Related papers: Interactive 4-D Visualization of Stereographic Ima…
The Hopf fibration mapping circles on a 3-sphere to points on a 2-sphere is well known to topologists. While the 2-sphere is embedded in 3-space, four-dimensional Euclidean space is needed to visualize the 3-sphere. Visualizing objects in…
This paper is concerned with the use of the stereographic projection to map the points of a design on the sphere in three dimensions onto a two-dimensional stereogram. Details of the projection and its attendant stereogram are given and the…
In this work, we present an adaptation of the classical stereographic projection, originally formulated for the sphere, now considering the context of the ellipsoid and the elliptic paraboloid. We begin by constructing the stereographic…
A method to visualize polytopes in a four dimensional euclidian space $(x,y,z,w)$ is proposed. A polytope is sliced by multiple hyperplanes that are parallel each other and separated by uniform intervals. Since the hyperplanes are…
We present a technique for Stereoscopic Cylindrical Screen (SCS) Projection of a world scene to a 360-degree canvas for viewing with 3D glasses. To optimize the rendering pipeline, we render the scene to four cubemaps, before sampling…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…
This paper introduces a method of calculating and rendering shapes in a non-Euclidean 2D space. In order to achieve this, we developed a physics and graphics engine that uses hyperbolic trigonometry to calculate and subsequently render the…
We present a method for real-time stereo scene capture and remote VR visualization that allows a human operator to freely move their head and thus intuitively control their perspective during teleoperation. The stereo camera is mounted on a…
This paper develops a simple and fast method to reconstruct reality from stereoscopic images. We bring together ideas from robust optical flow techniques, morphing deformations and lightfield 3D rendering in order to create unsupervised…
Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds.…
We construct a number of sculptures, each based on a geometric design native to the three-dimensional sphere. Using stereographic projection we transfer the design from the three-sphere to ordinary Euclidean space. All of the sculptures are…
Directionality in a holographic screen may be useful for projecting images to be seen in complete horizontal parallax. The continuous sequence of views from an object may be transferred from the object and enlarged at the screen giving the…
Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of…
This research pioneers a method for generating immersive worlds, drawing inspiration from elements of vintage adventure games like Myst and employing modern text-to-image models. We explore the intricate conversion of 2D panoramas into 3D…
We propose a new system to visualize depth-dependent patterns and images on solid objects with complex geometry using multiple projectors. The system, despite consisting of conventional passive LCD projectors, is able to project different…
Three dimensional images having continuous horizontal parallax were developed by wavelength enconding of view followed by a natural decoding process of projection onto a diffractive screen. It allows for the direct criation of "holoimages"…
We present a telepresence system based on a custom-made simulated holographic display that produces a full 3D model of the remote participants using commodity depth sensors. Our display is composed of a video projector and a quadrangular…
It is shown that each quadrangulation of the 2-torus by the Cartesian product of two cycles can be geometrically realized in (Euclidean) 4-space without hidden symmetries---that is, so that each combinatorial cellular automorphism of the…
Data visualizations summarize high-dimensional distributions in two or three dimensions. Dimensionality reduction entails a loss of information, and what is preserved differs between methods. Existing methods preserve the local or the…
We present a method to project a hypercube of arbitrary dimension on the plane, in such a way as to preserve, as well as possible, the distribution of distances between vertices. The method relies on a Montecarlo optimization procedure that…