- Type of paper
: Book
Title: Round Forms in the Construction
- Authors:
- Kučinić, Branko (24350)
- Kristoforović, Olga
- Saler, Ivan
- Editors
- Simović, Veselin
Publisher: Građevinar, časopis Saveya građevinskih inenjera i tehničara Hrvatske, Berislavićeva 6
ISBN: 86-81859-01-3
Year: 1992
Number of pages: 208
Number of references: 26
Language: hrvatski
Summary: First, there is an illustration of the basic elements and
relations of the real projective space - with the method of synthetic
geometry. A special attention has been given to the derivation of plane
curves and surfaces. Apart from the classical derivations of the surfaces:
inversion, Steiner's and Sturm's way of derivation, strophoidal, pedal in
cissoide surfaces, there are two new derivations worked out in details:
pedal surfaces of the
congruence (1,2), and the surfaces obtained by the cubic inversion. Rulled
surfaces are also being worked on, as well as the constructions connected
with them. The book is illustrated by a great number of plans for designs
of the objects belonging tothe higher social standard, the elements or the
unities of which are general or rulled surfaces. Thus we have suggestions
for schools, gymnasiums, churches, grain elevators, traffic and other
objects.
Keywords: real projective space, structure, general surfaces, rulled surfaces, designs, gymnasiums, churches, warehouses
- Type of paper
: Book
Title: Constructive Geometry
- Authors:
- Babić, Ivanka (70564)
- Gorjanc, Sonja (176314)
- Sliepčević, Ana (43680)
- Szirovicza, Vlasta (45794)
- Editors
- Babić, Ivanka (70564)
Publisher: Institut građevinarstva Hrvatske
ISBN: 953-6085-03-8
Year: 1994
Number of pages: 268
Number of references: 13
Language: hrvatski
Summary: Carefully chosen tasks from descriptive geometry and its
applications in tehnics are the base of this textbook. It is assigned to
the students on all of the branches of tehnical university in Croatia.
Introductional parts of some of the chapters supplement the existing
textbook and enable better understanding of the theory and application
specially in civil engineering.
The book contains a lot of original tasks presented in a way
which has spatial sollution, constructive sollution along with graphical
presentation. That is why it gives oppotunity for selfeducation in this
field.
Keywords: descriptive geometry, projection, Monge's method, axonometry, quoted projection, constructive elaboration of the ruled surfaces
- Type of paper
: Book
Title: Descriptive Geometry, Part I
- Authors:
- Sliepčević, Ana (43680)
- Szirovicza, Vlasta (45794)
Publisher: Element - HDKGKG
ISBN: 953-6098-93-8
Year: 1995
Number of pages: 150
Number of references: 10
Language: hrvatski
Summary: This book is the result of pedagogical work which authors
have been doing for many years. Understanding of the rules among elements
and geometrical products in the three-dimensional space has been gradualy
introduced. However, it is suitable for high schools and presents a base
for the successful study of the descriptive geometry on all of the branches
of the tehnical university. The brief theory is followed by the solved
examples with detailed explanations.
The book contains 113 pictures, 40 solved tasks and 36 tasks for
checking the knowledge.
Keywords: descriptive geometry, projection, Monge's method
- Type of paper
: Paper in journal
Title: Fast Industrial Construction of Sacral and Other Large
Structures
- Authors:
- Kučinić, Branko (24350)
Journal: Građevinar
Number: 3
ISSN: 0350-2465
Volume: 45
Year: 1993
Pages: from 141 to 145
Number of references: 1
Language: hrvatski
Summary: The paper shows how fast construction of different
structures maybe achieved with a composition of simple planar forms such as
hyperbolic paraboloids or conoids, without massive construction and
applying alternative materials (metal, wood, membranes). The possibilities
of industrial construction of sacral structures, aswell as others covering
very large areas (halls, warehousesetc.), are presented. Also shown are
several types of solutions where the described forms are applied.
