Paper Info
Title
Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3.
Abstract
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 objectu0027s shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional spacetime and space-scale objects can be visualised as projections from R4 to R3. We present three projections that we believe are particularly intuitive for this purpose: (i) a simple u0027long axisu0027 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 R4 to R3, but they are formulated from Rn to Rn-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.
Year
Venue
Field
2017
PeerJ Computer Science
Graphics,Oblique projection,Space time,Computer vision,Planar projection,Orthographic projection,Biology,Computer graphics (images),Stereographic projection,Artificial intelligence,Shader,Parallel projection
DocType
Volume
Citations 
Journal
3
0
PageRank 
References 
Authors
0.34
26
3
Name
Order
Citations
PageRank
Ken Arroyo Ohori1468.14
Hugo Ledoux223122.27
Jantien Stoter317519.35