Discrete Collision Detection (DCD) is a fundamental task in several domains including particle-based physics simulations. Efficient DCD uses indexing structures such as Bounding Volume Hierarchy (BVH), but accelerating irregular BVH traversals demands meticulous efforts to achieve performance. Modern GPUs feature Ray Tracing (RT) architecture that provides hardware acceleration for BVH traversal and optimized drivers for BVH construction. Recent work has attempted to exploit RT architecture to accelerate DCD on spherical particles by reducing DCD to fixed-radius neighbor search. However, this reduction breaks down for particles with different radii, necessitating the use of large bounding boxes that result in a higher number of duplicate collisions and poor performance.

In this paper, we introduce a verified framework for defining and composing sparse tensor formats. We extend the ATL tensor language and scheduling framework, which formerly could only express dense tensor kernels. We define a levelized abstraction to describe per-dimension tensor formats via their encoding routines, access and iteration functions, and formal properties enforcing soundness of the sparse structures as representations of the original dense tensors. Using this abstraction, we compositionally define format-agnostic, multidimensional compression and decompression functions that are used to express the top-level soundness theorem for these abstract sparse tensor formats. We then use this soundness theorem as an adjoint-pair rewrite theorem to introduce sparse data structures and iteration into a dense tensor kernel via the existing scheduling-rewrite framework of ATL. Overall, we are able to start with a program computing over dense operands and derive a proven semantically equivalent, optimized program computing over sparse structures. We further prove a minimal set of instances of the level-format abstraction, which can be composed and passed as parameters to compression to capture a broad range of canonical, multidimensional tensor-compression formats.

Previous C-to-Rust translators run the C preprocessor cpp on their input before translation. This discards configurability, and it loses programmer-defined abstractions expressed as C macros. We present Hayroll, a modular wrapper that makes C-to-Rust translation preprocessor-aware without modifying the underlying translator. Hayroll consists of two cooperating layers. The conditional compilation translation layer uses symbolic execution to derive activation conditions for each line of the source code. It splits the program into a set of configuration-specific translation tasks that together cover every line of code. These tasks are then passed independently to the macro translation layer. The macro translation layer classifies macros, annotates macro-expanded nodes with tags, and sends the code through the underlying translator. It then reconstructs C macros as Rust functions or macros by retrieving these tags from the translator’s output. Because the layers communicate only through task partitioning and source-code annotations, the underlying translator remains a black box; no invasive changes are required. Our implementation uses C2Rust, but the design is translator-agnostic. We evaluated Hayroll on CRUST-Bench, LibmCS, and zlib. Hayroll successfully reconstructs most syntactical macros and avoids configuration explosion through symbolic execution. Hayroll's output passes the same tests as the underlying C-to-Rust transpiler. These results show that decoupled preprocessor analysis can restore configurability and abstraction to C-to-Rust translation in a practical and modular way.

Incremental Potential Contact (IPC) has emerged as a robust and unifying formulation for contact-rich physical simulation by casting elasticity and collision handling as a single energy minimization problem. Achieving high performance, however, typically requires heavily specialized implementations that hard-code assumptions about energies, primitive types, and parameterizations, creating a major barrier to extensibility. Adding new energies or alternative parameterizations often requires re-deriving first and second-order derivatives, and implementing new assembly logic for the global Hessian and gradient. This challenge is further exacerbated by collision energies, where the same energy definition is often applied to mixed parameterizations, which can lead to a combinatorial explosion of parameterization-specific derivative and assembly cases. In this paper we introduce YASPS, a framework for physical simulation that resolves this limitation by making structural relationships explicit in a differentiable representation. YASPS introduces two relational operators, JOIN and UNION, which encode connectivity and heterogeneous parameterizations directly in the symbolic computation graph. Using symbolic differentiation over these operators, YASPS automatically derives local derivatives, and determines the induced sparsity and block structure of global gradients and Hessians from the same description while avoiding any code explosion induced by mixed-parameterizations. Targeting IPC workloads, YASPS compiles the resulting symbolic graphs into GPU kernels for local energy evaluation, derivative computation, and block-sparse matrix assembly, and solves the resulting Newton systems using a GPU-based iterative solver. This approach achieves performance competitive with state-of-the-art IPC implementations while enabling new energies and parameterizations to be added through localized symbolic definitions, without hand-written derivative or assembly code.