Keywords: planar form, hyperbolic paraboloid, conoid, industrial construction, sacral structure, halls, warehouses
- Type of paper
: Paper in journal
Title: A Feature of the Special Hyperbola of Isotropic Plane
- Authors:
- čurić, Vlasta (46205)
Journal: Sonderdruck aus Sitzungsberichte d. Oesterreichische
Akademie d. Wissenschaften
Number: 201
Year: 1992
Pages: from 111 to 115
Number of references: 8
Language: njemački
Summary: A real affine plane A2 is called an isotropic plane I2, if
in A2 a metric is induced by an absolute (f,F), where f is a line at
infinity of A2 and F a point on f.
The conic section k in I2, conveying the point F as a single point is
called a special hyperbola. This paper proves that the special hyperbola,
i.e. the hyperbola with one isotropic assimptote, is isotropicall analogous
to the equilateral hyperbola of Euclidean plane E2.
Keywords: isotropic plane, affine plane, Euclidean plane, conic section, special hyperbola, equilateral hyperbola
- Type of paper
: Paper in journal
Title: Further Researches in the Fammily (MF2), II Part, Complex
(VN)
- Authors:
- čurić, Vlasta (46205)
Journal: Rad HAZU
ISSN: 0351-8639
Volume: 456
Year: 1991
Pages: from 39 to 57
Number of references: 21
Language: njemački
Summary: The quadrics bundle (F2 are classified into one-parameter
family(MF2) of pencils (F2), so that the mutual surface of thesepencils is
a cone M2 (subset of (F2 ) with a vertex in the pointM which is element of
k6. The 6. order curve k6 is made of thevertices of all bundle cones. For
each of infinitely many pencilsof the group (MF2) for ray complexes are
determined. The paperinvestigates the structure constituated by the rays of
Niče's oriented complex and their points Z, i.e. I, when the points I, i.e.
points Z of those rays are on same straight lines. Such rays determine the
congruences, and the points Z, i.e. the points I associated to those rays,
determine the surfaces of interesting features.
Keywords: quadrics, quadrics pencil and bundle, ray complex, ray congruence, surfaces, curves
- Type of paper
: Paper in journal
Title: Contribution to the Theory of the Second Order Surfaces in
the Flag Space
- Authors:
- Sachs, Hans
- čurić, Vlasta (46205)
Journal: Rad HAZU
ISSN: 0351-8639
Volume: 456
Year: 1991
Pages: from 197 to 216
Number of references: 13
Language: njemački
Summary: According to H. Brauner a flag space I3(2) is a
tree-dimensional affine space with an absolute (o,f,F), where f is a line
in the plane of infinity o and F a point on f. In this paper the surfaces
of second order in the space I3(2) are completely classified with regard to
the group of isotropic motions in I3(2). All surfaces are described by
normal forms and the remaining invariants are interpreted in a geometrical
way. Finally some applications are given.
Keywords: isotropic plane, isotropic space, flag space, surfaces of second order, classify, normal-form
- Type of paper
: Paper in journal
Title: Classification Theory of Conic Section Pencil, Type IV, of
the Isotropic Plane, I
- Authors:
- čurić, Vlasta (46205)
- Sachs, Hans
Journal: Rad HAZU
Number: 12
ISSN: 0351-8639
Volume: 470
Year: 1995
Pages: from 119 to 137
Number of references: 12
Language: njemački
Summary: A real affine plane A2 is called an isotropic plane I2, if
in A2 a metric is induced by an absolute (f,F), consisting of the linear
infinity f of A2 an a point F on f. In this paper we classified a conic
section pencil of type IV, which is determined by one double and two real
and different fundamental points. This first part describes two subtypes
IV1 and IV2 with the total of 20 kinds and cases. For each of those pencils
is defined its normal form. The additional classification is carried out by
means of the curve of midpoints and of the curve of isotropic focal points.
Keywords: affine plane, isotropic plane, classify, conic section pencil, normal form
- Type of paper
: Paper in journal
Title: Isogonal Transformation and the Focal Curve of a Range of
Conics
- Authors:
- Sliepčević, Ana (43680)
Journal: Rad HAZU
Number: 12
ISSN: 0351-8639
Volume: 470
Year: 1995
Pages: from 157 to 167
Number of references: 6
Language: njemački
Summary: In this paper the focal curve of a range of conics is
connected with the pole curve of four positions of a stretchable
four-barlinkage by isogonal transformation. We prove the existance of an
isogonal transformation which maps the focal curve into itself and give a
suitable construction of the pole curve by means of the isogonal map.
