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  • GPU + Objetos matemáticos

    Graficando en el GPU con estándares Web

    Resumen (Abstract)

    Las herramientas más comunes que existen actualmente para graficar objetos matemáticos realizan sus cálculos en el CPU; pero no tienen porqué hacerlo, cada punto a dibujar normalmente es independiente del resto, por lo que sus cálculos bien pueden hacerse en el GPU mediante cómputo en paralelo.

    En este trabajo se plantea una aproximación al uso del GPU para la graficación de expresiones del álgebra implícitas usando estándares Web como WebGL 2.0 y WebGPU.

    TAGs: #GPU, #graficación, #educación, #visualización_científica, #procesamiento_en_paralelo

  • Materias beneficiadas

    • Geometría analítica
    • Cálculo diferencial
    • Cálculo integral
    • Cálculo multivaluado
    • Probabilidad
    • Teoría de grafos
  • Objetos matemáticos de interés

    Los objetos matemáticos que normalmente se utilizan para realizar gráficas diversas son:

    En el plano

    • Nubes de puntos
    • Gráfica de funciones de R -> R
    • Gráfica de funciones implícitas de dos incógnitas
    • Curvas paramétricas en R²
    • Curvas de nivel aplanadas
    • Grafos en el plano
    • Fractales planos

    En el espacio

    • Nubes de puntos
    • Gráfica de funciones de R² -> R
    • Gráfica de funciones implícitas de tres incógnitas
    • Curvas y superficies paramétricas en R³
    • Curvas de nivel sobre una superficie
    • Superficies de nivel
    • Intersecciones de superficies
    • Grafos en el espacio
    • Fractales en el espacio
  • Introduction - “The Setup”

    [In field X, we still don’t understand Y & Z.]

    Write a summary of the question(s) you are trying to answer.
    What is the state of the world before your research came along?
    Also, answer the harsh but important question: Who cares?

    In writing this, you can start general, but make sure clearly define the “before” state of the world’s knowledge for the specific area this paper is addressing.

  • Materials & Methods - “The Characters”

    [We have here method A, B, and our new method C.]

    You have established the core question(s) of your research. Now introduce the tools you are going to use to understand it.

  • Results

    What happened (objectively)?

    Do not interpret, simply state the facts.

    Let’s be honest: the first thing most of us do when skimming a paper is look at the figures. If your key results can be presented in figures, then start with that, and structure your paper around that.

  • Discussion

    Results are objective, but science isn’t about listing data, it’s about extracting meaning from what we observe.

    What do your results tell you about the core problem you were investigating?

  • Conclusion

    Bring it back to the big picture. How do your results fit into the current body of knowledge?

    Most importantly, how can these results help you ask better questions?

  • References

    We don’t have bibliography support yet, but we do have “named links” so you can refer to specific links by name rather than retyping it each time.

    “Black holes are cool.” [1], and DNA is cool too [2]. But black holes are still cool, though not “absolute zero” cool [1].

  • Intro - Assertive Statement 1

    Here you can expand on your introduction. To guide your writing, title this card with assertive statements:
    Instead of “Problem Description”, be direct: “The problem is that X doesn’t do Y.”

  • Intro - Assertive Statement 2

  • Intro - Assertive Statement 3

  • Method A

    More details on the method, experiment design, etc.

    Remember that these are cards, so you can drag and drop them to rearrange if necessary.

  • Method B

    More details on the method, experiment design, etc.

  • Method C

    More details on the method, experiment design, etc.

    If you need a checklist to make sure you address all points, go ahead:

  • Key Result

    You can add figures if you’d like:

  • Remember these are cards so you can rearrange your results at will.
    Any subcards will follow.

  • Conclusion (further detail)

    Expand on your conclusion summary, and add more details to it.

  • List

    Or you can simply list your references here:

    1. some ref
    2. some other ref. Numbering fixes itself automatically.
    3. A third ref.
  • Introduction

  • [You can write your actual paper here in this column. Then choosing “Export column 5” to Word or Markdown will help you move it to your final platform.]

