Three-dimensional curve drawing in Augmented Reality (AR) enables users to create 3D curves that fit within the real-world scene. It has applications in 3D design, sculpting, and animation. However, the task complexity increases when the desirable path for the curve is obstructed by the physical environment or by what the camera can see. For example, it is difficult to draw a curve that wraps around an object or scales to out-of-reach places. We propose WARPY, an environment-aware 3D curve drawing tool for mobile AR. Our system enables users to draw freeform curves from a distance in AR by combining 2D-to-3D sketch inference with geometric proxies. Geometric Proxies can be obtained via 3D scanning or from a list of pre-defined primitives. WARPY also provides a multi-view mode to enable users to sketch a curve from multiple viewpoints, which is useful if the target curve cannot fit within the camera's field of view. We conducted two user studies and found that WARPY can be a viable tool to help users create complex and large curves in AR.

Abstract Procedural modeling allows for an automatic generation of large amounts of similar assets, but there is limited control over the generated output. We address this problem by introducing Automatic Differentiable Procedural Modeling (ADPM). The forward procedural model generates a final editable model. The user modifies the output interactively, and the modifications are transferred back to the procedural model as its parameters by solving an inverse procedural modeling problem. We present an auto‐differentiable representation of the procedural model that significantly accelerates optimization. In ADPM the procedural model is always available, all changes are non‐destructive, and the user can interactively model the 3D object while keeping the procedural representation. ADPM provides the user with precise control over the resulting model comparable to non‐procedural interactive modeling. ADPM is node‐based, and it generates hierarchical 3D scene geometry converted to a differentiable computational graph. Our formulation focuses on the differentiability of high‐level primitives and bounding volumes of components of the procedural model rather than the detailed mesh geometry. Although this high‐level formulation limits the expressiveness of user edits, it allows for efficient derivative computation and enables interactivity. We designed a new optimizer to solve for inverse procedural modeling. It can detect that an edit is under‐determined and has degrees of freedom. Leveraging cheap derivative evaluation, it can explore the region of optimality of edits and suggest various configurations, all of which achieve the requested edit differently. We show our system's efficiency on several examples, and we validate it by a user study.

Procedural modeling has produced amazing results, yet fundamental issues such as controllability and limited user guidance persist. We introduce a novel procedural model called PICO (Procedural Iterative Constrained Optimizer) and PICO-Graph that is the underlying procedural model designed with optimization in mind. The key novelty of PICO is that it enables the exploration of generative designs by combining both user and environmental constraints into a single framework by using optimization without the need to write procedural rules. The PICO-Graph procedural model consists of a set of geometry generating operations and a set of axioms connected in a directed cyclic graph. The forward generation is initiated by a set of axioms that use the connections to send coordinate systems and geometric objects through the PICO-Graph, which in turn generates more objects. This allows for fast generation of complex and varied geometries. Moreover, we combine PICO-Graph with efficient optimization that allows for quick exploration of the generated models and the generation of variants. The user defines the rules, the axioms, and the set of constraints; for example, whether an existing object should be supported by the generated model, whether symmetries exist, whether the object should spin, etc. PICO then generates a class of geometric models and optimizes them so that they fulfill the constraints. The generation and the optimization in our implementation provides interactive user control during model execution providing continuous feedback. For example, the user can sketch the constraints and guide the geometry to meet these specified goals. We show PICO on a variety of examples such as the generation of procedural chairs with multiple supports, generation of support structures for 3D printing, generation of spinning objects, or generation of procedural terrains matching a given input. Our framework could be used as a component in a larger design workflow; its strongest application is in the early rapid ideation and prototyping phases.

Structural analysis is a foundational statics concept for students majoring in mechanical engineering, civil engineering, and engineering technology, among others. However, the mathematical emphasis of a typical statics courses lies in algebraic calculations, matrices, vectors, and sometimes deemphasizes student understanding of the behavior of the overall structure as a system, focusing instead on its individual elements. This study investigates students' conceptual understanding of forces acting and reacting in a truss structure as well as their corresponding representations in the form of Free Body Diagrams (FBDs). Our findings suggest that students primarily demonstrated partially coherent answers suggesting that they may hold some misconceptions about truss behavior. The most prevalent error was that students failed to account for the mutual (equal and opposite) forces between connected bodies that were separated for analysis. Based on our findings we propose the design of a learning experience that combines principles of embodied learning with the affordances of visuohaptic simulations to address students' misconceptions.

We explored the affordances of using visuo-haptic simulations to improve conceptual understanding and representational competence of the concept of friction. Visuohaptic simulations are computer-based simulations that encode mathematical and physical models of certain phenomena and provide visual and tactile feedback. Users can see the simulation and feel the friction with their hand by using a special device connected to a computer. We hypothesized that visual and haptic feedback together can help students to improve learning of friction. We recruited 24 engineering technology students with a previous experience in at least one physics course, and we examined their reasoning and understanding about statics concepts before and after engaging with visuo-haptic simulations. Our instructional approach included four steps: 1) lecture about friction, 2) pretest, 3) laboratory session, and 4) posttest. The laboratory session consisted of a pre-training session, guided learning materials based on a constructivist framework, and use of the friction visuo-haptic simulation. We report students' prior conceptions of statics concepts, ways in which they interacted and reasoned with each of the different pedagogical tools, and compared reasoning processes, explanations and learning gains. Our results suggest that the visuo-haptic simulation helped students refine their explanations and increased the coherence between their verbal explanation and mathematical representation.

We introduce Skippy, a novel algorithm for 3D interactive curve modeling from a single view. While positing curves in space can be a tedious task, our rapid sketching algorithm allows users to draw curves in and around existing geometry in a controllable manner. The key insight behind our system is to automatically infer the 3D curve coordinates by enumerating a large set of potential curve trajectories. More specifically, we partition 2D strokes into continuous segments that land both on and off the geometry, duplicating segments that could be placed in front or behind, to form a directed graph. We use distance fields to estimate 3D coordinates for our curve segments and solve for an optimally smooth path that follows the curvature of the scene geometry while avoiding intersections. Using our curve design framework we present a collection of novel editing operations allowing artists to rapidly explore and refine the combinatorial space of solutions. Furthermore, we include the quick placement of transient geometry to aid in guiding the 3D curve. Finally we demonstrate our interactive design curve system on a variety of applications including geometric modeling, and camera motion path planning.

Interactions play a key role in understanding objects and scenes for both virtual and real-world agents. We introduce a new general representation for proximal interactions among physical objects that is agnostic to the type of objects or interaction involved. The representation is based on tracking particles on one of the participating objects and then observing them with sensors appropriately placed in the interaction volume or on the interaction surfaces. We show how to factorize these interaction descriptors and project them into a particular participating object so as to obtain a new functional descriptor for that object, its interaction landscape , capturing its observed use in a spatiotemporal framework. Interaction landscapes are independent of the particular interaction and capture subtle dynamic effects in how objects move and behave when in functional use. Our method relates objects based on their function, establishes correspondences between shapes based on functional key points and regions, and retrieves peer and partner objects with respect to an interaction.