Keywords: focal curve, range of conics, stretchable four-bar, isogonal transformation
- Type of paper
: Paper in journal
Title: The Pencil of Conics with Two Conjugate-Imaginary
Coincident Fundamental Points in the Isotropic Plane
- Authors:
- Szirovicza, Vlasta (45794)
Journal: Rad HAZU
Number: 12
ISSN: 0351-8639
Volume: 470
Year: 1995
Pages: from 13 to 35
Number of references: 11
Language: njemački
Summary: An affine plane A2 is called an isotropic plane I2 if in A2
a metric is induced by an absolute (f,F) consisting of the line at infinity
of A2 and the point F on f. According to K. Strubecker on I2 exists a
3-parameter group B3 of isotropic motions. In this paper we give a complete
classification of pencils of conics with two conjugate-imaginary coincident
fundamental points. It is shown that 3 main types and 6 subtypes of these
pencils exist. We construct normal form with respect to the group B3 and
give an interpretation of all geometrical invariants. Finally we give a
generation of all types of pencils in a geometric way.
Keywords: geometry, isotropic plane, pencil of conics
- Type of paper
: Paper in journal
Title: Quartic Inversion in Space and Some of its Products
- Authors:
- Gorjanc, Sonja (176314)
Journal: Rad HAZU
Number: 12
ISSN: 0351-8639
Volume: 470
Year: 1995
Pages: from 187 to 199
Number of references: 11
Language: engleski
Summary: We define in this paper the transformation of the
projective space, which is done in such a way that attached points are
conjugated with respect to some quadric and incidental with the rays of
some (1,2) congruence. It has been proved that a straight line and a plane
are transformed into the space curve of order 4and quartic with a double
line, respectively. We deduce some properties of these curves and surfaces
and we show the connection of quartic inversion with pedal surfaces of
(1,2) congruences.
Keywords: inversion, quartic inversion, pedal surface of (1,2) congruence, space curve of order 4 and sort II, qurtic surface with a double line
- Type of paper
: Paper in journal
Title: M-Model of the Hyperbolic H3-Space on Moebius Plane
- Authors:
- Babić, Ivanka (70564)
Journal: Rad HAZU
ISSN: 0351-8639
Volume: 467
Year: 1994
Pages: from 67 to 75
Number of references: 7
Language: njemački
Summary: In this paper the model of H3-space is obtained by means
oforthogonal projection of H3-space onto the horysphere, then by isomorphic
mapping of horysphere onto the Moebius plane, Hesse's relation for angle
measure and Laguerre's formula for length measure is achieved in it. The
model is suitable for the constructive processing of H-geometry with
Euclidean means, especially after introducing the axial symetry.
Keywords: hyperbolic space, horysphere, Moebius-plane, model
- Type of paper
: Paper in journal
Title: Descriptive Geometry in the Hyperbolic H3-Space. Part I.
Fundamental Notions. Definitions. Position Relations.
- Authors:
- Babić, Ivanka (70564)
Journal: Rad HAZU
ISSN: 0351-8639
Volume: 470
Year: 1995
Pages: from 167 to 186
Language: njemački
Summary: In this paper the fundamental concepts of Mongean method of
projecting in H3-space, as well as positional relations are interpreted. It
has been proved that some concepts, relations and elements of the Euclidean
space have two or more counterparts inthe H3-space, and also, that there
are elements, relations, concepts and operations in H3-space that have no
counter parts in Euclidean space.