  • Methods

  • Method A

  • Method B…

  • Method C

  • Results

  • Final text for results goes here

  • Other results

  • Conclusion

  • Final text for conclusion goes here

  • in as many

  • cards as you like.

  • References

  • Some reference by J. Doe

  • Some other reference

  • You can keep notes & comments here.

  • Some other note. For example:
    #Xusheng, make sure you include the voltage you used.”

    (the # syntax makes it easier to search for & filter comments directed at a specific person).

  • Notes on this reference.

{"cards":[{"_id":"5b1b72970763230d27aa3484","treeId":"5b1b72970763230d27aa3483","seq":22985618,"position":1,"parentId":null,"content":"## GPU + Objetos matemáticos\n### Graficando en el GPU con estándares Web\n\n\n#### Resumen (Abstract)\nLas herramientas más comunes que existen actualmente para graficar objetos matemáticos realizan sus cálculos en el CPU; pero no tienen porqué hacerlo, cada punto a dibujar normalmente es independiente del resto, por lo que sus cálculos bien pueden hacerse en el GPU mediante cómputo en paralelo. \n\nEn este trabajo se plantea una aproximación al uso del GPU para la graficación de expresiones del álgebra implícitas usando estándares Web como WebGL 2.0 y WebGPU. \n\n\n*TAGs: #GPU, #graficación, #educación, #visualización_científica, #procesamiento_en_paralelo*"},{"_id":"5b1b72970763230d27aa3485","treeId":"5b1b72970763230d27aa3483","seq":22985633,"position":0.25,"parentId":"5b1b72970763230d27aa3484","content":"# Materias beneficiadas\n\n* Geometría analítica\n* Cálculo diferencial \n* Cálculo integral\n* Cálculo multivaluado\n* Probabilidad\n* Teoría de grafos"},{"_id":"5b1b72970763230d27aa3486","treeId":"5b1b72970763230d27aa3483","seq":13802244,"position":1,"parentId":"5b1b72970763230d27aa3485","content":"## Introduction - \"The Setup\"\n### [In field X, we still don't understand Y & Z.]\n\nWrite a summary of *the question(s) you are trying to answer*.\nWhat is the state of the world before your research came along?\nAlso, answer the harsh but important question: *Who cares*?\n\nIn writing this, you can start general, but make sure clearly define the \"before\" state of the world's knowledge for the *specific area* this paper is addressing."},{"_id":"5b1b72970763230d27aa3487","treeId":"5b1b72970763230d27aa3483","seq":13802245,"position":1,"parentId":"5b1b72970763230d27aa3486","content":"### Intro - Assertive Statement 1\n\nHere you can expand on your introduction. To guide your writing, title this card with assertive statements:\nInstead of \"Problem Description\", be direct: \"The problem is that X doesn't do Y.\""},{"_id":"5b1b72970763230d27aa3488","treeId":"5b1b72970763230d27aa3483","seq":13802246,"position":1,"parentId":"5b1b72970763230d27aa3487","content":"# Introduction"},{"_id":"5b1b72970763230d27aa3489","treeId":"5b1b72970763230d27aa3483","seq":13802247,"position":2,"parentId":"5b1b72970763230d27aa3487","content":"[You can write your actual paper here in this column. Then choosing \"Export column 5\" to Word or Markdown will help you move it to your final platform.]"},{"_id":"5b1b72970763230d27aa348a","treeId":"5b1b72970763230d27aa3483","seq":13802248,"position":1,"parentId":"5b1b72970763230d27aa3489","content":"You can keep notes & comments here."},{"_id":"5b1b72970763230d27aa348b","treeId":"5b1b72970763230d27aa3483","seq":13802249,"position":3,"parentId":"5b1b72970763230d27aa3487","content":"..."