Hasanisawi/geometric-loci

< href="https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/HasanISAWI.jpg/615px-HasanISAWI.jpg

 Geometric Loci

Project log

February 2023

Hasan Isawi has added an update

Feb 25,2023

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/trasformazione-iperbolica-conica.JPG" />

hyperbolic transformation of ellipse which can be the directrix of a quadric (ellipsoid, paraboloid, hyperboloid).

trasformazione iperbolica di ellisse. la quale puo essere la direttrice di una quadrica (ellissoide, paraboloide, iperboloide).

تحول زائدي لقطع الناقص. الذي يمكن أن تكون دالة سطح من الدرجة الثانية (ناقص، مكافئ ، زائد).
hyperbolic transformation of ellipse which can be the directrix of a quadric (ellipsoid, paraboloid, hyperboloid). Date25 February 2023

Hasan Isawi has added an update

Feb 24,2023

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/iperboloide-circolare.jpg" />

a circular hyperboloid can be interpreted as the enveloping surface of a sphere as it transforms along two corresponding hyperbolas

يمكن تفسير السطح الزائدي الدائري على أنه سطح مغلف كرة بينما هذه تتحول على طول قطعين زائدين متقابلين <a href="https://commons.wikimedia.org/wiki/File:Iperboloide-circolare.jpg">https://commons.wikimedia.org/wiki/File:Iperboloide-circolare.jpg</a>

Hasan Isawi has added an update

Feb 19,2023

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/tangenza-parabola-iperbole.jpg" />

tangency of a parabola with a hyperbola

تماس بين قطع مكافئ وقطع زائد avoiding symmetry and especially the circular rotation surfaces, it is possible to understand the genesis of things tangenza di un parabola con una iperbola <a href="https://commons.wikimedia.org/wiki/File:Tangenza-parabola-iperbole.jpg">https://commons.wikimedia.org/wiki/File:Tangenza-parabola-iperbole.jpg</a>

October 2022

Hasan Isawi has added an update

Oct 2,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/proiezione-solida.JPG" />

3d Volumetric projection

3d Volumetric projection is a descriptive geometry technique used to obtain a 3D object as a projection of another 3D object&quot; هي تقنية هندسية وصفية تستخدم للحصول على حجم ثلاثي الأبعاد كإسقاط لكيان آخر ثلاثي الأبعاد

September 2022

Hasan Isawi has added an update

Sep 16,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-in-verticale.jpg" />

تقريب متعدد السطوح لدويرية عامة

approssimazione geometrica di una ciclide generica تقريب متعدد السطوح لدويرية عامة polyhedral approximation of a generic cyclide https://commons.wikimedia.org/wiki/File:Ciclide-in-verticale.jpg

Hasan Isawi has added an update

Sep 15,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/cyclide-twisted.jpg" />

polyhedral approximation of a twisted cyclide

approssimazione poliedrica di una ciclide contorta - دويرية ملتوية <a href="https://commons.wikimedia.org/wiki/File:Twisted_cyclide.jpg">https://commons.wikimedia.org/wiki/File:Twisted_cyclide.jpg</a>

July 2022

Hasan Isawi has added an update

Jul 12,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/steiner-ma-ellissoidi-gen.jpg" />

Soddys hexlet but of 4 generic ellipsoids (corresponding two by two to each other)

في الشكل المرفق هناك اثنين من الأسطح الإهليجية كدالتين لتحول دوري لأربعة اسطح إهليلجية غير متشابهة (non-homothetic) لبعضها البعض. ويمكن اعتبارها، من وجهة نظري، كواحدة من التكوينات البديلة لسداسية سودي (Soddys hexlet) حيث الكرتين يعملان كدالتين لتحول دوري لست كرات. Nella figura allegata vi sono due ellissoidi interne tra loro che fanno da direttrici a una trasformazione ciclica di 4 ellissoidi non omotetiche tra loro. puo essere considerata, da me, come una configurazione alternativa alla hexlet di soddys che le direttrici sono due sfere e la trasformazione ciclica e' tra 6 sfere. In the attached figure there are two internal ellipsoids between them that act as directrixes to a cyclic transformation of 4 ellipsoids that are not homothetic to each other. it can be considered, as an alternative configuration to the soddys

Hasan Isawi has added an update

Jul 3,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/proiezione-volumetrica-ellissoidi-gen.jpg" />

Volumetric projection of a quadric

بمجرد ما تم تحديد سطح اهليجي ك بحيث يكون مغلف من قبل مخروط ف، فأي سطح تربيعي آخر ك^ يكون متقابل للسطح ك اذا كان مغلف من قبل المخروط نفسه.

June 2022

Hasan Isawi has added an update

Jun 19,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/comune-tre-cicliche-gen.JPG" />
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the determination of one of the two conics (yellow) common to three generic cyclics. A generic cyclical envelopes non-homothetic conics with each other.

تحديد أحد المخروطيتين (باللون الأصفر) التي يشاركها ثلاث دويريات عامة. الدورية العامة هي التي تحيط مخروطيات غير متشابهة فيما بينها.

Hasan Isawi has added an update

Jun 13,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/raccordo-2-cicliche.JPG" />

tangential connection between two cyclic transformations of generic conics

اتصال مماسي بين تحولين دوريين لمخروطيات عامة raccordo tra due cicliche di coniche generiche

Hasan Isawi has added an update

Jun 8,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/raccordo-2ciclidi-parab.jpg" />

Connection of 2 parabolic cyclids

توصيل دويرتين برواسم مكافئة

Hasan Isawi has added an update

Jun 5,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture.JPG" />

tangential connections between cyclics

التحول مماسي بين دويريات اهليجية tangential connections between 2 cycles. where the generatrices are circles and the director axes are ellipses <a href="https://ar.wikipedia.org/w/index.php?title=%D9%85%D9%85%D8%A7%D8%B3&amp;stable=0#/media/%D9%85%D9%84%D9%81:%D8%AA%D8%AD%D9%88%D9%84_%D9%85%D9%85%D8%A7%D8%B3%D9%8A.jpg">https://ar.wikipedia.org/w/index.php?title=%D9%85%D9%85%D8%A7%D8%B3&amp;stable=0#/media/%D9%85%D9%84%D9%81:%D8%AA%D8%AD%D9%88%D9%84_%D9%85%D9%85%D8%A7%D8%B3%D9%8A.jpg</a>

May 2022

Hasan Isawi has added an update

May 15,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-paraboloidica-direttrice-parab.jpg" />

paraboloidic cyclide

نمذجة دويرية كمغلف لاسطح مكافئة. حيث يكون الراسم والدليل المحوري قطوع مكافئة. the modeling of a cyclide as an envelope of corresponding paraboloids. where the directrix axis and the generatrix of the paraboloidic cyclide are parabolas. la modellazione di una ciclide inviluppante paraboloidi corrispondenti. l'asse direttore dei quali e' una parabola. O meglio la generatrice e l'asse direttore della Ciclide paraboloidica sono parabole.

