Theoretical and Linguistic Methods for Describing Straight Lines View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1985

AUTHORS

Reyer Brons

ABSTRACT

Two distinct approaches exist for the generation of a straight line in an arbitrary direction on a lattice, structural algorithms and conditional algorithms. A survey of these approaches is included in this paper.Structural algorithms are of great theoretical value. From numbertheory the Farey-series can be used for directions on a lattice with a rational slope. With continued fractions it is also possible to approximate irrational numbers.Knowing these properties it is possible to determine the set of all lines corresponding to a given chaincode for a segment of a line. This is useful for the estimation of properties of a line like length, slope and intercept. Research of this kind is related to pattern analysis and picture processing.The structural algorithm can be presented by linguistic methods, for instance a context-free programmed grammar and a TOL-grammar, a variant of the Lindenmayer grammar with the important property that in each derivation each relevant symboltype in a string is rewritten at the same time by the same rule.The principle of the conditional algorithm is more practical: given two points that determine the line, connected points on the lattice with minimal distance to the real line have to be selected. This method is very important for plotters and computer graphics displays.The conditional algorithm can be presented by linguistic methods too, by using a programmed grammar with a tail. The tail has a bookkeeping function. Consequentially the grammar is context-sensitive.Structural and conditional methods both generate lines satisfying the chord property, which is a conditional property. A structural property of a digitized straight line is spacing the least occurring type of chainelement as uniformly as possible. It is shown that this can be built into a conditional method. So an integration between both methods is achieved.Finally some remarks on progress in the science of line drawing are made. More... »

PAGES

19-57

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-84574-1_1

DOI

http://dx.doi.org/10.1007/978-3-642-84574-1_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1047964277


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Information and Computing Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0801", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Artificial Intelligence and Image Processing", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Economic Affairs and Planning, Catholic University of Nijmegen, 6500 HC, Nijmegen, The Netherlands", 
          "id": "http://www.grid.ac/institutes/grid.5590.9", 
          "name": [
            "Department of Economic Affairs and Planning, Catholic University of Nijmegen, 6500 HC, Nijmegen, The Netherlands"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Brons", 
        "givenName": "Reyer", 
        "id": "sg:person.013033257462.30", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013033257462.30"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1985", 
    "datePublishedReg": "1985-01-01", 
    "description": "Two distinct approaches exist for the generation of a straight line in an arbitrary direction on a lattice, structural algorithms and conditional algorithms. A survey of these approaches is included in this paper.Structural algorithms are of great theoretical value. From numbertheory the Farey-series can be used for directions on a lattice with a rational slope. With continued fractions it is also possible to approximate irrational numbers.Knowing these properties it is possible to determine the set of all lines corresponding to a given chaincode for a segment of a line. This is useful for the estimation of properties of a line like length, slope and intercept. Research of this kind is related to pattern analysis and picture processing.The structural algorithm can be presented by linguistic methods, for instance a context-free programmed grammar and a TOL-grammar, a variant of the Lindenmayer grammar with the important property that in each derivation each relevant symboltype in a string is rewritten at the same time by the same rule.The principle of the conditional algorithm is more practical: given two points that determine the line, connected points on the lattice with minimal distance to the real line have to be selected. This method is very important for plotters and computer graphics displays.The conditional algorithm can be presented by linguistic methods too, by using a programmed grammar with a tail. The tail has a bookkeeping function. Consequentially the grammar is context-sensitive.Structural and conditional methods both generate lines satisfying the chord property, which is a conditional property. A structural property of a digitized straight line is spacing the least occurring type of chainelement as uniformly as possible. It is shown that this can be built into a conditional method. So an integration between both methods is achieved.Finally some remarks on progress in the science of line drawing are made.", 
    "editor": [
      {
        "familyName": "Earnshaw", 
        "givenName": "Rae A.", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-642-84574-1_1", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-540-54397-8", 
        "978-3-642-84574-1"
      ], 
      "name": "Fundamental Algorithms for Computer Graphics", 
      "type": "Book"
    }, 
    "keywords": [
      "conditional algorithm", 
      "structural algorithm", 
      "computer graphics displays", 
      "linguistic methods", 
      "algorithm", 
      "graphic display", 
      "great theoretical value", 
      "Lindenmayer grammars", 
      "chord property", 
      "picture processing", 
      "straight line", 
      "grammar", 
      "rational slope", 
      "line drawings", 
      "chaincode", 
      "conditional properties", 
      "important properties", 
      "same time", 
      "minimal distance", 
      "same rules", 
      "distinct approaches", 
      "method", 
      "processing", 
      "estimation of properties", 
      "plotter", 
      "set", 
      "rules", 
      "integration", 
      "instances", 
      "estimation", 
      "display", 
      "arbitrary direction", 
      "conditional method", 
      "strings", 
      "point", 
      "kind", 
      "drawings", 
      "irrational numbers", 
      "generation", 
      "direction", 
      "principles", 
      "science", 
      "research", 
      "real line", 
      "distance", 
      "number", 
      "derivation", 
      "time", 
      "lines", 
      "progress", 
      "variants", 
      "segments", 
      "function", 
      "types", 
      "analysis", 
      "properties", 
      "remarks", 
      "structural properties", 
      "survey", 
      "values", 
      "lattice", 
      "length", 
      "theoretical values", 
      "tail", 
      "slope", 
      "fraction", 
      "approach", 
      "paper", 
      "numbertheory", 
      "Farey-series", 
      "TOL-grammar", 
      "relevant symboltype", 
      "symboltype", 
      "type of chainelement", 
      "chainelement"
    ], 
    "name": "Theoretical and Linguistic Methods for Describing Straight Lines", 
    "pagination": "19-57", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1047964277"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-642-84574-1_1"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-642-84574-1_1", 
      "https://app.dimensions.ai/details/publication/pub.1047964277"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2021-12-01T20:07", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/chapter/chapter_368.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-642-84574-1_1"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-84574-1_1'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-84574-1_1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-84574-1_1'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-84574-1_1'