User-schedulable languages (USLs) help programmers productively optimize programs by providing safe means of transforming them. Current USLs are designed to give programmers exactly the control they want, while automating all other concerns. However, there is no universal answer for what performance-conscious programmers want to control, how they want to control it, and what they want to automate, even in relatively narrow domains. We claim that USLs should, instead, be designed to grow. We present Exo 2, a scheduling language that enables users to define new scheduling operations externally to the compiler. By composing a set of trusted, fine-grained primitives, users can safely write their own scheduling library to build up desired automation. We identify actions (ways of modifying code), inspection (ways of interrogating code), and references (ways of pointing to code) as essential for any user-extensible USL. We fuse these ideas into a new mechanism called Cursors that enables the creation of scheduling libraries in user code. We demonstrate libraries that amortize scheduling effort across more than 80 high-performance kernels, reducing total scheduling code by an order of magnitude and delivering performance competitive with state-of-the-art implementations on three different platforms.

We present an algorithm that canonicalizes the algebraic representations of the topological semantics of machine knitting programs. Machine knitting is a staple technology of modern textile production where hundreds of mechanical needles are manipulated to form yarn into interlocking loop structures. Our semantics are defined using a variant of a monoidal category, and they closely correspond to string diagrams. We formulate our canonicalization as an Abstract Rewriting System (ARS) over words in our category, and prove that our algorithm is correct and runs in polynomial time.

FPGA technology mapping is the process of implementing a hardware design expressed in high-level HDL (hardware design language) code using the low-level, architecture-specific primitives of the target FPGA. As FPGAs become increasingly heterogeneous, achieving high performance requires hardware synthesis tools that better support mapping to complex, highly configurable primitives like digital signal processors (DSPs). Current tools support DSP mapping via handwritten special-case mapping rules, which are laborious to write, error-prone, and often overlook mapping opportunities. We introduce Lakeroad, a principled approach to technology mapping via sketch-guided program synthesis. Lakeroad leverages two techniques---architecture-independent sketch templates and semantics extraction from HDL---to provide extensible technology mapping with stronger correctness guarantees and higher coverage of mapping opportunities than state-of-the-art tools. Across representative microbenchmarks, Lakeroad produces 2--3.5× the number of optimal mappings compared to proprietary state-of-the-art tools and 6--44× the number of optimal mappings compared to popular open-source tools, while also providing correctness guarantees not given by any other tool.

One of the core promises of parametric Computer-Aided Design (CAD) is that users can easily edit their model at any point in time. However, due to the ambiguity of changing references to intermediate, updated geometry, parametric edits can lead to reference errors which are difficult to fix in practice. We claim that debugging reference errors remains challenging because CAD systems do not provide users with tools to understand where the error happened and how to fix it. To address these challenges, we prototype a graphical debugging tool, DeCAD, which helps comparing CAD model states both across operations and across edits. In a qualitative lab study, we use DeCAD as a probe to understand specific challenges that users face and what workflows they employ to overcome them. We conclude with design implications for future debugging tool developers.

The commonly used cut-and-sew garment construction process, in which 2D fabric panels are cut from sheets of fabric and assembled into 3D garments, contributes to widespread textile waste in the fashion industry. There is often a significant divide between the design of the garment and the layout of the panels. One opportunity for bridging this gap is the emerging study and practice of zero waste fashion design, which involves creating clothing designs with maximum layout efficiency. Enforcing the strict constraints of zero waste sewing is challenging, as edits to one region of the garment necessarily affect neighboring panels. Based on our formative work to understand this emerging area within fashion design, we present WasteBanned, a tool that combines CAM and CAD to help users prioritize efficient material usage, work within these zero waste constraints, and edit existing zero waste garment patterns. Our user evaluation indicates that our tool helps fashion designers edit zero waste patterns to fit different bodies and add stylistic variation, while creating highly efficient fabric layouts.