},{"_id":"5b1b72970763230d27aa348c","treeId":"5b1b72970763230d27aa3483","seq":13802250,"position":4,"parentId":"5b1b72970763230d27aa3487","content":"..."},{"_id":"5b1b72970763230d27aa348d","treeId":"5b1b72970763230d27aa3483","seq":13802251,"position":2,"parentId":"5b1b72970763230d27aa3486","content":"### Intro - Assertive Statement 2"},{"_id":"5b1b72970763230d27aa348e","treeId":"5b1b72970763230d27aa3483","seq":13802252,"position":1,"parentId":"5b1b72970763230d27aa348d","content":"..."},{"_id":"5b1b72970763230d27aa348f","treeId":"5b1b72970763230d27aa3483","seq":13802253,"position":2,"parentId":"5b1b72970763230d27aa348d","content":"..."},{"_id":"5b1b72970763230d27aa3490","treeId":"5b1b72970763230d27aa3483","seq":13802254,"position":3,"parentId":"5b1b72970763230d27aa3486","content":"### Intro - Assertive Statement 3"},{"_id":"5b1b72970763230d27aa3491","treeId":"5b1b72970763230d27aa3483","seq":13802255,"position":1,"parentId":"5b1b72970763230d27aa3490","content":"..."},{"_id":"5b1b72970763230d27aa3492","treeId":"5b1b72970763230d27aa3483","seq":13802256,"position":2,"parentId":"5b1b72970763230d27aa3490","content":"..."},{"_id":"5b1b72970763230d27aa3493","treeId":"5b1b72970763230d27aa3483","seq":13802257,"position":2,"parentId":"5b1b72970763230d27aa3485","content":"## Materials & Methods - \"The Characters\"\n### [We have here method A, B, and our new method C.]\nYou have established the core question(s) of your research. Now introduce the tools you are going to use to understand it."},{"_id":"5b1b72970763230d27aa3494","treeId":"5b1b72970763230d27aa3483","seq":13802258,"position":1,"parentId":"5b1b72970763230d27aa3493","content":"## Method A\nMore details on the method, experiment design, etc.\n\nRemember that these are cards, so you can drag and drop them to rearrange if necessary."},{"_id":"5b1b72970763230d27aa3495","treeId":"5b1b72970763230d27aa3483","seq":13802259,"position":1,"parentId":"5b1b72970763230d27aa3494","content":"# Methods"},{"_id":"5b1b72970763230d27aa3496","treeId":"5b1b72970763230d27aa3483","seq":13802260,"position":2,"parentId":"5b1b72970763230d27aa3494","content":"### Method A"},{"_id":"5b1b72970763230d27aa3497","treeId":"5b1b72970763230d27aa3483","seq":13802261,"position":1,"parentId":"5b1b72970763230d27aa3496","content":"Some other note. For example:\n\" #Xusheng, make sure you include the voltage you used.\"\n\n(the # syntax makes it easier to search for & filter comments directed at a specific person)."},{"_id":"5b1b72970763230d27aa3498","treeId":"5b1b72970763230d27aa3483","seq":13802262,"position":3,"parentId":"5b1b72970763230d27aa3494","content":"..."},{"_id":"5b1b72970763230d27aa3499","treeId":"5b1b72970763230d27aa3483","seq":13802263,"position":4,"parentId":"5b1b72970763230d27aa3494","content":"..."},{"_id":"5b1b72970763230d27aa349a","treeId":"5b1b72970763230d27aa3483","seq":13802264,"position":2,"parentId":"5b1b72970763230d27aa3493","content":"## Method B\nMore details on the method, experiment design, etc."},{"_id":"5b1b72970763230d27aa349b","treeId":"5b1b72970763230d27aa3483","seq":13802265,"position":1,"parentId":"5b1b72970763230d27aa349a","content":"### Method B..."},{"_id":"5b1b72970763230d27aa349c","treeId":"5b1b72970763230d27aa3483","seq":13802266,"position":2,"parentId":"5b1b72970763230d27aa349a","content":"..."},{"_id":"5b1b72970763230d27aa349d","treeId":"5b1b72970763230d27aa3483","seq":13802267,"position":3,"parentId":"5b1b72970763230d27aa349a","content":"..."