 

This table displays all metadata directly associated to this object as RDF triples.

135 TRIPLES      23 PREDICATES      101 URIs      94 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-642-84574-1_1 schema:about anzsrc-for:08
2 anzsrc-for:0801
3 schema:author N01b0027b7c1a4d3c9223a7be8a58117f
4 schema:datePublished 1985
5 schema:datePublishedReg 1985-01-01
6 schema:description Two distinct approaches exist for the generation of a straight line in an arbitrary direction on a lattice, structural algorithms and conditional algorithms. A survey of these approaches is included in this paper.Structural algorithms are of great theoretical value. From numbertheory the Farey-series can be used for directions on a lattice with a rational slope. With continued fractions it is also possible to approximate irrational numbers.Knowing these properties it is possible to determine the set of all lines corresponding to a given chaincode for a segment of a line. This is useful for the estimation of properties of a line like length, slope and intercept. Research of this kind is related to pattern analysis and picture processing.The structural algorithm can be presented by linguistic methods, for instance a context-free programmed grammar and a TOL-grammar, a variant of the Lindenmayer grammar with the important property that in each derivation each relevant symboltype in a string is rewritten at the same time by the same rule.The principle of the conditional algorithm is more practical: given two points that determine the line, connected points on the lattice with minimal distance to the real line have to be selected. This method is very important for plotters and computer graphics displays.The conditional algorithm can be presented by linguistic methods too, by using a programmed grammar with a tail. The tail has a bookkeeping function. Consequentially the grammar is context-sensitive.Structural and conditional methods both generate lines satisfying the chord property, which is a conditional property. A structural property of a digitized straight line is spacing the least occurring type of chainelement as uniformly as possible. It is shown that this can be built into a conditional method. So an integration between both methods is achieved.Finally some remarks on progress in the science of line drawing are made.
7 schema:editor N073223dcc07043569f8aa967e727de7a
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf N466ffbb73e644870a9808b4a0241235c
12 schema:keywords Farey-series
13 Lindenmayer grammars
14 TOL-grammar
15 algorithm
16 analysis
17 approach
18 arbitrary direction
19 chaincode
20 chainelement
21 chord property
22 computer graphics displays
23 conditional algorithm
24 conditional method
25 conditional properties
26 derivation
27 direction
28 display
29 distance
30 distinct approaches
31 drawings
32 estimation
33 estimation of properties
34 fraction
35 function
36 generation
37 grammar
38 graphic display
39 great theoretical value
40 important properties
41 instances
42 integration
43 irrational numbers
44 kind
45 lattice
46 length