Keywords: M-model, H3-space, orthogonal projection, polarity
- Type of paper
: Paper in proceedings
Title: Curve of All Isotropic Focal Points
- Authors:
- Lapaine, Miljenko (80442)
- čurić, Vlasta (46205)
Proceedings title: Proceedings, Vol. 2
Language: engleski
Place: Tokyo, Japan
Year: 1994
Pages: from 338 to 342
Meeting: 6th International Conference on Engineering Computer Graphics and Descriptive Geometry
Held: from 08/19/94 to 08/23/94
Summary: Generallz, a conic section pencil is defined with four real
different fundamental points (type I). In the type IV the two fundamental
points coincide. Any common tangent to all curves of pencil runs through
that double point. In the type VI there are two double fundamental points.
In classifying the conic section pencils the curve of 3rd degree of all
isotropic focal points can be applied. The graphic representation of conic
section pencils can be practically performed by using a computer and
plotter. In order to represent the curve of all isotropic focal points
graphically, one needs its equation in a parametric form. In the paper this
parametric equations are developed.
Keywords: isotropic geomtry, conic section pencils classification, curve of all isotropic focal points, computer graphics
- Type of paper
: Summary in proceedings
Title: M-Model of the Hyperbolic H3-Space on Moebius Plane
- Authors:
- Babić, Ivanka (70564)
- Editors
- Sachs, Hans
Proceedings title: Kolokvij za konstruktivnu geometriju u spomen prof. dr. H. Braunera
Language: njemački
Place: Leoben, Austrija
Year: 1991
Meeting: Kolokvij za konstruktivnu geometriju
Held: from 04/28/91 to 05/03/91
Summary: In this paper the model of H3-space is obtained by means of
orthogonal projection of H3-space onto the horysphere, then by isomorphic
mapping of horysphere onto the Moebius plane, Hesse's relation for angle
measure and Laguerre's formula for length measure is achieved in it. The
model is suitable for the constructive processing of H-geometry with
Euclidean means, especially after introducing the axial symetry.
Keywords: hyperbolic space, horysphere, Moebius-plane, model
- Type of paper
: Summary in proceedings
Title: Isogonal Transformation and the Focal Curve of a Range of
Conics
- Authors:
- Sliepčević, Ana (43680)
- Editors
- Sachs, Hans
Proceedings title: Kolokvij za konstruktivnu geometriju u spomen prof. dr. H. Braunera
Language: njemački
Place: Leoben, Austrija
Year: 1991
Meeting: Kolokvij za konstruktivnu geometriju
Held: from 04/28/91 to 05/03/91
Summary: In this paper the focal curve of a range of conics is
connected with the pole curve of four positions of a stretchable
four-barlinkage by isogonal transformation. We prove the existance of an
isogonal transformation which maps the focal curve into itself and give a
suitable construction of the pole curve by means of Wthe isogonal map.
Keywords: focal curve, range of conics, stretchable four-bar, isogonal transformation
- Type of paper
: Summary in proceedings
Title: The Pencil of Conics with Two Conjugate-Imaginary
Coincident Fundamental Points in the Isotropic Plane
- Authors:
- Szirovicza, Vlasta (45794)
- Editors
- Sachs, Hans
Proceedings title: Kolokvij za konstruktivnu geometriju u spomen prof. dr. H. Braunera
Language: njemački
Place: Leoben, Austrija
Year: 1991
Meeting: Kolokvij za konstruktivnu geometriju
Held: from 04/28/91 to 05/03/91
Summary: An affine plane A2 is called an isotropic plane I2 if in A2
a metric is induced by an absolute (f,F) consisting of the line at infinity
of A2 and the point F on f. According to K. Strubecker on I2 exists a
3-parameter group B3 of isotropic motions. In this paper we give a complete
classification of pencils of conics with two conjugate-imaginary coincident
fundamental points. It is shown that 3 main types and 6 subtypes of these
pencils exist. We construct normal form with respect to the group B3 and
give an interpretation of all geometrical invariants. Finally we give a
generation of all types of pencils in a geometric way.