Hasan Isawi has added an update

May 11,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/trasformazione-parabolica-coniche.jpg" />

parabolic transformation of coplanar conics

تحول مكافئ لمخروطيات متحدة المستوى trasformazione parabolica di coniche complanari

Hasan Isawi has added an update

May 9,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/trasformaz-iperb.jpg" />

تحول زائدي بين مخروطيات متحدة المستوى- Hyperbolic transformation between coplanar conics

تحول زائدي بين مخروطيات متحدة المستوى والذي يصبح تحول زائدي بين اسطح متقابلة من الدرجة الثانية عندما تكون المخروطيات أدلة للأسطح نفسها Hyperbolic transformation between coplanar conics Which becomes a hyperbolic transformation between corresponding quadrics, when these conics are directrixes of the same surfaces

April 2022

Hasan Isawi has added an update

Apr 27,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/proiez-volum-quadrica-gen.JPG" />

إسقاط حجمي لسطح عام من الدرجة الثانية

volumetric projection of a generic ellipsoid

Hasan Isawi has added an update

Apr 19,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/array-ottagonale-vari-livelli.jpg" />

الثماني كشكل مرجعي لتطوير تكوينات أكثر تعقيدا

l'ottagono come riferimento per elaborare configurazioni piu complesse

March 2022

Hasan Isawi has added an update

Mar 23,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/piani-coniugati-quadrica.jpg" />

the conjugate polar planes with respect to a quadratic are indispensable to solve the problem of nodes

i piani polari coniugati rispetto ad una quadrica sono indispensabili per risolvere il problema dei nodi

Hasan Isawi has added an update

Mar 21,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture_63fd08124c73e.JPG" />
  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture1.JPG" />

la superficie luogo dei vertici dei coni generatori

... che si può determinare in 2 modi: 1- come coniche comuni a coni generatori, v e w ecc., che hanno vertici su delta e direttrice comune omega. 2- come coniche comuni a coni direttori, p e q, che hanno vertici comuni e direttrici variabili lungo l'asse d

Hasan Isawi has added an update

Mar 14,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/paraboloide-parabolico.jpg" />

the projective genesis of a parabolic paraboloid

la genesi proiettiva di un paraboloide parabolico النشأة الإسقاطية للسطح المكافئ مكافئي

February 2022

Hasan Isawi has added an update

Feb 28,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/superficie-polare.JPG" />

Polar Surface

- السطح القطبي لتحول دوري لسطح ثنائي، هو سطح ثنائي من نفس النوع. على سبيل المثال (انظر الشكل المرفق) السطح القطبي لتحول دوري لسطح اهليجي هو سطح اهليجي.

Hasan Isawi has added an update

Feb 20,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-direttrici-esterne.JPG" />

cyclide which has parabolas as generators and two ellipses as directrixes of reference

ciclide che ha parabole come generatrici e come direttrici di riferimento due ellissi

Hasan Isawi has added an update

Feb 19,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/interchangeable-directrices-generatrices.JPG" />

the interchangeable roles between directrices and generatrices

le 2 coniche direttrici di riferimento possono essere interpretati a loro volta come generatrici

Hasan Isawi has added an update

Feb 16,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/retta-ellisse.jpg" />

una ciclide avente come direttrici di riferimento un ellisse ed una retta

The peculiarity of this cyclide is that its two reference directrices are formed by an ellipse and a straight line

Hasan Isawi has added an update

Feb 14,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-invilupp-ellissoidi.jpg" />

A Cyclide obtained as an envelope of a geometric transformation of ellipsoids not similar to each other

دويرية تم الحصول عليها كمغلف لتحول هندسي لاسطح اهليجية غير متشابهة لبعضها البعض <a href="https://commons.wikimedia.org/wiki/File:Ciclide-invilupp-ellissoidi.jpg">https://commons.wikimedia.org/wiki/File:Ciclide-invilupp-ellissoidi.jpg</a>

Hasan Isawi has added an update

Feb 2,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/gen-direttrici-ellissoide-asse-decentrato.jpg" />

the determination of a number of generatrices and directrixes (alternating) of an ellipsoid having a decentralized axis

la determinazione di alcuni generatrici e direttrici (ad alternanza) di un ellissoide avente asse decentrato

January 2022

Hasan Isawi has added an update

Jan 29,2022

a cyclide identified by three elliptical generatrices and an elliptical directrix

دويرية تم تحديدها بواسطة ثلاثة رواسم اهليجية ودالة اهليجية una ciclide individuata da tre generatrici ellittiche e da una direttrice ellittica https://commons.wikimedia.org/wiki/File:Sup-individuata-da-gen-ell-e-dir-ell.jpg

Hasan Isawi has added an update

Jan 26,2022

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-invilupp-parabolidi-scal.JPG" />

a cyclide enveloping a geometric transformation of three non-homothetic elliptical paraboloids

Una ciclide individuata da tre paraboloidi ellittici non omotetici

December 2021

Hasan Isawi has added an update

Dec 30,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/stella-rette-polo.JPG" />

a star of the pole lines

Stella di rette polo. in elaborazione

Hasan Isawi has added an update

Dec 18,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Untitled-1.jpg" />

two corresponding non-coplanar intersecting conics, and an axis of rotation, have been established

per costruire le interscambiabili generatrici e direttrici di un ellissoide, sono stati stabiliti due corrispondenti coniche, intersecanti, non complanari, ed un asse di rotazione

Hasan Isawi has added an update

Dec 7,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/proiez-3d.JPG" />

Proiezione volumetrica

Volumetric projection- الإسقاط الحجمي

November 2021

Hasan Isawi has added an update

Nov 30,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/bastano-due-conica-asse-centro.jpg" />

two generatrices, axis and center of rotation are needed...

يكفي راسمين ومحور ومركز للدوران ... sono sufficiente due coniche generatrici, asse e centro di rotazione ...

Hasan Isawi has added an update

Nov 20,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/in-elaboraz.JPG" />

In elaborazione

analizzando le 4 coppie di coniche tangenti a tre stabilite coniche complanari , ...

