Skaitļošanas ģeometrija (computational geometry)

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1
Graphics (from Greek γραφικός graphikos) are visual presentations on some
surface, such as a wall, canvas, computer screen, paper, or stone to brand, inform,
illustrate, or entertain.
Photographs Drawings Line Art Graphs Diagrams Typography Symbols
Geometric designs Maps Engineering drawings Other images
2
Computer graphics are graphics created using computers and,
more generally, the representation and manipulation of graphics data
by a computer.
Glabāšana
(storage)
Relāciju DBS
Relacijuobjektu DBS
XML DBS
Sameklēšana
un izgūšana
(search and
extraction)
Vizualizācija
(visualization)
The phrase “Computer Graphics” was coined in 1960 by William
Fetter, a graphic designer for Boeing.
Early projects like the Whirlwind and SAGE Projects introduced the
display and interaction interface and introduced the light pen as an
input device.
Computer graphics may be used in the following areas:
Computational biology, Computational physics, Computer-aided
design, Computer simulation, Digital art, Education, Graphic design,
Infographics, Information visualization, Rational drug design,
Scientific visualization, Video Games, Virtual reality, Web design
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Skaitļošanas ģeometrija (computational geometry)
Computational geometry is a branch of computer science devoted to the
study of algorithms which can be stated in terms of geometry.
The main branches of computational geometry are:
1. Combinatorial computational geometry, also called algorithmic
geometry, which deals with geometric objects as discrete entities. A
groundlaying book in the subject by Preparata and Shamos dates the first
use of the term "computational geometry" in this sense by 1975.
2. Numerical computational geometry, also called machine geometry,
computer-aided geometric design (CAGD), or geometric modeling, which
deals primarily with representing real-world objects in forms suitable for
computer computations in CAD/CAM systems.
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Ģeometrijas objekti kā diskrētas vienības (geometric
objects as discrete entities)
Problēma: nepārtrauktā telpa (reālā dzīve) un diskrētā telpa (datori)
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Ģeometrijas objektu modeļi
(geometry object model)
The Open Geospatial Consortium created the Simple Features specification and
sets standards for adding spatial functionality to database systems.
The base Geometry class has subclasses for Point, Curve, Surface and Geometry
Collection. Each geometric object is associated with a Spatial Reference System,
which describes the coordinate space in which the geometric object is defined.
IBM DB2 Spatial Extender
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Conceptual class diagram of the SDO_GEOMETRY
data type
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Ģeometrisko objektu tips SDO_GEOMETRY un tā
elementi
SDO_ELEM_INFO
SDO_ SDO_ SDO_
GTYPE SRID POINT SDO_STARTING_OFFSET
SDO_ORDINATES
X1, Y1, X2, Y2, . . .
SDO_ETYPE
SDO_INTERPRETATION
create type SDO_GEOMETRY as object(
SDO_GTYPE
number,
SDO_SRID
number,
SDO_POINT
SDO_POINT_TYPE,
SDO_ELEM_INFO
SDO_ELEM_INFO_ARRAY,
SDO_ORDINATES
SDO_ORDINATE_ARRAY);
create type SDO_POINT_TYPE as object(
X number,
Y number,
Z number);
create type SDO_ELEM_INFO_ARRAY as varray(1048576) of
number;
create type SDO_ORDINATE_ARRAY as varray(1048576) of
number;
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Skaitļošanas ģeometrijas nozīmīgākās
(computational geometry problems)
problēmas
1. The convex hull or convex envelope of a set X of
points in the Euclidean plane or Euclidean space is the
smallest convex set that contains X.
2. Line segment intersection problem supplies a list
of line segments in the plane and asks us to determine
whether any two of them intersect, or cross.
3. A Delaunay triangulation for a set P of points
in a plane is a
triangulation DT(P) such
that no point in P is inside the circumcircle of any triangle
in DT(P). Delaunay triangulations maximize the minimum
angle of all the angles of the triangles in the triangulation;
they tend to avoid skinny triangles. The triangulation is
named after Boris Delaunay for his work on this topic
from 1934.
