M. Wimmer

M. Wimmer

Computing the Pfaffian of a skew-symmetric matrix is a problem that arises in various fields of physics. Both computing the Pfaffian and a related problem, computing the canonical form of a skew-symmetric matrix under unitary congruence, can be solved easily once the skew-symmetric matrix has been reduced to skew-symmetric tridiagonal form. We develop efficient numerical methods for computing this tridiagonal form based on Gauss transformations, using a skew-symmetric, blocked form of the Parlett-Reid algorithm, or based on unitary transformations, using block Householder transformations and Givens rotations, that are applicable to dense and banded matrices, respectively. We also give a complete and fully optimized implementation of these algorithms in Fortran, and also provide Python, Matlab and Mathematica implementations for convenience. Finally, we apply these methods to compute the topological charge of a class D nanowire, and show numerically the equivalence of definitions based on the Hamiltonian and the scattering matrix.

S. Rasoulzadeh, M. Wimmer, P. Stauss et al.

We present Strokes2Surface, an offline geometry reconstruction pipeline that recovers well-connected curve networks from imprecise 4D sketches to bridge concept design and digital modeling stages in architectural design. The input to our pipeline consists of 3D strokes' polyline vertices and their timestamps as the 4th dimension, along with additional metadata recorded throughout sketching. Inspired by architectural sketching practices, our pipeline combines a classifier and two clustering models to achieve its goal. First, with a set of extracted hand-engineered features from the sketch, the classifier recognizes the type of individual strokes between those depicting boundaries (Shape strokes) and those depicting enclosed areas (Scribble strokes). Next, the two clustering models parse strokes of each type into distinct groups, each representing an individual edge or face of the intended architectural object. Curve networks are then formed through topology recovery of consolidated Shape clusters and surfaced using Scribble clusters guiding the cycle discovery. Our evaluation is threefold: We confirm the usability of the Strokes2Surface pipeline in architectural design use cases via a user study, we validate our choice of features via statistical analysis and ablation studies on our collected dataset, and we compare our outputs against a range of reconstructions computed using alternative methods.

S. Rasoulzadeh, M. Bank, I. Kovacic et al.

Recent advances in 3D generative models have shown promising results but often fall short in capturing the complexity of architectural geometries and topologies and fine geometric details at high resolutions. To tackle this, we present ArchComplete, a two-stage voxel-based 3D generative pipeline consisting of a vector-quantised model, whose composition is modelled with an autoregressive transformer for generating coarse shapes, followed by a hierarchical upsampling strategy for further enrichment with fine structures and details. Key to our pipeline is (i) learning a contextually rich codebook of local patch embeddings, optimised alongside a 2.5D perceptual loss that captures global spatial correspondence of projections onto three axis-aligned orthogonal planes, and (ii) redefining upsampling as a set of conditional diffusion models learning from a hierarchy of randomly cropped coarse-to-fine local volumetric patches. Trained on our introduced dataset of 3D house models with fully modelled exterior and interior, ArchComplete autoregressively generates models at the resolution of $64^{3}$ and progressively refines them up to $512^{3}$, with voxel sizes as small as $ \approx 9\text{cm}$. ArchComplete solves a variety of tasks, including genetic interpolation and variation, unconditional synthesis, shape and plan-drawing completion, as well as geometric detailisation, while achieving state-of-the-art performance in quality, diversity, and computational efficiency.