Hasan Isawi has added an update

Nov 11,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/parab-luogo-poli.JPG" />

the parabola as the locus of the poles

la parabola come luogo dei poli delle rette tangenti ad una conica rispetto ad un'altra conica القطع المكافئ كموقع هندسي لأقطاب الخطوط المتماسة لمخروطية بالنسبة لمخروطية آخرى the parabola as the locus of the poles of the lines tangent to a conic with respect to another conic

Hasan Isawi has added an update

Nov 10,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/distanza-min-max-2-coniche-non-omotetiche.JPG" />

determine the minimum and maximum distances between two non-homothetic conics and internal to each other

تحديد المسافتين الأدنى الأقصى بين اثنين من المخروطيات غير المتشابهة والداخلية لبعضهما البعض Determinare le distanza minima e massima tra due coniche non-omotetiche e interne tra loro

Hasan Isawi has added an update

Nov 7,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/approssimaz-poliedric-parab-ell.jpg" />

عملية تقريب متعدد السطوح لمكافئ اهليجي

durante il processo di una approssimazione poliedrica di un paraboloide ellittico

Hasan Isawi has added an update

Nov 3,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/un-piano-corrispondente.jpg" />

only one corresponding polar plane

un solo piano polare corrispondente

October 2021

Hasan Isawi has added an update

Oct 29,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/approssimazione-piramidale-ellissoide.jpg" />

Geometric approximation of an elliptical ellipsoid. Where the axis of rotation does not pass through the center of the directrix

Approssimazione geometrica di un ellissoide ellittico. In cui l'asse di rotazione non passa per il centro della direttrice التقريب الهندسي لسطح اهليجي. حيث لا يمر محور الدوران بمركز الدالة

Hasan Isawi has added an update

Oct 29,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/poliedro-18-tang-ellissoide.jpg" />

an 18-sided polyhedron enveloping an ellipsoid

un poliedro a 18 facce inviluppante un ellissoide

Hasan Isawi has added an update

Oct 27,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/24-facce-dinviluppo-ellissoide.jpg" />

a 18-sided polyhedron enveloping an ellipsoid

un poliedro a 18 facce inviluppante un ellissoide متعدد الوجوه (18) محيط بسطح إهليلجي

Hasan Isawi has added an update

Oct 19,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/coniche-non-coniug.jpg" />

Elliptical revolution

Superficie di rotazione ellittica . In cui le due ellissi che fanno da generatrice e direttrice si intersecano in un solo punto.

Hasan Isawi has added an update

Oct 19,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/poli-coniugati-quadrica.JPG" />

Conjugated poles with respect to a quadric

Poli coniugati rispetto ad una quadrica Due poli sono coniugati nello spazio se il piano polare di un polo passa per l’altro polo e viceversa. In altre parole, due poli sono coniugati rispetto ad una quadrica K, se il conica di contorno apparente di k rispetto ad un polo appartiene ad un piano che passa per l’altro polo, e viceversa اقطاب متقارنة بالنسبة لسطح ثنائي نعتبر اثنين من الاقطاب متقارنة بالنسبة لسطح ثنائي س، إذا كان المستوى القطبي لأحدهما يمر بالقطب الآخر، والعكس صحيح. بمعنى آخر ، يكونان قطبين متقارنين بالنسبة لـلسطح س ، إذا كان الكفاف الظاهر لـلسطح س بالنسبة لقطب منهما، ينتمي للمستوى الذي يمر بالقطب الآخر ، والعكس صحيح.

Hasan Isawi has added an update

Oct 16,2021

the pole line&quot; can be straight, flat curve or skewed curve

يمكن أن يكون خط القطب مستقيما أو منحنى مستويا أو منحنى متخالفا. la linea polo&quot; può essere retta, curva piana o curva sghemba

Hasan Isawi has added an update

Oct 14,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/approximation-elliptical-paraboloid.jpg" />

conical and pyramidal approximation of an elliptical paraboloid

تقريب مخروطي وهرمي لسطح مكافئ اهليجي approssimazione conica e piramidale di un paraboloide ellittico

Hasan Isawi has added an update

Oct 12,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ellissoide-ellittico2.jpg" />

..the name of the surface starts with the type of the generatrix and then follows that of the directrix.

يُطلق على السطح الناتج عن دوران اهليج (أزرق) حول آخر (أحمر) سطح ناقص إهليلجي. وإذا وضعنا قطع مكافئ بدلاً من القطع الناقص الأزرق، فإن السطح يسمى سطح مكافئ إهليلجي. وبالنظر إلى حقيقة أن الراسم (أزرق) والدليل (أحمر) يمكنهما تبادل الأدوار ، لذلك إذا قمنا بتثبيت القطع المكافئ وتدوير القطع الناقص، فإن السطح يسمى سطح ناقص مكافئ . لذا فإن اسم السطح ، في هذه الحالات ، يبدأ بنوع الراسم ثم يتبعه الدليل. La superficie che viene generata dalla rotazione di un ellisse (blue) intorno ad un'altra (rossa) si chiama ellissoide ellittico. Se al posto dell'ellisse generatrice (blue) mettiamo una parabola, la superficie si chiama paraboloide ellittico. In considerazione del fatto che le generatrice e la direttrice possono scambiarsi i ruoli, percui se fissiamo la parabola e ruotiamo l'ellisse, la superficie si chiama ellissoide parabolico. Quindi il nome della superficie, in questi casi, inizia con il tipo della conica generatrice e poi lo segue quello della direttrice.

Hasan Isawi has added an update

Oct 9,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/prodotto-in-croce.JPG" />

&quot;Il prodotto in Corce&quot; in una involuzione

Il cosiddetto &quot;prodotto in croce&quot; in una corrispondenza involutoria G , non e' altro che l'operazione di individuare l'asse u di G mediante la congiunzione di due punti uniti. l'asse u rappresenta la polare del centro U dell'involuzione (polo) rispetto a due coniche coincidenti, DeltaV e DeltaW. Che si ottengono come proiezioni di una stessa conica delta da due centri di proiezione distinti.

