A 4D marine data model: Design and application in ice monitoring

Hamre, Torill; Mughal, Khalid A.; Jacob, Anita

doi:10.1080/01490419709388100

Cited by 8 publications

(5 citation statements)

References 6 publications

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“…For instance, space can be modelled using primitive instancing (Foley et al, 1995;Kada, 2007), constructive solid geometry (Requicha & Voelcker, 1977) or various boundary representation approaches (Muller & Preparata, 1978;Guibas & Stolfi, 1985;Lienhardt, 1994), among others. Time can be modelled on the basis of snapshots (Armstrong, 1988;Hamre, Mughal & Jacob, 1997), space-time composites (Peucker & Chrisman, 1975;Chrisman, 1983), events (Worboys, 1992;Peuquet, 1994;Peuquet & Duan, 1995), or a combination of all of these (Abiteboul & Hull, 1987;Worboys, Hearnshaw & Maguire, 1990;Worboys, 1994;Wachowicz & Healy, 1994). Scale is usually modelled based on independent datasets at each scale (Buttenfield & DeLotto, 1989;Friis-Christensen & Jensen, 2003;Meijers, 2011b), although approaches to combine them into single datasets (Gröger et al, 2012) or to create progressive and continuous representations also exist (Ballard, 1981;Jones & Abraham, 1986;Günther, 1988;Van Oosterom, 1990;Filho et al, 1995;Rigaux & Scholl, 1995;Plümer & Gröger, 1997;Van Oosterom, 2005).…”

Section: Higher-dimensional Modelling Of Space Time and Scalementioning

confidence: 99%

Visualising higher-dimensional space-time and space-scale objects as projections to ℝ³

Ohori

Ledoux

Stoter

2017

PeerJ Computer Science

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Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object’s shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from ℝ4to ℝ3. We present three projections that we believe are particularly intuitive for this purpose: (i) a simple ‘long axis’ projection that puts 3D objects side by side; (ii) the well-known orthographic and perspective projections; and (iii) a projection to a 3-sphere (S3) followed by a stereographic projection to ℝ3, which results in an inwards-outwards fourth axis. Our focus is in using these projections from ℝ4to ℝ3, but they are formulated from ℝnto ℝn−1so as to be easily extensible and to incorporate other non-spatial characteristics. We present a prototype interactive visualiser that applies these projections from 4D to 3D in real-time using the programmable pipeline and compute shaders of the Metal graphics API.

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Section: Higher-dimensional Modelling Of Space Time and Scalementioning

confidence: 99%

Visualising higher-dimensional space-time and space-scale objects as projections to ℝ³

Ohori

Ledoux

Stoter

2017

PeerJ Computer Science

View full text Add to dashboard Cite

show abstract

“…Time can be modelled on the basis of snapshots (Armstrong, 1988;Hamre et al, 1997), space-time composites (Peucker and Chrisman, 1975;Chrisman, 1983), events (Worboys, 1992;Peuquet, 1994;Peuquet and Duan, 1995), or a combination of all of these (Abiteboul and Hull, 1987;Worboys et al, 1990;Worboys, 1994;Wachowicz and Healy, 1994). Scale is usually modelled based on independent datasets at each scale (Buttenfield and DeLotto, 1989;Friis-Christensen and Jensen, 2003;Meijers, 2011b), although approaches to combine them into single datasets (Gröger et al, 2012) or to create progressive and continuous representations also exist (Ballard, 1981;Jones and Abraham, 1986;Günther, 1988;van Oosterom, 1990;Filho et al, 1995;Rigaux and Scholl, 1995;Plümer and Gröger, 1997;van Oosterom, 2005).…”

Section: Computer Sciencementioning

confidence: 99%

Peer Review #3 of "Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3 (v0.1)"

2017

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Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object's shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from \(\mathbb{R}^4\) to \(\mathbb{R}^3\). We present three projections that we believe are particularly intuitive for this purpose: (i) a simple `long axis' projection that puts 3D objects side by side; (ii) the well-known orthographic and perspective projections; and (iii) a projection to a 3-sphere (\(S^3\)) followed by a stereographic projection to \(\mathbb{R}^3\), which results in an inwards-outwards fourth axis. Our focus is in using these projections from \(\mathbb{R}^4\) to \(\mathbb{R}^3\), but they are formulated from \(\mathbb{R}^n\) to \(\mathbb{R}^{n-1}\) so as to be easily extensible and to incorporate other non-spatial characteristics. We present a prototype interactive visualiser that applies these projections from 4D to 3D in real-time using the programmable pipeline and compute shaders of the Metal graphics API.

show abstract

Section: Computer Sciencementioning

confidence: 99%

Peer Review #1 of "Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3 (v0.2)"

2017

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Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object's shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from \(\mathbb{R}^4\) to \(\mathbb{R}^3\). We present three projections that we believe are particularly intuitive for this purpose: (i) a simple `long axis' projection that puts 3D objects side by side; (ii) the well-known orthographic and perspective projections; and (iii) a projection to a 3-sphere (\(S^3\)) followed by a stereographic projection to \(\mathbb{R}^3\), which results in an inwards-outwards fourth axis. Our focus is in using these projections from \(\mathbb{R}^4\) to \(\mathbb{R}^3\), but they are formulated from \(\mathbb{R}^n\) to \(\mathbb{R}^{n-1}\) so as to be easily extensible and to incorporate other non-spatial characteristics. We present a prototype interactive visualiser that applies these projections from 4D to 3D in real-time using the programmable pipeline and compute shaders of the Metal graphics API.

show abstract

A 4D marine data model: Design and application in ice monitoring

Cited by 8 publications

References 6 publications

Visualising higher-dimensional space-time and space-scale objects as projections to ℝ³

Visualising higher-dimensional space-time and space-scale objects as projections to ℝ³

Peer Review #3 of "Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3 (v0.1)"

Peer Review #1 of "Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3 (v0.2)"

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