Abstract In multiplayer, first‐person shooter games like Counter‐Strike: Global Offensive (CS:GO), coordinated movement is a critical component of high‐level strategic play. However, the complexity of team coordination and the variety of conditions present in popular game maps make it impractical to author hand‐crafted movement policies for every scenario. We show that it is possible to take a data‐driven approach to creating human‐like movement controllers for CS:GO. We curate a team movement dataset comprising 123 hours of professional game play traces, and use this dataset to train a transformer‐based movement model that generates human‐like team movement for all players in a “Retakes” round of the game. Importantly, the movement prediction model is efficient. Performing inference for all players takes less than 0.5 ms per game step (amortized cost) on a single CPU core, making it plausible for use in commercial games today. Human evaluators assess that our model behaves more like humans than both commercially‐available bots and procedural movement controllers scripted by experts (16% to 59% higher by TrueSkill rating of “human‐like”). Using experiments involving in‐game bot vs. bot self‐play, we demonstrate that our model performs simple forms of teamwork, makes fewer common movement mistakes, and yields movement distributions, player lifetimes, and kill locations similar to those observed in professional CS:GO match play.

Producing efficient array code is crucial in high-performance domains like image processing and machine learning. It requires the ability to control factors like compute intensity and locality by reordering computations into different stages and granularities with respect to where they are stored. However, traditional pure, functional tensor languages struggle to do so. In a previous publication, we introduced ATL as a pure, functional tensor language capable of systematically decoupling compute and storage order via a set of high-level combinators known as reshape operators. Reshape operators are a unique functional-programming construct since they manipulate storage location in the generated code by modifying the indices that appear on the left-hand sides of storage expressions. We present a formal correctness proof for an implementation of the compilation algorithm, marking the first verification of a lowering algorithm targeting imperative loop nests from a source functional language that enables separate control of compute and storage ordering. One of the core difficulties of this proof required properly formulating the complex invariants to ensure that these storage-index remappings were well-formed. Notably, this exercise revealed a soundness bug in the original published compilation algorithm regarding the truncation reshape operators. Our fix is a new type system that captures safety conditions that were previously implicit and enables us to prove compiler correctness for well-typed source programs. We evaluate this type system and compiler implementation on a range of common programs and optimizations, including but not limited to those previously studied to demonstrate performance comparable to established compilers like Halide.

Computations in physical simulation, computer graphics, and probabilistic inference often require the differentiation of discontinuous processes due to contact, occlusion, and changes at a point in time. Popular differentiable programming languages, such as PyTorch and JAX, ignore discontinuities during differentiation. This is incorrect for parametric discontinuities —conditionals containing at least one real-valued parameter and at least one variable of integration. We introduce Potto, the first differentiable first-order programming language to soundly differentiate parametric discontinuities. We present a denotational semantics for programs and program derivatives and show the two accord. We describe the implementation of Potto, which enables separate compilation of programs. Our prototype implementation overcomes previous compile-time bottlenecks achieving an 88.1x and 441.2x speed up in compile time and a 2.5x and 7.9x speed up in runtime, respectively, on two increasingly large image stylization benchmarks. We showcase Potto by implementing a prototype differentiable renderer with separately compiled shaders.