Hasan Isawi has added an update

Oct 8,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclica-gen-ellissoidi-non-omotetiche.jpg" />

A Cyclide surface generated by a cyclic transformation of a scalene ellipsoid

Una superficie Ciclide generata da una trasformazione ciclica di un ellissoide scaleno

Hasan Isawi has added an update

Oct 7,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ellissoide-ellittico.jpg" />

construction of a scalene ellipsoid through two sections, the pole line and the corresponding plane

إنشاء سطح إهليلجي من خلال مقطعين ، خط القطب والمستوى المقابل https://commons.wikimedia.org/wiki/File:Ellissoide-ellittico.jpg

Hasan Isawi has added an update

Oct 6,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/conica-intera.jpg" />

conic approximation of a cyclide which has an integer conic as its meridian generatrix

approssimazione conica di una ciclide che ha come generatrice meridiana una intera conica

Hasan Isawi has added an update

Oct 4,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture_63fd08124c90a.JPG" />

but then the homological correspondence was always a product of two involutions

ma allora la corrispondenze omologica era sempre un prodotto di due involuzioni

Hasan Isawi has added an update

Oct 3,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/pre-approssimazione-ciclide-elicoidale.jpg" />

checking the &quot;skew pole line&quot;

verificando la linea polo sghemba

Hasan Isawi has added an update

Oct 3,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/pre-approssimazione-ciclide-libera.jpg" />

pre geometric approximation of a free cyclide

pre approssimazione di una ciclide libera مرحلة ما قبل التقريب الهندسي لدويرية براسم حر https://ar.wikipedia.org/wiki/%D8%AC%D9%8A%D9%88%D9%85%D9%8A%D8%AA%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D8%B9%D9%85%D8%A7%D8%B1%D8%A9#%D9%85%D8%B9%D8%B1%D8%B6_%D8%B5%D9%88%D8%B1

September 2021

Hasan Isawi has added an update

Sep 26,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture_63fd08124c93c.JPG" />

approssimazione di una ciclide con sezioni trasversali non appartenenti allo stesso fascio di piani

Le fasi di costruzioni di una approssimazione di una ciclide k. In cui una delle due coniche direttrici di basi e' degenere in un punto. inoltre i piani delle sezioni trasversali di k non appartengono ad uno stesso fascio

Hasan Isawi has added an update

Sep 20,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/offset-conica-dato-polo.JPG" />

l'offset di una conica generica

l'offset di una conica Δ, e', in tutti i casi un prodotto di due involuzioni omotetiche. Questa informazione e' molto utile quando il centro di tale corrispondenza e' punto decentrato rispetto al centro di Δ.

Hasan Isawi has added an update

Sep 19,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/approssimazione-piramid.JPG" />

تقريب هرمي لدويرية مخروطية

approssimazione piramidale di una ciclide conica

Hasan Isawi has added an update

Sep 19,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/curve-parallele.JPG" />

CURVE PARALLELE - Toroide

Le curve parallele di un'ellisse sono curve toroidi, perché assomigliano il contorno apparente di un toro visto da un centro improprio. Volume II: curve trascendenti -curve dedotte da altre, (17.6 MB) http://mathematica.sns.it/media/volumi/309/CURVE_ALG_TRASC_II.pdf

Hasan Isawi has added an update

Sep 17,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/curva-policentrica-circ.JPG" />

curve policentriche composte da archi di coniche

بالنظر إلى حقيقة أن الإسقاط المركزي (أو الموازي) لمنحنيات مخروطية، على مستوى معين، تكون دائمًا كذلك، أي مخروطية. وبما أن المخروطيات هي محل هندسي بخصائص معروفة، فمن الضروري، في مرحلة تصميم رواسم لأسطح معمارية، استخدام هذا النوع من المنحنيات؛ وليس منحنيات أخرى (مثلا سبلاين) يصعب التحكم بها في كل من مرحلة التصميم والتنفيذ. In considerazione del fatto che la proiezione, centrale o parallela, di una conica su un piano e' sempre una conica, e poiché la conica e' un luogo geometrico con caratteristiche molto note. Per cui, in fase di progettazione di profili di elementi architettonici, e' consigliabile utilizzare questo tipo di curve, e non altre curve grafiche, come spline, che sono di difficili controllo sia nella fase di progettazione che in quella di costruzione.

Hasan Isawi has added an update

Sep 16,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/fascio-arbitrario.JPG" />

fascio arbitrario

la conferma dell'esistenza di corrispondenza involutoria, anche, nel caso in cui il fascio delle sezioni trasversali viene scelto in modo arbitrario

Hasan Isawi has added an update

Sep 15,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-piramid-variaz-trasvers.JPG" />

transverse variation (pyramidal cyclide)

variazione delle sezioni trasversali di una ciclide piramidale

Hasan Isawi has added an update

Sep 14,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/variaz-fuso-trasvers.jpg" />

transverse variation

variazione delle sezioni trasversali di una ciclide conica

Hasan Isawi has added an update

Sep 14,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/approssim-piramid-ciclide-liber-.jpg" />

Pyramidal approximation of a cyclide with free generatrix

Approssimazione piramidale di una ciclide avente generatrice libera تقريب هرمي لسطح دويري براسم حر

Hasan Isawi has added an update

Sep 12,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/polarity.JPG" />

polarity

geometric modeling of an elliptical cyclide with free generatrix

Hasan Isawi has added an update

Sep 12,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/retta-polo.jpg" />

La determinazione della retta polo di un stabilito piano gamma rispetto ad un cono quadrico

Stabilito un piano gamma passante per il vertice V di un cono quadrico v, si vuole determinare la retta polo di gamma rispetto al cono v. - si sceglie una retta s di gamma - per s si fa passare un piano alfa che taglia il cono v secondo una conica delta - si sceglie un punto P di s - si determina il piano polare beta di P rispetto a v - si la retta d'intersezione n tra i piani beta e gamma - si determina il punto R come intersezione di n con s - si determina il piano polare sigma di R rispetto a v - si determina la retta polo cercata come intersezione tra i piani beta e delta note: - si può determinare la retta polo cercata come intersezione di beta con un qualsiasi piano polare di un qualsiasi punto di s rispetto a v. - La retta polo del piano corrispondente rispetto ad un cono quadrico e' il luogo dei poli delle rette appartenente a gamma rispetto alle coniche ottenute come sezioni di v con piani passanti per tali rette. Per cui la retta polo e' il sostegno del fascio dei piani polari dei punti di gamma rispetto a v - quando la retta polo di gamma rispetto a v, e' ortogonale a gamma, significa che essa coincide con l'asse principale del cono.

