Related papers: Grassmannian Shape Representations for Aerodynamic…

Reconstructing 3D representations from 2D inputs is a fundamental task in computer vision and graphics, serving as a cornerstone for understanding and interacting with the physical world. While traditional methods achieve high fidelity,…

Modeling the time-varying 3D appearance of plants during growth poses unique challenges: unlike most dynamic scenes, plants continuously generate new geometry as they expand, branch, and differentiate. Existing dynamic scene representations…

We propose a data-driven 3D shape design method that can learn a generative model from a corpus of existing designs, and use this model to produce a wide range of new designs. The approach learns an encoding of the samples in the training…

Representing 3D shape is a fundamental problem in artificial intelligence, which has numerous applications within computer vision and graphics. One avenue that has recently begun to be explored is the use of latent representations of…

In this work, we perform a systematic comparison of the effectiveness and efficiency of generative and non-generative models in constructing design spaces for novel and efficient design exploration and shape optimization. We apply these…

Deep generative models of 3D shapes have received a great deal of research interest. Yet, almost all of them generate discrete shape representations, such as voxels, point clouds, and polygon meshes. We present the first 3D generative model…

The real Grassmannian is both a projective variety (via Pl\"ucker coordinates) and an affine variety (via orthogonal projections). We connect these two representations, and we develop the commutative algebra of the latter variety. We…

The inverse approach is computationally efficient in aerodynamic design as the desired target performance distribution is prespecified. However, it has some significant limitations that prevent it from achieving full efficiency. First, the…

With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions…

A vortex-lattice method for wing aerodynamics that uses nonlinear airfoil data is presented. Two applications of this procedure are presented: Direct Design of a Flying Wing and Inverse Identification from wind tunnel measurements with…

Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…

Data-driven generative 3D face models are used to compactly encode facial shape data into meaningful parametric representations. A desirable property of these models is their ability to effectively decouple natural sources of variation, in…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

The evolution of 3D visual content calls for innovative methods for modelling shapes based on their intended usage, function and role in a complex scenario. Even if different attempts have been done in this direction, shape modelling still…

Deep implicit surfaces excel at modeling generic shapes but do not always capture the regularities present in manufactured objects, which is something simple geometric primitives are particularly good at. In this paper, we propose a…

We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying…

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains…

Affine deformations serve as basic examples in the continuum mechanics of deformable 3-dimensional bodies (referred as homogeneous deformations). They preserve parallelism and are often used as an approximation to general deformations.…

While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more…

Computational fluid dynamics plays a key role in the design process across many industries. Recently, there has been increasing interest in data-driven methods, in order to exploit the large volume of data generated by such computations.…