Related papers: Sculptures in S^3
We analyze human poses and motion by introducing three sequences of easily calculated surface descriptors that are invariant under reparametrizations and Euclidean transformations. These descriptors are obtained by associating to each…
A transformation based on mean curvature is introduced which morphs triangulated surfaces into round spheres.
We follow our general model in Ref. [3] and analyze the formation of retinotopic projections for the biologically relevant situation of spherical geometries. To this end we elaborate both a linear and a nonlinear synergetic analysis which…
A model invariant under a supersymmetric extension of the rotation group O(3) is mapped, using a stereographic projection, from the spherical surface S2 to two dimensional Euclidean space. The resulting model does not have a manifest local…
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 describe decomposition formulas for rotations of $R^3$ and $R^4$ that have special properties with respect to stereographic projection. We use the lower dimensional decomposition to analyze stereographic projections of great circles in…
We show how to convert models of complex systems such as 2D cellular automata into a 3D printed object. Our method takes into account the limitations inherent to 3D printing processes and materials. Our approach automates the greater part…
Texture is an essential property of physical objects that affects aesthetics, usability, and functionality. However, designing and applying textures to 3D objects with existing tools remains difficult and time-consuming; it requires…
3D objects (artefacts) are made to fulfill functions. Designing an object often starts with defining a list of functionalities that it should provide, also known as functional requirements. Today, the design of 3D object models is still a…
Deformable object manipulation remains a key challenge in developing autonomous robotic systems that can be successfully deployed in real-world scenarios. In this work, we explore the challenges of deformable object manipulation through the…
Tomographic volumetric 3D printing offers layer free, rapid fabrication of objects with high design freedom, but is limited to relatively small curing volumes because of the optical constraints imposed by an assumed need for telecentricity.…
Creating realistic 3D head assets for virtual characters that match a precise artistic vision remains labor-intensive. We present a novel framework that streamlines this process by providing artists with intuitive control over generated 3D…
This paper introduces a method for learning to generate line drawings from 3D models. Our architecture incorporates a differentiable module operating on geometric features of the 3D model, and an image-based module operating on view-based…
We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology,…
This paper develops an explicit and implementable framework for constructing spherical designs by lifting point sets from tight fusion frames. By combining existing ingredients, we obtain, in every dimension, explicit spherical $5$-designs…
We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with $m_1 = 3$.
Recent works on text-to-3d generation show that using only 2D diffusion supervision for 3D generation tends to produce results with inconsistent appearances (e.g., faces on the back view) and inaccurate shapes (e.g., animals with extra…
We introduce a new way to implicitly represent swept volumes in 3D. We first implicitize the base volume and then apply the time-dependent rigid transformation to build an implicit representation of the swept volume. This way, we build a…
n this paper, we consider a method of constructing flat surfaces based on Ribaucour transformations in the sphere 3-space. By applying the theory to the flat torus, we obtain a families of complete flat surfaces in $S^3$ which are…
In this paper, on envelopes created by sphere families in Euclidean 3-space, all four basic problems (existence problem, representation problem, problem on the number of envelopes, problem on relationships of definitions) are solved.