47 line drawings
48 lines
49 linguistic methods
50 method
51 minimal distance
52 number
53 numbertheory
54 paper
55 picture processing
56 plotter
57 point
58 principles
59 processing
60 progress
61 properties
62 rational slope
63 real line
64 relevant symboltype
65 remarks
66 research
67 rules
68 same rules
69 same time
70 science
71 segments
72 set
73 slope
74 straight line
75 strings
76 structural algorithm
77 structural properties
78 survey
79 symboltype
80 tail
81 theoretical values
82 time
83 type of chainelement
84 types
85 values
86 variants
87 schema:name Theoretical and Linguistic Methods for Describing Straight Lines
88 schema:pagination 19-57
89 schema:productId N67e1d9d08ff74badaf419edf6c075ea1
90 N8c2b46747339410d86b8f47f567a0fd7
91 schema:publisher N6dc42525d3a44f5194e882687ef6aa25
92 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047964277
93 https://doi.org/10.1007/978-3-642-84574-1_1
94 schema:sdDatePublished 2021-12-01T20:07
95 schema:sdLicense https://scigraph.springernature.com/explorer/license/
96 schema:sdPublisher N3b48b61afff64b41ab56d9069fedde09
97 schema:url https://doi.org/10.1007/978-3-642-84574-1_1
98 sgo:license sg:explorer/license/
99 sgo:sdDataset chapters
100 rdf:type schema:Chapter
101 N01b0027b7c1a4d3c9223a7be8a58117f rdf:first sg:person.013033257462.30
102 rdf:rest rdf:nil
103 N073223dcc07043569f8aa967e727de7a rdf:first N0ed7701413df4c4e9676dede762b62a2
104 rdf:rest rdf:nil
105 N0ed7701413df4c4e9676dede762b62a2 schema:familyName Earnshaw
106 schema:givenName Rae A.
107 rdf:type schema:Person
108 N3b48b61afff64b41ab56d9069fedde09 schema:name Springer Nature - SN SciGraph project
109 rdf:type schema:Organization
110 N466ffbb73e644870a9808b4a0241235c schema:isbn 978-3-540-54397-8
111 978-3-642-84574-1
112 schema:name Fundamental Algorithms for Computer Graphics
113 rdf:type schema:Book
114 N67e1d9d08ff74badaf419edf6c075ea1 schema:name doi
115 schema:value 10.1007/978-3-642-84574-1_1
116 rdf:type schema:PropertyValue
117 N6dc42525d3a44f5194e882687ef6aa25 schema:name Springer Nature
118 rdf:type schema:Organisation
119 N8c2b46747339410d86b8f47f567a0fd7 schema:name dimensions_id
120 schema:value pub.1047964277
121 rdf:type schema:PropertyValue
122 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
123 schema:name Information and Computing Sciences
124 rdf:type schema:DefinedTerm
125 anzsrc-for:0801 schema:inDefinedTermSet anzsrc-for:
126 schema:name Artificial Intelligence and Image Processing
127 rdf:type schema:DefinedTerm
128 sg:person.013033257462.30 schema:affiliation grid-institutes:grid.5590.9
129 schema:familyName Brons
130 schema:givenName Reyer
131 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013033257462.30
132 rdf:type schema:Person
133 grid-institutes:grid.5590.9 schema:alternateName Department of Economic Affairs and Planning, Catholic University of Nijmegen, 6500 HC, Nijmegen, The Netherlands
134 schema:name Department of Economic Affairs and Planning, Catholic University of Nijmegen, 6500 HC, Nijmegen, The Netherlands
135 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...