Keywords: geometry, isotropic plane, pencil of conics
- Type of paper
: Summary in proceedings
Title: Classification Theory of Conic Section Pencil, Type IV, of
the Isotropic Plane, II
- Authors:
- čurić, Vlasta (46205)
- Editors
- Sachs, Hans
Proceedings title: Kolokvij za konstruktivnu geometriju u spomen prof. dr. H. Braunera
Language: njemački
Place: Leoben, Austrija
Year: 1991
Meeting: Kolokvij za konstruktivnu geometriju
Held: from 04/28/91 to 05/03/91
Summary: In this paper we continue one complete classication of
pencils ofconics (Type IV) with two real and different fundamental
pointsand one double fundamental point. With respect to the 3-parameter
group B3 of isotropic motions we construct normal forms for the 13
remaining main-types and we study some subtypes. Finaly we give an
interpretation of all geometrical invariants, using the curve of midpoints
and the curve of focal points of the pencil.
Keywords: affine plane, isotropic plane, classify, conic section pencil, normal form
- Type of paper
: Summary in proceedings
Title: Special Hyperbola in I2 as Isotropic Analogue of
Equilateral Hyperbola in E2
- Authors:
- čurić, Vlasta (46205)
- Editors
- Sachs, Hans
Proceedings title: 7. ungarisch-oesterreichisches Geometrie-Symposium
Language: njemački
Year: 1992
Meeting: 7. ungarisch-oesterreichisches Geometrie-Symposium
Held: from 04/26/92 to 05/02/92
Summary: Equilateral hyperbola of Euclidean plane has got the
properties by which it is distinguished from the other conics. If these
properties should be transferred into the isotropic plane, it is to be
seen, that they of all properties characterize a special hyperbola of this
plane. It proves that the special hyperbola is an isotropic analogue of the
equilateral hyperbola in the Euclidean plane.
Keywords: isotropic plane, affine plane, Euclidean plane, conic section, special hyperbola, equilateral hyperbola
- Type of paper
: Summary in proceedings
Title: Classification Theory of Conic Section Pencil, Type VI, of
the Isotropic Plane
- Authors:
- čurić, Vlasta (46205)
- Editors
- Sachs, Hans
Proceedings title: Welttagung ueber Geometrie
Language: njemački
Year: 1995
Pages: from 29 to 29
Meeting: Welttagung ueber Geometrie
Held: from 05/14/95 to 05/19/95
Summary: In an isotropic plane I2 a metric is induced by an absolute
(f,F), consisting of the line at infinity f of I2 and a point F on f. In
this paper a complete classification of pencils of conics with two real
double fundamental points - typ VI - is given. We construct normal forms
for all main types and we study 11 subtypes. Finally we give an
interpretation of some geometrical invariants, using the curve of midpoints
and the curve of focal points of the pencil.
Keywords: affine plane, isotropic plane, classify, conic section pencil, normal form
- Type of paper
: Summary in proceedings
Title: Descriptive Geometry in the Hyperbolic H3-Space, Part I
- Authors:
- Babić, Ivanka (70564)
- Editors
- Molnar, Emil
Proceedings title: Konstruktive Geometrie
Language: njemački
Place: Budapest, Mađarska
Year: 1995
Meeting: Konstruktive Geometrie
Held: from 09/11/95 to 09/15/95
Summary: In this paper the fundamental concepts of Mongean mathod of
projecting in H3-space, as well as positional relations are interpreted. It
has been proved that some concepts, relations and elements of the Euclidean
space have two or more counterparts in the H3-space, and also, that there
are elements, relations, concepts and operations in H3-space that have no
counterparts in Euclidean space.
Keywords: M-model, H3-space, orthogonal projection, polarity
- Type of paper
: Summary in proceedings
Title: Quartic Inversion in Space and Some of its Products
- Authors:
- Gorjanc, Sonja (176314)
- Editors
- Molnar, Emil
Proceedings title: Konstruktive Geometrie
Language: engleski
Place: Budapest, Mađarska
Year: 95
Meeting: Konstruktive Geometrie
Held: from 09/11/95 to 09/19/95
Summary: Quartic inversion in projective space is defined, and some
of its products are deduced.
Keywords: inversion, quartic inversion, pedal surface of (1,2) congruence,space curve of order 4 and sort II, qurtic surface with a doubleline
- Type of paper
: M.A.
