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The topology part of these textbooks is the hardest for me. Understanding the 2d representations of the shapes. Where can one get a more bottom up explanation o

The topology part of these textbooks is the hardest for me. Understanding the 2d representations of the shapes. Where can one get a more bottom up explanation of the crucial topology concepts? Also bad at geometry in general

pvarangot 8y ago
Control or spatial-related DSP has a lot of geometry going on and it's really hard to get with a good working knowledge. I don't know if there's a short path. Start with a good linear algebra course maybe in parallel to actually trying to solve or hack though the type of problems you want to solve, and thinking about how the basic stuff you are learning complements with the high level one. Besides the courses recommended here this are other online materials related to planning, location and control I found really useful and consider to be high quality: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Pyt... https://www.coursera.org/learn/mobile-robot https://www.coursera.org/learn/mobile-robot For Linear Algebra I really like Strang's course on OCW taken together with reading through his book.
- mrcoder111 8y ago
  I took a linear algebra course. Maybe I need to restudy but I would rather have links to exact chapters than reading the whole thing, as I don't see a direct path from the linear algebra I studied to the topology concepts and geometry here. Specifically there weren't any curves in linear algebra. Ex 4.10 and 4.11 here: http://planning.cs.uiuc.edu/node143.html http://planning.cs.uiuc.edu/node143.html Are examples of things that are hard for me to understand. Especially that 2d picture in 4.11
  - chongli 8y ago
    You have to study quite a lot of linear algebra before you can tackle functional analysis, the subject which includes the study of topological vector spaces. I don't know anything about robotics, however, so I don't know how functional analysis would apply, if at all.
    - tnecniv 8y ago
      Functional analysis shows up all over the place. Everywhere you can take a Fourier transform, you can use functional analysis. For robotics, control theory and computer vision both come to mind.
salamanderman 8y ago
As a start, I recommend reading about Winding Numbers. I've found that to be the most important topology concept for 2d geometry. Computational Geometry is probably deeper than you want to go, but it would answer most of your questions. For curves, I recommend a Numerical Methods reference. Honestly, wander around Wikipedia links starting from topics like winding numbers and spatial partitioning, and you'll probably get a better primer than any book.
- mrcoder111 8y ago
  The topology in planning usually deals with higher dimensional geometry. Does the same answer still apply?

pvarangot 8y ago

Control or spatial-related DSP has a lot of geometry going on and it's really hard to get with a good working knowledge. I don't know if there's a short path. Start with a good linear algebra course maybe in parallel to actually trying to solve or hack though the type of problems you want to solve, and thinking about how the basic stuff you are learning complements with the high level one. Besides the courses recommended here this are other online materials related to planning, location and control I found really useful and consider to be high quality: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Pyt... https://www.coursera.org/learn/mobile-robot https://www.coursera.org/learn/mobile-robot For Linear Algebra I really like Strang's course on OCW taken together with reading through his book.

mrcoder111 8y ago
I took a linear algebra course. Maybe I need to restudy but I would rather have links to exact chapters than reading the whole thing, as I don't see a direct path from the linear algebra I studied to the topology concepts and geometry here. Specifically there weren't any curves in linear algebra. Ex 4.10 and 4.11 here: http://planning.cs.uiuc.edu/node143.html http://planning.cs.uiuc.edu/node143.html Are examples of things that are hard for me to understand. Especially that 2d picture in 4.11
- chongli 8y ago
  You have to study quite a lot of linear algebra before you can tackle functional analysis, the subject which includes the study of topological vector spaces. I don't know anything about robotics, however, so I don't know how functional analysis would apply, if at all.
  - tnecniv 8y ago
    Functional analysis shows up all over the place. Everywhere you can take a Fourier transform, you can use functional analysis. For robotics, control theory and computer vision both come to mind.

salamanderman 8y ago

As a start, I recommend reading about Winding Numbers. I've found that to be the most important topology concept for 2d geometry. Computational Geometry is probably deeper than you want to go, but it would answer most of your questions. For curves, I recommend a Numerical Methods reference. Honestly, wander around Wikipedia links starting from topics like winding numbers and spatial partitioning, and you'll probably get a better primer than any book.

mrcoder111 8y ago
The topology in planning usually deals with higher dimensional geometry. Does the same answer still apply?