Hasan Isawi has added an update

Sep 11,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/poli-coniugati.JPG" />

Conjugate poles

Poli coniugati- أقطاب متقارنة stabiliti un cono v, ed un piano gamma passante per il vertice V di v. La base DeltaV di v appartiene al piano p1 . Si vuole capire il significato spaziale del termine poli coniugati. Sezionando gamma e v con un piano alfa non passante per V, si hanno rispettivamente la retta s e la conica Delta . Stabilendo su s un qualsiasi punto P e determinando la sua polare p rispetto a Delta; si individua, cosi, il piano di contorno apparente di v rispetto a P. Prolungando la polare p fino ad intersecare s, si ha il polo coniugato R di P rispetto a Delta. Determinando il piano di contorno apparente beta di v rispetto ad R, si nota che beta passa per P. Per cui, due poli, P e R, si dicono coniugati se il piano di contorno apparente del cono v rispetto all'uno passa per l'altro polo. https://commons.wikimedia.org/wiki/File:Conjugate_poles.jpg

Hasan Isawi has added an update

Sep 11,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/centro-involuzione.jpg" />

a Variation of an elliptical cyclide

Variazione di una ciclide ellittica https://commons.wikimedia.org/wiki/File:Centro-involuzione.jpg

Hasan Isawi has added an update

Sep 8,2021

la retta polo come sostegno del fascio dei piani di contorno apparente di un cono

Percorrendo una retta con centri di proiezioni che vedono un cono v , si ha un fascio di piani contenenti, rispettivamente, i contorni apparenti di v. Il sostegno di tale fascio e' la retta polo d del piano corrispondente gamma rispetto a v. il piano gamma e' individuato da vertice di v e dalla retta d.

Hasan Isawi has added an update

Sep 8,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/piani-corrispond-coni-inversi.JPG" />

I piani polari corrispondenti rispetto a due coni inversi tra loro

Due coni inversi tra loro rispetto a due loro sezioni, hanno una stessa retta polo di due piani corrispondenti che hanno in comune la retta d'intersezione dei piani di tali sezioni. Il piano corrispondente gamma di una retta polo d rispetto ad un cono v, e' il luogo delle polari dei poli rispetto alle coniche ottenute, rispettivamente, come sezioni di v con dei piani passanti per tali polari. L'insieme di questi poli appartengono a tale retta d

August 2021

Hasan Isawi has added an update

Aug 2,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/max-min-inversa.JPG" />

the maximum and the minimum distances in the cyclic transformation of an ellipse

العربية: في التحويل الدويري للقطع الناقص (بما في ذلك الدائرة كحالة معينة)، يأخذ الاهليج، من بين الأبعاد اللانهائية، بعدين مهمين وهما الأقصى والأدنى. التي في المثال المرفق ملونين بالأصفر والأخضر على التوالي. أما اللون الأرجواني فيشير إلى دالتي التحول المعني. الذي نوعه في هذه الحالة عكسي. Italiano: Nella trasformazione ciclica di un'ellisse (compresa la circonferenza come caso particolare), l'ellisse assume, tra le infinite dimensioni, due importanti dimensioni, che sono la massima e la minima. nell'esempio allegato sono colorati rispettivamente in giallo e verde. invece il colore viola indica le direttrici della trasformazione in questione. la cui tipo è inverso. English: in the cyclic transformation of an ellipse (including the circumference as a particular case), the ellipse assumes, among the infinite dimensions, two important, which are the maximum and the minimum. in the attached example they are colored in yellow and green respectively. instead the purple color indicates the directrices of the transformation in question. which is inverse. https://www.researchgate.net/project/Geometric-Loci https://commons.wikimedia.org/wiki/File:Max-min-inversa.jpg

Hasan Isawi has added an update

Aug 1,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/dist-max-min-ciclica-di-coniche-non-omot-con-polari-distinti.JPG" />

maximum and minimum distance of an elliptical cyclic

The determination of the four generating conics of maximum and minimum distance of an elliptical cyclic. In which the two directrices conic are not homothetic, nor do they have coincident polars. https://commons.wikimedia.org/wiki/File:Dist-max-min-ciclica-di-coniche-non-omot-con-polari-distinti.jpg

July 2021

Hasan Isawi has added an update

Jul 29,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/poligonati-elliss-gen-secondo-min-max-dist.JPG" />

the minimum polygonal approximation of two non-homothetic ellipses

تقريب متعدد الأضلاع لمخروطيتين ا و ب غير متشابهتين. المضلع في هذه الحالة عبارة عن مثمن له أضلاع متماسة للمخروطيتين عند المسافات القصوى والدنيا. الأضلاع الأخرى متماسة ا و ب في الأجزاء &quot;الوسطية نسبيا بالنسبة للأضلاع الأولى. https://commons.wikimedia.org/wiki/File:Poligonati-elliss-gen-secondo-min-max-dist.jpg

Hasan Isawi has added an update

Jul 27,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/distanza-min-max-image-circ.JPG" />

المسافة القصوى والدنيا بين منظور دائرتين متحدتا المركز (أحدث إصدار)

la distanza max e minima tra le immagini prospettiche di due circonferenze concentriche (ultima versione)

Hasan Isawi has added an update

Jul 26,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/appross-piramidale-fortezz.JPG" />

تقريب هرمي لدويرية مخروطية

The pyramidal approximation of a cyclide can be applied to fortress constructions

Hasan Isawi has added an update

Jul 25,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/distanza-min-max-due-conic-gen.JPG" />

تحديد المسافتين القصوى والدنيا بين مخروطيتين

la determinazione delle distanze massima e minima tra due coniche proiettivamente parallele che sono rispettivamente in colore giallo e verde The determination of the maximum and minimum distances between two projectively parallel conics which are respectively in yellow and green color https://commons.wikimedia.org/wiki/File:Distanza-min-max-due-conic-gen.jpg

Hasan Isawi has added an update

Jul 24,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/sezione-retta.JPG" />

sezione retta di un cono quadrico generico

un procedimento per determinare una sezione retta di un cono quadrico generico v, data la base ed un polo della stessa. Il polo in questo caso rappresenta la prima traccia di una retta appartenenete al piano corrispondente della retta polo rispetto a v إجراء هندسي لتحديد مقطع قائم لمخروط ثنائي بوضع عام . معلوم: القاعدة وقطب. الذي يمثل في هذه الحالة الأثر الأول لخط ينتمي إلى المستوى المقابل للخط القطبي بالنسبة للمخروط نفسه https://commons.wikimedia.org/wiki/File:Sezione-retta-cono-generico.jpg

Hasan Isawi has added an update

Jul 22,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/vera-forma-sez-circ-cono-ell.JPG" />

الشكل الحقيقي لزوج من المقاطع الدائرية لمخروط إهليجي

vera forma di una coppia di sezioni circolari di un cono ellittico https://commons.wikimedia.org/wiki/File:Vera-forma-sez-circ-cono-ell.jpg

Hasan Isawi has added an update

Jul 22,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/sez-circ-cono-ell.JPG" />

offset proiettivo di un cono ellittico

lo spessore costante di un cono ellittico v, si determina solo su una sezione circolare di v يحدد السمك الثابت لمخروط إهليجي على مقطع دائري للمخروط نفسه https://commons.wikimedia.org/wiki/File:Sez-circ-cono-ell.jpg