4. Closest point pair problem is a problem of
computational geometry: given n points in metric
space, find a pair of points with the smallest distance
between them.
5. The Euclidean shortest path problem: is given a
set of polyhedral obstacles in a Euclidean space, and two
points, find the shortest path between the points that does
not intersect any of the obstacles.
6. Polygon triangulation is the decomposition of a
polygonal area (simple polygon) P into a set of
triangles, i.e., finding the set of triangles with pairwise
non-intersecting interiors whose union is P.
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Vektoru un rastra grafika (vector and raster graphics)
In computer graphics, a raster graphics image or bitmap is a data structure
representing a generally rectangular grid of pixels, or points of color, viewable via a
monitor, paper, or other display medium. Raster images are stored in image files with
varying formats.
Vector graphics is the use of geometrical primitives such as points, lines, curves,
and shapes or polygon(s), which are all based on mathematical equations, to represent
images in computer graphics.
Rastra grafika
Vektoru grafika (objekti un
telpa)
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Vektoru un rastra grafika (vector and raster graphics)
Rastra grafikas attēls
Vektoru grafikas attēls
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Grafiskās sistēmas (graphical systems)
1. CAD/CAM (computer aided design/ computer aided
manufacturing) sistēmas
2. GIS (geographical information systems) sistēmas
3. Vadības informācijas sistēmas (management information systems)
4. Pētniecības informācijas sistēmas (research information systems).
12
CAD/CAM sistēmas
13
a) projektēšana (design)
b) izstrāde (manufacturing)
14
GIS sistēmas
15
Vadības informācijas sistēmas (management
information systems) ar grafikas izmantošanu
"A picture is worth a thousand words" refers to the
notion that a complex idea can be conveyed with just a
single still image. It also aptly characterizes one of the
main goals of visualization, namely making it possible to
absorb large amounts of data quickly.
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GIS companies with High Market Share
1. Autodesk – Products include Map 3D, Topobase, MapGuide and other products
that interface with its flagship AutoCAD software package.
2. Bentley Systems – Products include Bentley Map, Bentley PowerMap and other
products that interface with its flagship MicroStation software package.
3. ERDAS IMAGINE by ERDAS Inc; products include Leica Photogrammetry
Suite, ERDAS ER Mapper, and ERDAS ECW JPEG2000 SDK (ECW (file
format))are used throughout the entire mapping community (GIS, Remote
Sensing, Photogrammetry, and image compression).
4. ESRI – Products include ArcView 3.x, ArcGIS, ArcSDE, ArcIMS, ArcWeb
services and ArcGIS Server.
5. IDRISI – GIS product developed by Clark Labs, a part of Clark University.
Economical but capable, it is used for both operations and education.
6. Intergraph – Products include GeoMedia, GeoMedia Professional, GeoMedia
WebMap, and add-on products for industry sectors, as well as photogrammetry.
7. MapInfo by Pitney Bowes – Products include MapInfo Professional and
MapXtreme. integrates GIS software, data and services.
8. RegioGraph by GfK GeoMarketing; GIS software for business planning and
analyses; company also provides compatible maps and market data.
9.Smallworld – developed in Cambridge, England (Smallworld, Inc.) and
purchased by General Electric and used primarily by public utilities.
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Open source desktop GIS projects
GRASS GIS – Originally developed by the U.S.
Army Corps of Engineers, open source: a complete
GIS
SAGA GIS – System for Automated Geoscientific
Analyses- a hybrid GIS software. SAGA has a
unique Application Programming Interface (API)
and a fast growing set of geoscientifc methods,
bundled in exchangeable Module Libraries.
Quantum GIS – QGIS is an Open Source GIS that
runs on Linux, Unix, Mac OS X, and Windows.
MapWindow GIS – Free, open source GIS desktop
application and programming component.