Programming low-level controls for knitting machines is a meticulous, time-consuming task that demands specialized expertise. Recently, there has been a shift towards automatically generating low-level knitting machine programs from high-level knit representations that describe knit objects in a more intuitive, user-friendly way. Current high-level systems trade off expressivity for ease-of-use, requiring ad-hoc trapdoors to access the full space of machine capabilities, or eschewing completeness in the name of utility. Thus, advanced techniques either require ad-hoc extensions from domain experts, or are entirely unsupported. Furthermore, errors may emerge during the compilation from knit object representations to machine instructions. While the generated program may describe a valid machine control sequence, the fabricated object is topologically different from the specified input, with little recourse for understanding and fixing the issue. To address these limitations, we introduce instruction graphs , an intermediate representation capable of capturing the full range of machine knitting programs. We define a semantic mapping from instruction graphs to fenced tangles, which make them compatible with the established formal semantics for machine knitting instructions. We establish a semantics-preserving bijection between machine knittable instruction graphs and knit programs that proves three properties - upward, forward, and ordered (UFO) - are both necessary and sufficient to ensure the existence of a machine knitting program that can fabricate the fenced tangle denoted by the graph. As a proof-of-concept, we implement an instruction graph editor and compiler that allows a user to transform an instruction graph into UFO presentation and then compile it to a machine program, all while maintaining semantic equivalence. In addition, we use the UFO properties to more precisely characterize the limitations of existing compilers. This work lays the groundwork for more expressive and reliable automated knitting machine programming systems by providing a formal characterization of machine knittability.

We introduce SLANG.D, an extension to the Slang shading language that incorporates first-class automatic differentiation support. The new shading language allows us to transform a Direct3D-based path tracer to be fully differentiable with minor modifications to existing code. SLANG.D enables a shared ecosystem between machine learning frameworks and pre-existing graphics hardware API-based rendering systems, promoting the interchange of components and ideas across these two domains. Our contributions include a differentiable type system designed to ensure type safety and semantic clarity in codebases that blend differentiable and non-differentiable code, language primitives that automatically generate both forward and reverse gradient propagation methods, and a compiler architecture that generates efficient derivative propagation shader code for graphics pipelines. Our compiler supports differentiating code that involves arbitrary control-flow, dynamic dispatch, generics and higher-order differentiation, while providing developers flexible control of checkpointing and gradient aggregation strategies for best performance. Our system allows us to differentiate an existing real-time path tracer, Falcor, with minimal change to its shader code. We show that the compiler-generated derivative kernels perform as efficiently as handwritten ones. In several benchmarks, the SLANG.D code achieves significant speedup when compared to prior automatic differentiation systems.

Machine knitting is a well-established fabrication technique for complex soft objects, and both companies and researchers have developed tools for generating machine knitting patterns. However, existing representations for machine knitted objects are incomplete (do not cover the complete domain of machine knittable objects) or overly specific (do not account for symmetries and equivalences among knitting instruction sequences). This makes it difficult to define correctness in machine knitting, let alone verify the correctness of a given program or program transformation. The major contribution of this work is a formal semantics for knitout, a low-level Domain Specific Language for knitting machines. We accomplish this by using what we call the fenced tangle , which extends concepts from knot theory to allow for a mathematical definition of knitting program equivalence that matches the intuition behind knit objects. Finally, using this formal representation, we prove the correctness of a sequence of rewrite rules; and demonstrate how these rewrite rules can form the foundation for higher-level tasks such as compiling a program for a specific machine and optimizing for time/reliability, all while provably generating the same knit object under our proposed semantics. By establishing formal definitions of correctness, this work provides a strong foundation for compiling and optimizing knit programs.

High-performance kernel libraries are critical to exploiting accelerators and specialized instructions in many applications. Because compilers are difficult to extend to support diverse and rapidly-evolving hardware targets, and automatic optimization is often insufficient to guarantee state-of-the-art performance, these libraries are commonly still coded and optimized by hand, at great expense, in low-level C and assembly. To better support development of high-performance libraries for specialized hardware, we propose a new programming language, Exo, based on the principle of exocompilation: externalizing target-specific code generation support and optimization policies to user-level code. Exo allows custom hardware instructions, specialized memories, and accelerator configuration state to be defined in user libraries. It builds on the idea of user scheduling to externalize hardware mapping and optimization decisions. Schedules are defined as composable rewrites within the language, and we develop a set of effect analyses which guarantee program equivalence and memory safety through these transformations. We show that Exo enables rapid development of state-of-the-art matrix-matrix multiply and convolutional neural network kernels, for both an embedded neural accelerator and x86 with AVX-512 extensions, in a few dozen lines of code each.