Hasan Isawi has added an update

Jul 21,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/offset-ciclide-affine.jpg" />

sezione di una ciclide conica a spessore costante

e' allegata l'immagine di uno dei due casi in cui e' possibile fare un offset proeittivo costante di una ciclide conica

Hasan Isawi has added an update

Jul 21,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture_63fd08124cac4.JPG" />

dictatorship_of_mathematics

عند استخدام اجراءات النمذجة ثلاثية الابعاد، بهدف توليدبشكل تلقائي، مخروط م^ موازي لمخروط اهليجي م بقاعدة دائرية ق (اللون الابيض)، حصلت، في هذه الحالة، على منحنى غريب (اللون الاصفر) كقاعدة للمخروط م^، والذي لا يوجد بينه وبين ق أي علاقة تقابلية او قياسية. أما من ناحية أخرى ، وعند استخدام الإجراءات الهندسية الوصفية ، حصلت بسهولة على دائرة ، كما هو مفترض ومتوقع (اللون الازرق). ما أعنيه، بشكل عام، هو أن هناك، للأسف، الكثير من الإجراءات الرقمية، التي تحاول بواسطة إجراءاتها التقريية (أحادية الاتجاه) ، ايجاد حل واحد للكثير من المسائل المتنوعة.

Hasan Isawi has added an update

Jul 20,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture_63fd08124cad3.JPG" />

مقطع مستوي لدويرية مخروطية بسمك ثابت

الصورة المرفقة عبارة عن مقطع مستوي لدويرية مخروطية بسمك ثابت. واعتقد أن نمذجة سطح حلزوني دويري منها ستكون عملية سريعة. the attached image is a plan section of a conical cyclid with constant thickness. but it shouldn't be laborious to build a cyclic helicoid out of it https://commons.wikimedia.org/wiki/File:%D9%85%D9%82%D8%B7%D8%B9_%D9%85%D8%B3%D8%AA%D9%88%D9%8A_%D9%84%D8%AF%D9%88%D9%8A%D8%B1%D9%8A%D8%A9_%D9%85%D8%AE%D8%B1%D9%88%D8%B7%D9%8A%D8%A9_%D8%A8%D8%B3%D9%85%D9%83_%D8%AB%D8%A7%D8%A8%D8%AA.jpg

Hasan Isawi has added an update

Jul 14,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/offset-approssimazione-ciclide.PNG" />

Offset proiettivo di una trasformazione ciclica sia di 3 coniche non omotetiche che dei loro inviluppi corrispondenti

توازي إسقاطي لتحول دويري لثلاث مخروطيات غير متشابهة ولمغلفاتها المتقابلة

Hasan Isawi has added an update

Jul 10,2021

projective parallelism

بالنظر إلى حقيقة أن جميع الإجراءات الهندسية المستخدمة لحل مشكلة التوازي بين دويريات مخروطية تعتمد على مفاهيم التقابل نفسها، فإن استخدام مصطلح واحد: &quot;التوازي الإسقاطي&quot; ، يصبح ضروري للإشارة إلى جميع حالات التوازي سواء كانت ثابتة أو متغيرة بشكل منتظم.

Hasan Isawi has added an update

Jul 9,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture_63fd08124cb02.JPG" />

Affinità involutoria

vedi pagina 264, in Geometria proiettiva. Con 112 figure intercalate nel testo. Severi, Francesco, 1879-1961. https://archive.org/details/geometria-proiettiva-severi-francesco-1879-1961/page/262/mode/2up?q=%22rapporto+delle+distanze%22

Hasan Isawi has added an update

Jul 5,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/offset-ciclide-circ.jpg" />

ترشيد متعدد السطوح لدويرية ذات سمك

polyhedral approximation of a cyclide-offset لقد اعطت برمجيات النمذجة الرقمية للمصممين فرصة جديدة في عمليات التقريب أو الترشيد الهندسي للأسطح المنحنية. يمكن تقريب كل سطح منحني بواسطة سطح متعدد السطوح. إن اهمية الأسطح المستوية الرباعية في العمارة تتخلص في خاصية التوازي . تعتبر دراسة وتطبيق عمليات التقريب الهندسي للاسطح المنحنية تطور طبيعي لمفهوم التقابل الالتفافي بين المستويات، وهو موضوع متجذر على نطاق واسع في تاريخ الهندسة الوصفية والذي يجد في الفضاء الافتراضي الفرصة المثلى للتجربة والتعميم. https://commons.wikimedia.org/wiki/File:Approssimazione-offset-ciclide-sfere.jpg

Hasan Isawi has added an update

Jul 3,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/offset-ciclide-circ_63fd08124cb1f.jpg" />

توازي اسقاطي لتحول اهليجي من الدوائر

projective offset of an elliptic transformation of circles https://commons.wikimedia.org/wiki/File:Offset-ciclide-circ.jpg

Hasan Isawi has added an update

Jul 3,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/offset-proiettivo.JPG" />

(Projective offset)

توازي إسقاطي إن التوازي المحتمل بين مخروطيتين متحدتي المستوى - وبالتالي بين مغلفاتهما متعددة الأضلاع- ليس سوى حالة خاصة من التقابل الالتفافي (involuntary correspondence) .في هذه الحالة يتطابق مركز التقابل مع مراكز المخروطيتين. https://commons.wikimedia.org/wiki/File:Offset-proiettivo.jpg

Hasan Isawi has added an update

Jul 2,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-circ-poliedrica.jpg" />

razionalizzazione poliedrica di una ciclide d'inviluppo di sfere

ترشيد متعدد السطوح لدويرية مغلفة كرات

June 2021

Hasan Isawi has added an update

Jun 29,2021

parallel meshes

Nel articolo di Helmut Pottmann (vedi link pag. 5), vi e' l'affermazione che &quot;le costruzioni a multistrato (vedi Figura 2 ) è naturale richiedere che la distanza delle facce corrispondenti sia costante.&quot; Questa affermazione, secondo me, e' troppo generica. La costanza tra due superfici corrispondenti dipende appunto dalla corrispondenza e non da un numero prefissato. la corrispondenza tra le due superfici corrispondenti ha elementi inequivocabili, che non possono essere modificati a piacere. altrimenti la corrispondenza non e' biunivoca. per esempio la distanza tra due due superfici di rotazioni con assi coincidenti, può' essere, in questo caso, costante. Invece la distanza, ad esempio, tra due coni ellittici e' variabile e dipende dalla posizione della loro comune retta polo. il link dell'articolo in questione Geometry of Multi-Layer Freeform Structures for Architecture

