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1. Planar and poly-arc Lombardi drawings

   https://doi.org/https://doi.org/10.20382/jocg.v9i1a11  

   Duncan, Christian A.; Eppstein, David; Goodrich, Michael T.; Kobourov, Stephen G.; Löffler, Maarten; Nöllenburg, Martin (January 2018, Journal of computational geometry)

   In Lombardi drawings of graphs, edges are represented as circular arcs and the edges incident on vertices have perfect angular resolution. It is known that not every planar graph has a planar Lombardi drawing. We give an example of a planar 3-tree that has no planar Lombardi drawing and we show that all outerpaths do have a planar Lombardi drawing. Further, we show that there are graphs that do not even have any Lombardi drawing at all. With this in mind, we generalize the notion of Lombardi drawings to that of (smooth) k-Lombardi drawings, in which each edge may be drawn as a (differentiable) sequence of k circular arcs; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We further investigate related topics connecting planarity and Lombardi drawings. 

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2. Phenotyping Cognitive Impairment using Graphomotor and Latency Features in Digital Clock Drawing Test*

   https://doi.org/10.1109/EMBC44109.2020.9176469  

   Davoudi, Anis; Dion, Catherine; Amini, Shawna; Libon, David J.; Tighe, Patrick J.; Price, Catherine C.; Rashidi, Parisa (July 2020, 2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC))

   null (Ed.)

   The Clock Drawing Test, where the participant is asked to draw a clock from memory and copy a model clock, is widely used for screening of cognitive impairment. The digital version of the clock test, the digital clock drawing test (dCDT), employs accelerometer and pressure sensors of a digital pen to capture time and pressure information from a participant's performance in a granular digital format. While visual features of the clock drawing test have previously been studied, little is known about the relationship between demographic and cognitive impairment characteristics with dCDT latency and graphomotor features. Here, we examine dCDT feature clusters with respect to sociodemographic and cognitive impairment outcomes. Our results show that the clusters are not significantly different in terms of age and gender, but did significantly differ in terms of education, Mini-Mental State Exam scores, and cognitive impairment diagnoses.This study shows that features extracted from digital clock drawings can provide important information regarding cognitive reserve and cognitive impairments. 

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3. Lombardi drawings of knots and links

   https://doi.org/10.1007/978-3-319-73915-1_10  

   Kindermann, P; Kobourov, S; Loeffler, M; Noellenburg, M; Schulz, A.; Vogtenhuber, B (January 2019, Journal of computational geometry)

   Knot and link diagrams are projections of one or more 3-dimensional simple closed curves into lR2, such that no more than two points project to the same point in lR2. These diagrams are drawings of 4-regular plane multigraphs. Knots are typically smooth curves in lR3, so their projections should be smooth curves in lR2 with good continuity and large crossing angles: exactly the properties of Lombardi graph drawings (defned by circular-arc edges and perfect angular resolution). We show that several knots do not allow crossing-minimal plane Lombardi drawings. On the other hand, we identify a large class of 4-regular plane multigraphs that do have plane Lombardi drawings. We then study two relaxations of Lombardi drawings and show that every knot admits a crossing-minimal plane 2-Lombardi drawing (where edges are composed of two circular arcs). Further, every knot is near-Lombardi, that is, it can be drawn as a plane Lombardi drawing when relaxing the angular resolution requirement by an arbitrary small angular offset ε, while maintaining a 180◦ angle between opposite edges. 

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4. Equitable Math Instruction: visualizing a Vision of High-Quality, Equitable Mathematics Instruction

   Baker, K; Schwartz, C; Whitehead, A; Adefope, O (January 2025, NCSM journal of mathematics education leadership)

   In this article, we overview a professional learn- ing task that involves drawing one’s vision for high-quality, equitable mathematics instruction (HQEMI). The task is part of the ongoing work of a statewide research practice partnership that supports a shared vision of mathematics across the state K–12 system. Our work of HQEMI is rooted in the development of Munter’s (2014) four dimensions for visions of high-quality mathematics instruction (VHQMI): the role of the teacher, classroom discourse, mathematical tasks, and student engagement. The first three dimensions are particularly useful in the work of the drawing task. In this article, we share an overview of the drawing task, its implementa- tion with educators, and sample drawings, de- tailing how personal drawings were made visible across participants and the conversations result- ing from viewing and reflecting on one another’s drawings. These conversations helped surface disparities in notions of ideal mathematics in- struction and provided space for negotiation of shared meaning. We provide themes and over- arching considerations from these conversations to highlight discussions that might be elicited through this task in future iterations. Finally, we provide recommendations for implementing the task and consider how the task might be adapt- ed for others’ contexts to support professional learning about and development of a shared vision for mathematics. 

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5. Learning a Style Space for Interactive Line Drawing Synthesis from Animated 3D Models

   Wang, Z.; Wang, T.; Dorsey, J. (October 2022, PG2022 Short Papers, Posters, and Work-in-Progress Papers)

   Umetani, N.; Wojtan, C.; Vouga, E. (Ed.)

   Most non-photorealistic rendering (NPR) methods for line drawing synthesis operate on a static shape. They are not tailored to process animated 3D models due to extensive per-frame parameter tuning needed to achieve the intended look and natural transition. This paper introduces a framework for interactive line drawing synthesis from animated 3D models based on a learned style space for drawing representation and interpolation. We refer to style as the relationship between stroke placement in a line drawing and its corresponding geometric properties. Starting from a given sequence of an animated 3D character, a user creates drawings for a set of keyframes. Our system embeds the raster drawings into a latent style space after they are disentangled from the underlying geometry. By traversing the latent space, our system enables a smooth transition between the input keyframes. The user may also edit, add, or remove the keyframes interactively, similar to a typical keyframe-based workflow. We implement our system with deep neural networks trained on synthetic line drawings produced by a combination of NPR methods. Our drawing-specific supervision and optimization-based embedding mechanism allow generalization from NPR line drawings to user-created drawings during run time. Experiments show that our approach generates high-quality line drawing animations while allowing interactive control of the drawing style across frames. 

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