We present a method to automatically compute correct gradients with respect to geometric scene parameters in neural SDF renderers. Recent physically-based differentiable rendering techniques for meshes have used edge-sampling to handle discontinuities, particularly at object silhouettes, but SDFs do not have a simple parametric form amenable to sampling. Instead, our approach builds on area-sampling techniques and develops a continuous warping function for SDFs to account for these discontinuities. Our method leverages the distance to surface encoded in an SDF and uses quadrature on sphere tracer points to compute this warping function. We further show that this can be done by subsampling the points to make the method tractable for neural SDFs. Our differentiable renderer can be used to optimize neural shapes from multi-view images and produces comparable 3D reconstructions to recent SDF-based inverse rendering methods, without the need for 2D segmentation masks to guide the geometry optimization and no volumetric approximations to the geometry.

Foundation paper piecing is a widely used quilt-making technique in which fabric pieces are sewn onto a paper guide to facilitate construction. But, designing paper pieceable quilt patterns is challenging because the sewing process imposes constraints on both the geometry and sewing order of the fabric pieces. Based on a formative study with expert quilt designers, we develop a novel sketch-based tool for designing such quilt patterns. Our tool lets designers sketch a partial design as a set of edges, which may intersect but do not have to form closed polygons, and our tool automatically completes it into a fully paper pieceable pattern. We contribute a new sketch-completion algorithm that extends the input sketched edges into a planar mesh composed of closed polygonal faces representing fabric pieces, determines a paper pieceable sewing order for the faces, and breaks complicated sketches into independently paper pieceable sections when necessary. A partial input design often admits multiple visually different completions. Thus, our tool lets designers specify completion heuristics, which are based on current quilt design practices, to control the appearance of the completed quilt. Initial user evaluations with novice and expert quilt designers suggest that our tool fits within current design workflows and greatly facilitates designing foundation paper pieceable quilts by allowing users to focus on the visual design rather than tedious constraint checks.

We present a lightweight Coq framework for optimizing tensor kernels written in a pure, functional array language. Optimizations rely on user scheduling using series of verified, semantics-preserving rewrites. Unusually for compilation targeting imperative code with arrays and nested loops, all rewrites are source-to-source within a purely functional language. Our language comprises a set of core constructs for expressing high-level computation detail and a set of what we call reshape operators, which can be derived from core constructs but trigger low-level decisions about storage patterns and ordering. We demonstrate that not only is this system capable of deriving the optimizations of existing state-of-the-art languages like Halide and generating comparably performant code, it is also able to schedule a family of useful program transformations beyond what is reachable in Halide.

Emerging research in computer graphics, inverse problems, and machine learning requires us to differentiate and optimize parametric discontinuities. These discontinuities appear in object boundaries, occlusion, contact, and sudden change over time. In many domains, such as rendering and physics simulation, we differentiate the parameters of models that are expressed as integrals over discontinuous functions. Ignoring the discontinuities during differentiation often has a significant impact on the optimization process. Previous approaches either apply specialized hand-derived solutions, smooth out the discontinuities, or rely on incorrect automatic differentiation. We propose a systematic approach to differentiating integrals with discontinuous integrands, by developing a new differentiable programming language. We introduce integration as a language primitive and account for the Dirac delta contribution from differentiating parametric discontinuities in the integrand. We formally define the language semantics and prove the correctness and closure under the differentiation, allowing the generation of gradients and higher-order derivatives. We also build a system, Teg, implementing these semantics. Our approach is widely applicable to a variety of tasks, including image stylization, fitting shader parameters, trajectory optimization, and optimizing physical designs.