Hasan Isawi has added an update

Jun 27,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/applicazione-ciclide-conica.jpg" />

application example of the offset of a conical cyclide

مثال تطبيقي لموازي دويرية مخروطية esempio d'applicazione di un offset di una Ciclida conica https://commons.wikimedia.org/wiki/File:Applicazione-ciclide-conica.jpg

Hasan Isawi has added an update

Jun 27,2021

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the offset of a cyclic transformation of non-homothetic conics

l'offset di una trasformazione ciclica di coniche non omotetiche https://commons.wikimedia.org/wiki/File:Offset-ciclica-ellissi-non-omotet.jpg

Hasan Isawi has added an update

Jun 26,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/approssim-ciclide-ell.jpg" />

تقريب هندسي مخروطي وآخر هرمي لسطح دويري مزدوج المنحني

approssimazione conica ed un'altra piramidale di superficie Ciclida ellittica a doppia curvatura

Hasan Isawi has added an update

Jun 4,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/luogo-poli-rette-tan.JPG" />
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il luogo dei poli delle rette

The problem of tangency to three non-homothetic conics https://archive.org/details/questioniriguard00enri/page/214/mode/2up?q=%22il+luogo+geometrico+dei+poli+delle+rette%22

March 2021

Hasan Isawi has added an update

Mar 27,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/steiner-costruz-geom.jpg" />
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catena di Steiner- costruzione geometrica

finalmente sono riuscito a formulare una procedura geometrica descrittiva per costruire la catena di Steiner

  1. Steiner_chain
سلسلة شتاينر، في الجيومتري، هي سلسلة من الدوائر المتماسة لدائرتين معلومتين وغير متقاطعتين. كل دائرة من السلسلة تكون ايضا متماسة للدائرة السابقة والتالية لها. تكون سلسلة شتاينر مغلقة عندما تكون الدائرتين الأولى والأخيرة متماسة لبعضهما البعض. يجب البدء بدائرتين غير متقاطعتين لبناء السلسلة. وهذا يعني ان الدائرة الأصغر يمكن ان تكون داخلية او خارجية بالنسبة للدائرة الاكبر. وفي هاتين الحالتين، تقع مراكز الدوائر المكونة للسلسلة على قطع ناقص أو قطع الزائد ، على التوالي.

February 2021

Hasan Isawi has added an update

Feb 26,2021

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Approssimare un raccordo tangenziale tre cicliche generiche

Approssimare un raccordo tangenziale tre cicliche generiche

Hasan Isawi has added an update

Feb 15,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ellissoide-di-rotaz.PNG" />

one of 4 pairs of conics tangent to three sections of an ellipsoid of rotation

تم حفظ الصورة في موضوع المماس فئة الهندسة الوصفية: تظهر الصورة أحد الأزواج الأربعة من المخروطيات المتماسة ثلاثة قطوع لسطح اهليجي دوراني

Hasan Isawi has added an update

Feb 13,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-sulla-sfera.jpg" />

Ciclide sulla sfera

date tre sezioni di una sfera, determinare una delle ciclide d'inviluppo

Hasan Isawi has added an update

Feb 8,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/polarita-come-involuzione.PNG" />

polarity is involution

e' stata verificata la polarità nel piano come proiezione di una involuzione nello spazio https://commons.wikimedia.org/wiki/File:Polarita-come-involuzione.png

Hasan Isawi has added an update

Feb 7,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/ciclide-ellittico-par-ell.jpg" />

Elliptic cyclide

Elliptic cyclide - the enveloping surfaces are formed in this case by two cones: parabolic and elliptical - the enveloping cones are all elliptical except one parabolic - the anterior plane for the objective pole is external with respect to the involutory conic, therefore the directrix axis of the cyclide is elliptical https://commons.wikimedia.org/wiki/File:Ciclide-ellittico-par-ell.jpg

Hasan Isawi has added an update

Feb 3,2021

واحد من أربعة أزواج من المخروطيات المتماسة لثلاث مخروطيات متحدة المستوى: قطع ناقص وقطع مكافئ وقطع زائد

una delle quattro coppie di coniche tangenti a tre coniche complanari: ellisse parabola e iperbole one of the four pairs of conics tangent to three coplanar conics: ellipse parabola and hyperbola واحد من أربعة أزواج من المخروطيات المتماسة لثلاث مخروطيات متحدة المستوى: قطع ناقص وقطع مكافئ وقطع زائد https://commons.wikimedia.org/wiki/File:Cyclic_transformation.png

January 2021

Hasan Isawi has added an update

Jan 31,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture.PNG" />

Raccordo tangenziale di cicliche non omotetiche

اتصال مماسي بين دويريتين غير متجانستين. وهنا ، أغتنم الفرصة للتأكيد على حقيقة أنه بدون معرفة التكوين الإسقاطي للأسطح ، وبالتالي للمنحنيات التي ولّدتها ، فإن عملية تقسيمها بهدف البناء تصبح صعبة وغير دقيقة. https://commons.wikimedia.org/wiki/File:Raccordare_cicliche_non_omotetiche.png

Hasan Isawi has added an update

Jan 28,2021

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تم الوصول الى حل للعقدة بين دورتين من المخاريط الثنائية، بحيث تكون بدورها مخروطية

https://commons.wikimedia.org/wiki/File:Nodo-conico-tra-2ciclidi.png

Hasan Isawi has added an update

Jan 25,2021

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/solco-facciata-freeform.jpg" />

tassellatura descrittiva di una facciata a forma organica

una delle fasi più importanti per la realizzazione di una superficie organica, e' la tassellature a priori. A tale fine Le procedure geometriche, in questo caso descrittive, devono identificare le coniche (eventualmente degeneri) che fungono da assi direttori e generatrici.

Hasan Isawi has added an update

Jan 21,2021

Cyclide surface rationalization

to rationalize a Cyclide(channel surface), conics (eventually degenerate) were used as generatrices, and therefore curves and surfaces that are not classified as geometric loci were excluded ...