},{"_id":"5b1b72970763230d27aa349e","treeId":"5b1b72970763230d27aa3483","seq":13802268,"position":3,"parentId":"5b1b72970763230d27aa3493","content":"## Method C\nMore details on the method, experiment design, etc.\n\nIf you need a checklist to make sure you address all points, go ahead:\n[ ] e.g. \"Mention pH of the setup\"\n[ ] What temperature?\n[ ] For how long?"},{"_id":"5b1b72970763230d27aa349f","treeId":"5b1b72970763230d27aa3483","seq":13802269,"position":1,"parentId":"5b1b72970763230d27aa349e","content":"### Method C"},{"_id":"5b1b72970763230d27aa34a0","treeId":"5b1b72970763230d27aa3483","seq":13802270,"position":2,"parentId":"5b1b72970763230d27aa349e","content":"..."},{"_id":"5b1b72970763230d27aa34a1","treeId":"5b1b72970763230d27aa3483","seq":13802271,"position":3,"parentId":"5b1b72970763230d27aa349e","content":"..."},{"_id":"5b1b72970763230d27aa34a2","treeId":"5b1b72970763230d27aa3483","seq":13802272,"position":3,"parentId":"5b1b72970763230d27aa3485","content":"## Results\nWhat happened (objectively)?\n\nDo not interpret, simply state the facts.\n\nLet's be honest: the first thing most of us do when skimming a paper is look at the figures. If your key results can be presented in figures, then start with that, and structure your paper around that.\n"},{"_id":"5b1b72970763230d27aa34a3","treeId":"5b1b72970763230d27aa3483","seq":13802273,"position":1,"parentId":"5b1b72970763230d27aa34a2","content":"## Key Result\nYou can add figures if you'd like:\n\n![](https://dl.dropboxusercontent.com/s/gieldum0s47m25v/1-plot.jpg)"},{"_id":"5b1b72970763230d27aa34a4","treeId":"5b1b72970763230d27aa3483","seq":13802274,"position":1,"parentId":"5b1b72970763230d27aa34a3","content":"# Results"},{"_id":"5b1b72970763230d27aa34a5","treeId":"5b1b72970763230d27aa3483","seq":13802275,"position":2,"parentId":"5b1b72970763230d27aa34a3","content":"Final text for results goes here"},{"_id":"5b1b72970763230d27aa34a6","treeId":"5b1b72970763230d27aa3483","seq":13802276,"position":3,"parentId":"5b1b72970763230d27aa34a3","content":"..."},{"_id":"5b1b72970763230d27aa34a7","treeId":"5b1b72970763230d27aa3483","seq":13802277,"position":4,"parentId":"5b1b72970763230d27aa34a3","content":"..."},{"_id":"5b1b72970763230d27aa34a8","treeId":"5b1b72970763230d27aa3483","seq":13802278,"position":2,"parentId":"5b1b72970763230d27aa34a2","content":"Remember these are **cards** so you can rearrange your results at will.\nAny subcards will follow."},{"_id":"5b1b72970763230d27aa34a9","treeId":"5b1b72970763230d27aa3483","seq":13802279,"position":1,"parentId":"5b1b72970763230d27aa34a8","content":"Other results"},{"_id":"5b1b72970763230d27aa34aa","treeId":"5b1b72970763230d27aa3483","seq":13802280,"position":4,"parentId":"5b1b72970763230d27aa3485","content":"## Discussion\nResults are objective, but science isn't about listing data, it's about extracting meaning from what we observe.\n\nWhat do your results tell you about the core problem you were investigating?"},{"_id":"5b1b72970763230d27aa34ab","treeId":"5b1b72970763230d27aa3483","seq":13802281,"position":5,"parentId":"5b1b72970763230d27aa3485","content":"## Conclusion\nBring it back to the big picture. How do your results fit into the current body of knowledge?\n\nMost importantly, how can these results help you [ask better questions](http://www.youtube.com/watch?v=nq0_zGzSc8g#t=493)?"