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Penrose: from mathematical notation to beautiful diagrams

Authors:

Jonathan Aldrich,

Joshua Sunshine,

Keenan CraneAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 39, Issue 4

Article No.: 144, Pages 144:1 - 144:16

https://doi.org/10.1145/3386569.3392375

Published: 12 August 2020 Publication History

Abstract

We introduce a system called Penrose for creating mathematical diagrams. Its basic functionality is to translate abstract statements written in familiar math-like notation into one or more possible visual representations. Rather than rely on a fixed library of visualization tools, the visual representation is user-defined in a constraint-based specification language; diagrams are then generated automatically via constrained numerical optimization. The system is user-extensible to many domains of mathematics, and is fast enough for iterative design exploration. In contrast to tools that specify diagrams via direct manipulation or low-level graphics programming, Penrose enables rapid creation and exploration of diagrams that faithfully preserve the underlying mathematical meaning. We demonstrate the effectiveness and generality of the system by showing how it can be used to illustrate a diverse set of concepts from mathematics and computer graphics.

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Cited By

Bohrer R(2024)Programming Language Case Studies Can Be DeepElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.405.4405(56-79)Online publication date: 10-Jul-2024
https://doi.org/10.4204/EPTCS.405.4
Li YKamil SCrane KJacobson AGingold Y(2024)IMESH: A DSL for Mesh ProcessingACM Transactions on Graphics10.1145/366218143:5(1-17)Online publication date: 25-Jun-2024
https://dl.acm.org/doi/10.1145/3662181
Sassen JSchumacher HRumpf MCrane K(2024)Repulsive ShellsACM Transactions on Graphics10.1145/365817443:4(1-22)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658174
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Index Terms

Penrose: from mathematical notation to beautiful diagrams
1. Human-centered computing
  1. Visualization
    1. Visualization systems and tools
      1. Visualization toolkits
2. Software and its engineering
  1. Software notations and tools
    1. Context specific languages
      1. Domain specific languages

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 39, Issue 4

August 2020

1732 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3386569

Editor:
Szymon Rusinkiewicz
Princeton University

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Copyright © 2020 Owner/Author.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 August 2020

Published in TOG Volume 39, Issue 4

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Cited By

Bohrer R(2024)Programming Language Case Studies Can Be DeepElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.405.4405(56-79)Online publication date: 10-Jul-2024
https://doi.org/10.4204/EPTCS.405.4
Li YKamil SCrane KJacobson AGingold Y(2024)IMESH: A DSL for Mesh ProcessingACM Transactions on Graphics10.1145/366218143:5(1-17)Online publication date: 25-Jun-2024
https://dl.acm.org/doi/10.1145/3662181
Sassen JSchumacher HRumpf MCrane K(2024)Repulsive ShellsACM Transactions on Graphics10.1145/365817443:4(1-22)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658174
Ni WEstep SHarriman HKoedinger KSunshine JJoyner DKim MWang XXia M(2024)Edgeworth: Efficient and Scalable Authoring of Visual Thinking ActivitiesProceedings of the Eleventh ACM Conference on Learning @ Scale10.1145/3657604.3662034(98-109)Online publication date: 9-Jul-2024
https://dl.acm.org/doi/10.1145/3657604.3662034
Pollock JMei CHuang GEvans EJackson DSatyanarayan A(2024)Bluefish: Composing Diagrams with Declarative RelationsProceedings of the 37th Annual ACM Symposium on User Interface Software and Technology10.1145/3654777.3676465(1-21)Online publication date: 13-Oct-2024
https://dl.acm.org/doi/10.1145/3654777.3676465
Minarčík JEstep SNi WCrane K(2024)Minkowski Penalties: Robust Differentiable Constraint Enforcement for Vector GraphicsACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657495(1-12)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657495
Mei YJones BCascaval DMankoff JVouga ESchulz A(2024)FabHacks: Transform Everyday Objects into Home Hacks Leveraging a Solver-aided DSLProceedings of the 9th ACM Symposium on Computational Fabrication10.1145/3639473.3665788(1-16)Online publication date: 7-Jul-2024
https://dl.acm.org/doi/10.1145/3639473.3665788
Yang JMcNutt ABattle L(2024)Considering Visualization Example Galleries2024 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)10.1109/VL/HCC60511.2024.00043(329-343)Online publication date: 2-Sep-2024
https://doi.org/10.1109/VL/HCC60511.2024.00043
Edson AFabry AKohar ABondaryk LPhillips E(2024)Addressing Design Challenges When Integrating Machine Learning with a Digital Annotation System to Examine Student Proportional ReasoningDigital Experiences in Mathematics Education10.1007/s40751-024-00163-8Online publication date: 16-Oct-2024
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Ni WEstep SHarriman HMinarčík JSunshine J(2024)Codifying Visual RepresentationsDiagrammatic Representation and Inference10.1007/978-3-031-71291-3_37(454-457)Online publication date: 9-Sep-2024
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