  1. Elliptic_Cyclide_with_straight_generatrices
  2. channel_surface_rationalization

May 2019

Hasan Isawi has added an update

May 26,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/out-of-equator.jpg" />

Out of Equator

Ogni sfera, nel caso illustrato, e' tangente a quattro sfere. in questo modo, e con procedimenti geometrici descrittivi, si poteva continuare a determinare tantissime altre sfere nello spazio comune alle due assegnate sfere che sono tangenti internamente tra loro

Hasan Isawi has added an update

May 17,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/4-punti-una-sfera.jpg" />

Determine circumscribed sphere of an arbitrary tetrahedron, or in other words determine the sphere passing through 4 points not belonging to the same plane

la sfera individuata da 4 punti non appartenenti allo stesso piano Analogamente al fatto che tre punti non allineati individuano una circonferenza, si può dire la stessa cosa nello spazio quando sono dati 4 punti non appartenenti allo stesso piano individuano una sfera. poiché 4 punti non appartenenti allo stesso piano individuano un tetraedro, allora il centro di tale sfera rappresenta l'incentroide del tetraedro https://isawi.blogspot.com/2019/04/luoghi-geometrici.html

Hasan Isawi has added an update

May 16,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/incentroide.jpg" />

incentroide di un tetraedro irregolare

Dati 4 punti non appartenenti ad un stesso piano si ha una piramide triangolare K. l'incentroide di K si determina come punto comune alle bisettrici dei 4 angoloidi formanti K. e quindi tale punto rappresenta il centro della sfera tangenti tutte facce di K.

Hasan Isawi has added an update

May 16,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/incentroide_e_circocentroide-di-angolide-triedrico.jpg" />

Incentroide e Circocentroide di una piramide triangolare

analogamente ad un triangolo, dove esiste l'incentro e il circocentro, anche nello spazio esiste l'ncentroide e il circocentroide di una tetraedro R, che sono rispettivamente i centri di due sfere, una tangenti i vertici di R e l'altra tangente le facce di R. poiché il tetraedro e' composta da 4 angoloidi triedrici, per cui e' sufficiente determinare, come e' stato parzialmente illustrato nel caso allegato, il punto d'intersezione delle bisettrici di tali angoloidi per determinare il cosiddetti incentroide di una qualsiasi Tetrahedron

Hasan Isawi has added an update

May 12,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/cap.png" />
  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/cap2.png" />

superficie di raccordo tangenziale tra gli enti geometrici fondamentali: punto, retta e piano

superficie di raccordo tangenziale tra gli enti geometrici fondamentali: punto, retta e piano

Hasan Isawi has added an update

May 8,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/cilindri-non-intersecanti2.jpg" />
  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/cilindri-non-intersecanti.jpg" />

Raccordo tangenziale tra tre cilindri di rotazione non intersecanti tra loro

Raccordo tangenziale tra tre cilindri di rotazione non intersecanti tra loro https://isawi.blogspot.com/2019/04/luoghi-geometrici.html

Hasan Isawi has added an update

May 6,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/cap_63fd08124ccf9.png" />
  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/cap_63fd08124cd10.png" />

Raccordo tangenziale di tre coni di rotazione non corrispondenti tra loro

Prendendo in considerazione tre coni di rotazione non corrispondenti tra loro, la questione di raccordo diretto diventa laboriosa. invece per quanto riguarda il raccordo inverso, non sono riuscito ancora a determinarlo 🤨 https://isawi.blogspot.com/2019/04/luoghi-geometrici.html una delle due curve che funge da luogo geometrico dei centri delle sfere tangenti tre coni non corrispondenti e' una curva sghemba

Hasan Isawi has added an update

May 5,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/.JPG" />

Superfici di raccordo tangenziale (diretto ed inverso) di tre cono di rotazione

testo in preparazione, ma intanto l'immagine mostra le superfici di raccordo tangenziale (diretto, ed inverso) di tre coni di rotazione. ..

Hasan Isawi has added an update

May 4,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/Capture_1.JPG" />

a modellazione geometrica descrittiva di una Superficie di raccordo tangenziale di tre cilindri di rotazione uguali tra loro ed aventi i propri assi coincidenti con gli spigoli di un tetraedro

le generatrici della Bisettroide (il luogo geometrico dei centri delle sfere tangenti le date superfici) secondo il quadriche di rotazione date, e le loro reciproche posizioni, possono essere composte da tutti i tipi coniche (eventualmente degeneri)

Hasan Isawi has added an update

May 3,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/_63fd08124cd4e.JPG" />

nella figura allegata, e' stata costruita da due superfici rigate che hanno in comune una quartica monogrammica che funge da luogo geometrico dei centri di sfere uguali tra loro e che tangono le due superfici di rotazione date: cono e cilindro. le generatrice delle due rigate sono perpendicolari rispettivamente alla superficie del cono e a quella del cilindro

Hasan Isawi has added an update

May 2,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/_63fd08124cd70.JPG" />

Nel caso in cui le due superficie date non sono intersecanti tra loro, si ha che ciascuna generatrice della bisettroide cercata e' una quartica monogrammica simile alla quartica che si ottiene quando si costruiscono le superfici parallele alle due superficie di rotazione date, ad una medesima distanza. La citata quartica si degenera in un punto quando le dette due superfici parallele sono tangenti tra loro.

Hasan Isawi has added an update

May 2,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/_63fd08124cd81.JPG" />

come abbiamo detto : il luogo geometrico dei punti equidistanti dalle due date superfici di rotazioni rappresenta le generatrici della bisettroide cercata. ma poiché esistono due e non una parabole come luoghi geometrici dei punti equidistanti da un retta (sezione del cono) e da un ellisse (sezione del cilindro), allora sono due le bisettroidi cercate https://isawi.blogspot.com/2019/04/luoghi-geometrici.html

Hasan Isawi has added an update

May 1,2019

  • <img alt="" src="file:///C:/Users/Admin/AppData/Local/Temp/Temp1_Project_Geometric_Loci.zip/files/_63fd08124cd90.JPG" />

In questo modo sarebbe interessante poter modellare la superficie di un progetto architettonico come luogo geometrico di due o più superfici di rotazione, eventualmente degeneri ... https://isawi.blogspot.com/2019/04/luoghi-geometrici.html

Hasan Isawi has added an update

May 1,2019

this research concerns the drawing up of 3d descriptive geometric procedures aimed to determine the geometric loci of the points equidistant from two or more quadric surfaces منهجية البحث تتعلق اولا بتحديد المحل الهندسي للكرات المتماسة لثلاث اسطح دورانية معلومة (كرات مخاريط، اسطوانات ... الخ). ومن ثم استخدام المحل الهندسي المذكور لتحديد السطح (او الاسطح) المتماسة لتلك الاسطح الدوارنية المعلومة الهدف العملي يتجه نحو تعليم طلاب العمارة والتصميم كيفية نمذجة اسطح عضوية معقدة من خلال اجراءات هندسية وصفية. وبالتالي فإن الاجراءات المستخدمة تتعلق بشكل مباشر ورئيسي بالهندسة الاسقاطية والهندسة الوصفية la ricerca riguarda la stesura di procedimenti geometrici descrittivi 3d atti alla determinazione dei luoghi geometrici dei punti equidistanti da due o piu superfici quadriche https://isawi.blogspot.com/2019/04/luoghi-geometrici.html



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