Title: Object-Oriented Model of Projective Geometry
Faculty: Tehnika fakulteta - Elektrotehnika, računalnitvo in informatika Univerza v Mariboru
Date of defense: 06/11/93
Language: hrvatski
Number of pages: 177
Summary: This thesis presents the kernel of the library of new data
types(in object-oriented programming called classes) that representbasic
concepts of projective geometry of n-dimensional real andcomplex projective
space. The classes can be divided in threegroups: primary geometric
elements (points and hyperplanes),collections of points (lists and ordered
sets) and projectivetransformations. The representation of primary elements
and thetransformations corresponds to vector and matrix representationin
algebraic treatment respectively. The functions and operatorsof the classes
are based on procedures of the algebraic model.
Keywords: projective geometry, geometric element, projective transformation, projection, computer graphics, object-oriented programming
- Type of paper
: Manuscript
Title: Classification Theory of Conic Section Pencil, Type IV, of
the Isotropic Plane, II
- Authors:
- čurić, Vlasta (46205)
- Sachs, Hans
Language: njemački
Summary: In this paper we continue one complete classication of
pencils ofconics (Type IV) with two real and different fundamental
pointsand one double fundamental point. With respect to the
3-parametergroup B3 of isotropic motions we construct normal forms for
the13 remaining main-types and we study some subtypes. Finaly wegive an
interpretation of all geometrical invariants, using thecurve of midpoints
and the curve of focal points of the pencil.
Keywords: affine plane, isotropic plane, classify, conic section pencil, normal form
Other: PRIHVAĆENO ZA TISAK U RADU HAZU
- Type of paper
: Manuscript
Title: Descriptive Geometry in the Hyperbolic H3-Space. Part II.
Metric Investigations
- Authors:
- Babić, Ivanka (70564)
Language: njemački
Summary: There are three fundamental metric problems referring to
thedescriptive geometry of H3-space constructively worked out andproved in
this paper.
The real size of the plane figure is determined throughH-rotation of
the plane belonging to the given figure around its
trace into the plane of the picture. H-perspective collineationis
established between the projection and the rotated position ofthe field of
plane points. Mutual perpendicularity of straightline and plane is
interpreted in the same way as in the Euclideanspace, while the solving
method has the characteristic od beingadjusted to the M-model.
Keywords: M-model, H3-space, H-rotation of plane, H-perspective collineation, polarity
Other: PRIHVAĆENO ZA TISAK U RADU HAZU
- Type of paper
: Manuscript
Title: Classification Theory of Conic Section Pencil, Type VI, of
the Isotropic Plane
- Authors:
- čurić, Vlasta (46205)
Language: njemački
Summary: In an isotropic plane I2 a metric is induced by an absolute
(f,F), consisting of the line at infinity f of I2 and a point F on f. In
this paper a complete classification of pencils of conics with two real
double fundamental points - typ VI - is given. We construct normal forms
for all main types and we study 11 subtypes. Finally we give an
interpretation of some geometrical invariants, using the curve of midpoints
and the curve of focal points of the pencil.
Keywords: affine plane, isotropic plane, classify, conic section pencil, normal form
Other: Prihvaćeno za tisak u međunarodnom časopisu MATHEMATICA
PANNONICA
- Type of paper
: Other
Title: Computer Application in a Classification of Conic Section
Pencils in the Isotropic Plane
- Authors:
- Lapaine, Miljenko (80442)
- čurić, Vlasta (46205)
- Sachs, Hans
Type of work: Poster na First European Congress of Mathematics, Paris 1992.
Language: engleski
Summary: In classifying of conic section pencils the application
ofcomputer and plotter can be useful. The poster brifly describesthe
mathematical basis of the own software which is developed inorder to enable
the fully automated representation of conicsection pencils. The
classification is based on the two specialcurves: the curve of all centres
of conic sections, and the curveof all isotropic fical points, so that
these curves are alsorepresented. The procedure is illustrated with some
figures ofpencils where the fundamental points are a double point and
twodifferent real points in the isotropic plane.
Keywords: isotropic geometry, classification of conic section pencils, computer application