ILWIS – ILWIS (Integrated Land and Water
Information System) integrates image, vector and
thematic data.
uDig
gvSIG – Open source GIS written in Java.
JUMP GIS / OpenJUMP – (Open) Java Unified Mapping Platform (the desktop
GIS OpenJUMP, SkyJUMP, deeJUMP and Kosmo emerged from JUMP)
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Raster graphics editors
Proprietary software
Commercial
Freeware
Ability Photopaint Digimage Arts
PhotoPerfect
ArtRage Starter Edition
ACD Canvas
Color It!
PicMaster
Artweaver
(formerly Deneba ERDAS
Pictor Paint
Brush Strokes Image Editor
Canvas)
IMAGINE
PixBuilder Photo Effectbank
Adobe Fireworks GraphicConverter Editor
FastStone Image Viewer
Adobe Photoshop Helicon Filter
Pixel image editor Fotografix
Adobe Photoshop Home/Pro
(formerly Pixel32) IrfanView
Lightroom
iPhoto
Pixelmator
Lunapic
Adobe Photoshop Konvertor
Portrait
Paint.NET
Elements
LView Pro
Professional
Picasa
Autodesk
Manga Studio
Project Dogwaffle Picnik
SketchBook Pro Microsoft Office QFX
Pixia
Aperture
Picture Manager SAI
Project Dogwaffle 1.2 Free
ArtRage
Microsoft Paint Serif Photoplus
Version
CodedColor
MST Viewer
TVPaint
StylePix
Corel Painter
Naked light
TwistedBrush Pro SView5
Corel Painter
NeoPaint
Studio
TwistedBrush Open Studio
Essentials
OpenCanvas
Unified Color
Xnview
Corel Paint Shop Photobrush
HDR PhotoStudio
Pro Photo
Photogenics
Ulead
Corel Photo-Paint Photoline
PhotoImpact
cosmigo Pro
Photo Mechanic Ultimate Paint
Motion
WinImages
Zoner Photo
Studio
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Vector graphics editors
Raven
Aviary
First
released
2009
CorelDRAW
Graphics Suite
Corel
1989
X5 (15)
Adobe Systems
1988
MX (11)
Adobe Systems
1987
CS5 (15)
Creator
Macromedia
Freehand
Adobe Illustrator
Drawit [3]
Bohemian Coding
Chittram
Inkscape
Intaglio [4]
MagicTracer
Mayura Draw [5]
Chittram
Inkscape Team
Purgatory Design
Elgorithms
Mayura Software
2010
2003
2003
2005
Microsoft Visio
Microsoft
1992
Microsoft
2007
Microsoft
Expression Design
OpenOffice.org
Draw
PhotoLine
Serif DrawPlus
sK1
Sodipodi
Swift 3D
Synfig
Xara Xtreme
Xara Xtreme LX
ZCubes
The OpenOffice.org
community
Computerinsel GmbH
Serif Europe
sK1 Team
Sodipodi
Electric Rain
Synfig Team
Xara
Xara
ZCubes
Latest version
List price (USD)
1.00.00b
Free (closed source)
$489, $189 upgrade
(includes
Photopaint)
$399, $99 upgrade
$599, $199 upgrade
€29, Free Drawit
3.7.3 (March 2009)
Lite version
1.0 (July 2010)
Free (closed source)
0.48 (Aug 2010)
Free (open source)
3.1.2
$89
1.0
$49
4.3 (Sept. 2007)
€39
$560, $350 upgrade
12.0
(Pro), $260, $130
upgrade (Standard)
4.0 (7.0.20516.9)
(closed source)
(June 2010)
2000
3.2.1 (June 2010)
Free (open source)
1995
2010
2009
2000
2000
2005
1995
2006
2006
14.01
X4
0.9.0 (May 2009)
0.34 (Feb 2004)
6.0 (June 2009)
0.61.09
3.2
0.7
2007 Dec
€59
£79.99
Free (open source)
Free (open source)
$249
Free (open source)
$79
Free (open source)
Free (closed source)
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