},{"_id":"5b1b72970763230d27aa34ac","treeId":"5b1b72970763230d27aa3483","seq":13802282,"position":1,"parentId":"5b1b72970763230d27aa34ab","content":"## Conclusion (further detail)\n\nExpand on your conclusion summary, and add more details to it."},{"_id":"5b1b72970763230d27aa34ad","treeId":"5b1b72970763230d27aa3483","seq":13802283,"position":1,"parentId":"5b1b72970763230d27aa34ac","content":"# Conclusion"},{"_id":"5b1b72970763230d27aa34ae","treeId":"5b1b72970763230d27aa3483","seq":13802284,"position":2,"parentId":"5b1b72970763230d27aa34ac","content":"Final text for conclusion goes here"},{"_id":"5b1b72970763230d27aa34af","treeId":"5b1b72970763230d27aa3483","seq":13802285,"position":3,"parentId":"5b1b72970763230d27aa34ac","content":"in as many"},{"_id":"5b1b72970763230d27aa34b0","treeId":"5b1b72970763230d27aa3483","seq":13802286,"position":4,"parentId":"5b1b72970763230d27aa34ac","content":"cards as you like."},{"_id":"5b1b72970763230d27aa34b1","treeId":"5b1b72970763230d27aa3483","seq":13802287,"position":6,"parentId":"5b1b72970763230d27aa3485","content":"## References\nWe don't have bibliography support yet, but we do have \"named links\" so you can refer to specific links by name rather than retyping it each time.\n\n\"Black holes are cool.\" [[1]][prl2010], and DNA is cool too [[2]][dnaRef]. But black holes are still cool, though not \"absolute zero\" cool [[1]][prl2010].\n\n[prl2010]: http://arxiv.org/abs/1311.3007\n[dnaRef]: http://biorxiv.org/content/early/2013/11/07/000026"},{"_id":"5b1b72970763230d27aa34b2","treeId":"5b1b72970763230d27aa3483","seq":13802288,"position":1,"parentId":"5b1b72970763230d27aa34b1","content":"## List\nOr you can simply list your references here:\n\n1. some ref\n1. some other ref. Numbering fixes itself automatically.\n2. A third ref."},{"_id":"5b1b72970763230d27aa34b3","treeId":"5b1b72970763230d27aa3483","seq":13802289,"position":1,"parentId":"5b1b72970763230d27aa34b2","content":"# References"},{"_id":"5b1b72970763230d27aa34b4","treeId":"5b1b72970763230d27aa3483","seq":13802290,"position":2,"parentId":"5b1b72970763230d27aa34b2","content":"Some reference by J. Doe"},{"_id":"5b1b72970763230d27aa34b5","treeId":"5b1b72970763230d27aa3483","seq":13802291,"position":1,"parentId":"5b1b72970763230d27aa34b4","content":"Notes on this reference. "},{"_id":"5b1b72970763230d27aa34b6","treeId":"5b1b72970763230d27aa3483","seq":13802292,"position":3,"parentId":"5b1b72970763230d27aa34b2","content":"Some other reference"},{"_id":"5b1b72970763230d27aa34b7","treeId":"5b1b72970763230d27aa3483","seq":22985632,"position":0.5,"parentId":"5b1b72970763230d27aa3484","content":"## Objetos matemáticos de interés\n\nLos objetos matemáticos que normalmente se utilizan para realizar gráficas diversas son:\n\n### En el plano\n* Nubes de puntos\n* Gráfica de funciones de R -> R\n* Gráfica de funciones implícitas de dos incógnitas\n* Curvas paramétricas en R²\n* Curvas de nivel aplanadas\n* Grafos en el plano\n* Fractales planos\n\n### En el espacio\n* Nubes de puntos\n* Gráfica de funciones de R² -> R\n* Gráfica de funciones implícitas de tres incógnitas\n* Curvas y superficies paramétricas en R³\n* Curvas de nivel sobre una superficie\n* Superficies de nivel\n* Intersecciones de superficies\n* Grafos en el espacio\n* Fractales en el espacio"}],"tree":{"_id":"5b1b72970763230d27aa3483","name":"Plantilla de Investigación","publicUrl":"plantilla_investigacion"}}