
2023_Hendersonville_tornado
Resolution Fly's Eye Cosmic Ray Detector high-altitude airship (HAA) hodograph humid continental climate humid subtropical climate (humidex) heat index
Index_of_meteorology_articles
1968 studio album by John Fahey
on the cover. Directly underneath the main title is "Being a Musical Hodograph & Chronologue of the Music of John Fahey, including his most recent composition
The Voice of the Turtle (album)
The_Voice_of_the_Turtle_(album)
Weather event in the United States
Veering winds—winds that turn clockwise with height—acted to lengthen hodographs and provide significant directional wind shear, with 0–6 km shear of 35–45 mph
Tornado outbreak of February 7, 2017
Tornado_outbreak_of_February_7,_2017
Tornado outbreak in the Southeastern United States in December 2019
of 1,000–2,000 J/kg, and a 40–60 kn (46–69 mph) contributing to large hodographs and strong cyclonic updraft potential. In addition, advection of drier
Tornado outbreak of December 16–17, 2019
Tornado_outbreak_of_December_16–17,_2019
(Princeton University Press), p. 392 Farouki, Rida T. (2007). Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. (Springer), p. 161. Ruestow
List_of_Dutch_discoveries
thermodynamics History of variational principles in physics Hjulström curve Hodograph Hofmeister series Hofstadter's butterfly Hohlraum Hole argument Holevo's
Index_of_physics_articles_(H)
Severe weather effect in the Southeastern United States
shear throughout the entirety of the atmosphere led to large, looping hodographs, and effective storm relative helicity values ranging from 250 to 600 J/kg
Tornado outbreak of April 13–15, 2019
Tornado_outbreak_of_April_13–15,_2019
Weather event in the central US
a result of backed surface winds contributed to enlarged bell-shaped hodographs, with dew points upwards of 60 °F (16 °C), resulting in an outbreak of
Tornado outbreak of November 30 – December 2, 2018
Tornado_outbreak_of_November_30_–_December_2,_2018
Armenian Soviet geologist, engineer-builder
the mechanisms of earthen streams and developed a method for drawing hodographs of the depth creep of slopes. He identified the causes for, and proposed
George_Ter-Stepanian
2022 tornado in Iowa, U.S.
However, the SPC noted uncertainty regarding morning convection. Model hodographs noted that wind profiles near the low pressure system, as well as the
Winterset_tornado
HODOGRAPH
HODOGRAPH
HODOGRAPH
HODOGRAPH
Boy/Male
Hindu, Indian
Giving Shelter
Boy/Male
Arabic, Muslim
Devoted Worshipper of Allah
Girl/Female
Tamil
Samanta | ஸமாநதா, ஸமாநà¯à®¤à®¾Â
Equality, Bordering
Male
Basque
, thanks.
Female
Native American
Native American Osage name NIABI means "fawn."
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : Anglicized form of Welsh ap Adda ‘son of Adda’, a byform of Adam.
Girl/Female
Tamil
Fearless
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : patronymic from the personal name Randel (see Randall).
Boy/Male
Tamil
Trishoolin | தà¯à®°à¯€à®·à¯‚லீந
One who has a trident in his hands, Lord Shiva
Boy/Male
Arabic
Unique; Single
HODOGRAPH
HODOGRAPH
HODOGRAPH
HODOGRAPH
HODOGRAPH
n.
A curve described by the moving extremity of a line the other end of which is fixed, this line being constantly parallel to the direction of motion of, and having its length constantly proportional to the velocity of, a point moving in any path; -used in investigations respecting central forces.