Here, we provide a complete morphological description of mammalian heart tube formation based on detailed imaging of a temporally dense collection of mouse embryonic hearts. In particular, the study of early heart development in mammals remains a challenging problem due to imaging limitations and complexity. The high morphological variability in mammalian embryos hinders the quantitative analysis of organogenesis. Understanding organ morphogenesis requires a precise geometrical description of the tissues involved in the process. Best Paper Award (1st place) at SGP 2022.TinyAD is available to the community as an open source library. This enables not only fast prototyping of new research ideas, but also improves replicability of existing algorithms in geometry processing. By showcasing compact implementations of methods from parametrization, deformation, and direction field design, we demonstrate how TinyAD lowers the barrier to exploring non-linear optimization techniques.

TinyAD provides the basic ingredients to quickly implement first and second order Newton-style solvers, allowing for flexible adjustment of both problem formulations and solver details.

Its simplicity enables easy integration no restrictions on, e.g., looping and branching are imposed. We introduce TinyAD: a lightweight C++ library that automatically computes gradients and Hessians, in particular of sparse problems, by differentiating small (tiny) sub-problems. We show that for many geometric problems, in particular on meshes, the simplest form of forward-mode automatic differentiation is not only the most flexible, but also actually the most efficient choice. limiting the set of supported language features, imposing restrictions on a program's control flow, incurring a significant run time overhead, or making it hard to exploit sparsity patterns common in geometry processing. Automatic differentiation techniques address this problem, but can introduce a diverse set of obstacles themselves, e.g. Deriving and manually implementing gradients and Hessians is both time-consuming and error-prone. However, when experimenting with different problem formulations or when prototyping new algorithms, a major practical obstacle is the need to figure out derivatives of objective functions, especially when second-order derivatives are required. Non-linear optimization is essential to many areas of geometry processing research. We run an extensive evaluation on the Thingi10K dataset to demonstrate that our method outperforms state-of-the-art algorithms, even inexact ones like QuickCSG, by orders of magnitude. With a careful implementation and a work-stealing multi-threading architecture, we are able to compute Boolean operations between meshes with millions of triangles at interactive rates. By leveraging a number of early-out termination criteria, we can avoid the generation and inspection of regions that do not contribute to the output. Instead, our algorithm performs an adaptive recursive subdivision of the scene’s bounding box while generating and tracking all required data on the fly. High performance is achieved by avoiding the (pre-)construction of a global acceleration structure. Reliability and robustness emerge from a formulation of the algorithm via generalized winding numbers and mesh arrangements.

Exactness is guaranteed by using a plane-based representation for the input meshes along with recently introduced homogeneous integer coordinates. We present a novel method, EMBER, to compute Boolean operations on polygon meshes which is exact, reliable, and highly performant at the same time. Boolean operators are an essential tool in a wide range of geometry processing and CAD/CAM tasks.

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