Foundation paper piecing is a popular technique for constructing fabric patchwork quilts using printed paper patterns. But, the construction process imposes constraints on the geometry of the pattern and the order in which the fabric pieces are attached to the quilt. Manually designing foundation paper pieceable patterns that meet all of these constraints is challenging. In this work we mathematically formalize the foundation paper piecing process and use this formalization to develop an algorithm that can automatically check if an input pattern geometry is foundation paper pieceable. Our key insight is that we can represent the geometric pattern design using a certain type of dual hypergraph where nodes represent faces and hyperedges represent seams connecting two or more nodes. We show that determining whether the pattern is paper pieceable is equivalent to checking whether this hypergraph is acyclic, and if it is acyclic, we can apply a leaf-plucking algorithm to the hypergraph to generate viable sewing orders for the pattern geometry. We implement this algorithm in a design tool that allows quilt designers to focus on producing the geometric design of their pattern and let the tool handle the tedious task of determining whether the pattern is foundation paper pieceable.

Designing efficient, application-specialized hardware accelerators requires assessing trade-offs between a hardware module’s performance and resource requirements. To facilitate hardware design space exploration, we describe Aetherling, a system for automatically compiling data-parallel programs into statically scheduled, streaming hardware circuits. Aetherling contributes a space- and time-aware intermediate language featuring data-parallel operators that represent parallel or sequential hardware modules, and sequence data types that encode a module’s throughput by specifying when sequence elements are produced or consumed. As a result, well-typed operator composition in the space-time language corresponds to connecting hardware modules via statically scheduled, streaming interfaces.

Algorithms that create and mutate graph data structures are challenging to implement correctly. However, verifying even basic properties of low-level implementations, such as referential integrity and memory safety, remains non-trivial. Furthermore, any extension to such a data structure multiplies the complexity of its implementation, while compounding the challenges in reasoning about correctness. We take a language design approach to this problem. We propose Seam, a language for expressing local edits to graph-like data structures, based on a relational data model, and such that data integrity can be verified automatically. We present a verification method that leverages an SMT solver, and prove it sound and precise (complete modulo termination of the SMT solver). We evaluate the verification capabilities of Seam empirically, and demonstrate its applicability to a variety of examples, most notably a new class of verification tasks derived from geometric remeshing operations used in scientific simulation and computer graphics. We describe our prototype implementation of a Seam compiler that generates low-level code, which can then be integrated into larger applications. We evaluate our compiler on a sample application, and demonstrate competitive execution time, compared to hand-written implementations.

Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these functions are extremely concise, but their implementation in real code is tedious, especially when optimized for real-time performance on modern GPUs in interactive applications. In this work, we propose a new language, Opt, 1 for writing these objective functions over image- or graph-structured unknowns concisely and at a high level. Our compiler automatically transforms these specifications into state-of-the-art GPU solvers based on Gauss-Newton or Levenberg-Marquardt methods. Opt can generate different variations of the solver, so users can easily explore tradeoffs in numerical precision, matrix-free methods, and solver approaches. In our results, we implement a variety of real-world graphics and vision applications. Their energy functions are expressible in tens of lines of code and produce highly optimized GPU solver implementations. These solvers are competitive in performance with the best published hand-tuned, application-specific GPU solvers, and orders of magnitude beyond a general-purpose auto-generated solver.

Writing highly performant simulations requires a lot of human effort to optimize for an increasingly diverse set of hardware platforms, such as multi-core CPUs, GPUs, and distributed machines. Since these optimizations cut across both the design of geometric data structures and numerical linear algebra, code reusability and portability is frequently sacrificed for performance. We believe the key to make simulation programmers more productive at developing portable and performant code is to introduce new linguistic abstractions, as in rendering and image processing. In this perspective, we distill the core ideas from our two languages, Ebb and Simit, that are published in this journal.

Patterns play a central role in 2D graphic design. A critical step in the design of patterns is evaluating multiple design alternatives. Exploring these alternatives with existing tools is challenging because most tools force users to work with a single fixed representation of the pattern that encodes a specific set of geometric relationships between pattern elements. However, for most patterns, there are many different interpretations of its regularity that correspond to different design variations. The exponential nature of this variation space makes the problem of finding all variations intractable. We present a method called PATEX to characterize and efficiently identify distinct and valid pattern variations, allowing users to directly navigate the variation space. Technically, we propose a novel linear approximation to handle the complexity of the problem and efficiently enumerate suitable pattern variations under proposed element movements. We also present two pattern editing interfaces that expose the detected pattern variations as suggested edits to the user. We show a diverse collection of pattern edits and variations created with PATEX. The results from our user study indicate that our suggested variations can be useful and inspirational for typical pattern editing tasks.

Designing programming environments for physical simulation is challenging because simulations rely on diverse algorithms and geometric domains. These challenges are compounded when we try to run efficiently on heterogeneous parallel architectures. We present Ebb, a Domain-Specific Language (DSL) for simulation, that runs efficiently on both CPUs and GPUs. Unlike previous DSLs, Ebb uses a three-layer architecture to separate (1) simulation code, (2) definition of data structures for geometric domains, and (3) runtimes supporting parallel architectures. Different geometric domains are implemented as libraries that use a common, unified, relational data model. By structuring the simulation framework in this way, programmers implementing simulations can focus on the physics and algorithms for each simulation without worrying about their implementation on parallel computers. Because the geometric domain libraries are all implemented using a common runtime based on relations, new geometric domains can be added as needed, without specifying the details of memory management, mapping to different parallel architectures, or having to expand the runtime’s interface. We evaluate Ebb by comparing it to several widely used simulations, demonstrating comparable performance to handwritten GPU code where available, and surpassing existing CPU performance optimizations by up to 9 × when no GPU code exists.

Good icons are legible, and legible icons are scale-dependent. Experienced icon designers use a set of common strategies to create legible scale variations of icons, but executing those strategies with current tools can be challenging. In part, this is because many apparent objects, like hairlines formed by negative space, are not explicitly represented as objects in vector drawings. We present transient widgets as a mechanism for selecting and manipulating apparent objects that is independent of the underlying drawing representation. We implement transient widgets using a constraint-based editing framework; demonstrate their utility for performing the kinds of edits most common when producing scale variations of icons; and report qualitative feedback on the system from professional icon designers.

This paper presents a method for computing topology changes for triangle meshes in an interactive geometric modeling environment. Most triangle meshes in practice do not exhibit desirable geometric properties, so we develop a solution that is independent of standard assumptions and robust to geometric errors. Specifically, we provide the first method for topology change applicable to arbitrary non-solid, non-manifold, non-closed, self-intersecting surfaces. We prove that this new method for topology change produces the expected conventional results when applied to solid (closed, manifold, non-self-intersecting) surfaces---that is, we prove a backwards-compatibility property relative to prior work. Beyond solid surfaces, we present empirical evidence that our method remains tolerant to a variety of surface aberrations through the incorporation of a novel error correction scheme. Finally, we demonstrate how topology change applied to non-solid objects enables wholly new and useful behaviors.

We propose a novel representation of motion data and control that enables characters with both highly agile responses to user input and natural handling of arbitrary external disturbances. The representation organizes motion data as samples in a high dimensional generalization of a vector field we call a 'motion field'. Our runtime motion synthesis mechanism freely 'flows' in the motion field and is capable of creating novel and natural motions that are highly-responsive to the real time user input, and generally not explicitly specified in the data.

Abstract We present a new system for robustly performing Boolean operations on linear, 3D polyhedra. Our system is exact, meaning that all internal numeric predicates are exactly decided in the sense of exact geometric computation. Our BSP‐tree based system is 16‐28× faster at performing iterative computations than CGAL's Nef Polyhedra based system, the current best practice in robust Boolean operations, while being only twice as slow as the non‐robust modeler Maya. Meanwhile, we achieve a much smaller substrate of geometric subroutines than previous work, comprised of only 4 predicates, a convex polygon constructor, and a convex polygon splitting routine. The use of a BSP‐tree based Boolean algorithm atop this substrate allows us to explicitly handle all geometric degeneracies without treating a large number of cases.