Geometric algebra and simple geometric operations












2












$begingroup$


I'm not an expert on the subject, but If it is worth I'd like to start on getting some grasp on the subject.



Assuming geometric algebra framework, Is there somewhere a list of formulas where for example the intersection between a line and a plane, line and sphere, if the point belong to a plane etc?



I want to compare those formulas against the one would classically use to see whether or not possibly there's a benefit.






reference-request geometric-algebras







share|cite|improve this question









$endgroup$












  • $begingroup$
    There are some references listed in the Wikipedia page on Geometric algebra, which you might find interesting.
    $endgroup$
    – Jose Arnaldo Bebita Dris
    Jun 23 '17 at 9:52










  • $begingroup$
    You want to study line-plane intersections using Clifford algebras? Really?
    $endgroup$
    – Gerry Myerson
    Jun 23 '17 at 9:53






  • 2




    $begingroup$
    @GerryMyerson what's wrong with that? Can't I just be curious?
    $endgroup$
    – user8469759
    Jun 23 '17 at 9:55










  • $begingroup$
    Sure. Go for it.
    $endgroup$
    – Gerry Myerson
    Jun 23 '17 at 9:56






  • 2




    $begingroup$
    Geometric algebra for computer science, by Dorst, Fontijne, and Mann covers all these intersection topics. amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/…
    $endgroup$
    – Peeter Joot
    Jun 27 '17 at 0:58
















2












$begingroup$


I'm not an expert on the subject, but If it is worth I'd like to start on getting some grasp on the subject.



Assuming geometric algebra framework, Is there somewhere a list of formulas where for example the intersection between a line and a plane, line and sphere, if the point belong to a plane etc?



I want to compare those formulas against the one would classically use to see whether or not possibly there's a benefit.






reference-request geometric-algebras







share|cite|improve this question









$endgroup$












  • $begingroup$
    There are some references listed in the Wikipedia page on Geometric algebra, which you might find interesting.
    $endgroup$
    – Jose Arnaldo Bebita Dris
    Jun 23 '17 at 9:52










  • $begingroup$
    You want to study line-plane intersections using Clifford algebras? Really?
    $endgroup$
    – Gerry Myerson
    Jun 23 '17 at 9:53






  • 2




    $begingroup$
    @GerryMyerson what's wrong with that? Can't I just be curious?
    $endgroup$
    – user8469759
    Jun 23 '17 at 9:55










  • $begingroup$
    Sure. Go for it.
    $endgroup$
    – Gerry Myerson
    Jun 23 '17 at 9:56






  • 2




    $begingroup$
    Geometric algebra for computer science, by Dorst, Fontijne, and Mann covers all these intersection topics. amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/…
    $endgroup$
    – Peeter Joot
    Jun 27 '17 at 0:58














2












2








2





$begingroup$


I'm not an expert on the subject, but If it is worth I'd like to start on getting some grasp on the subject.



Assuming geometric algebra framework, Is there somewhere a list of formulas where for example the intersection between a line and a plane, line and sphere, if the point belong to a plane etc?



I want to compare those formulas against the one would classically use to see whether or not possibly there's a benefit.






reference-request geometric-algebras







share|cite|improve this question









$endgroup$




I'm not an expert on the subject, but If it is worth I'd like to start on getting some grasp on the subject.



Assuming geometric algebra framework, Is there somewhere a list of formulas where for example the intersection between a line and a plane, line and sphere, if the point belong to a plane etc?



I want to compare those formulas against the one would classically use to see whether or not possibly there's a benefit.






reference-request geometric-algebras




reference-request geometric-algebras






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jun 23 '17 at 9:49









user8469759user8469759

1,5331618




1,5331618












  • $begingroup$
    There are some references listed in the Wikipedia page on Geometric algebra, which you might find interesting.
    $endgroup$
    – Jose Arnaldo Bebita Dris
    Jun 23 '17 at 9:52










  • $begingroup$
    You want to study line-plane intersections using Clifford algebras? Really?
    $endgroup$
    – Gerry Myerson
    Jun 23 '17 at 9:53






  • 2




    $begingroup$
    @GerryMyerson what's wrong with that? Can't I just be curious?
    $endgroup$
    – user8469759
    Jun 23 '17 at 9:55










  • $begingroup$
    Sure. Go for it.
    $endgroup$
    – Gerry Myerson
    Jun 23 '17 at 9:56






  • 2




    $begingroup$
    Geometric algebra for computer science, by Dorst, Fontijne, and Mann covers all these intersection topics. amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/…
    $endgroup$
    – Peeter Joot
    Jun 27 '17 at 0:58


















  • $begingroup$
    There are some references listed in the Wikipedia page on Geometric algebra, which you might find interesting.
    $endgroup$
    – Jose Arnaldo Bebita Dris
    Jun 23 '17 at 9:52










  • $begingroup$
    You want to study line-plane intersections using Clifford algebras? Really?
    $endgroup$
    – Gerry Myerson
    Jun 23 '17 at 9:53






  • 2




    $begingroup$
    @GerryMyerson what's wrong with that? Can't I just be curious?
    $endgroup$
    – user8469759
    Jun 23 '17 at 9:55










  • $begingroup$
    Sure. Go for it.
    $endgroup$
    – Gerry Myerson
    Jun 23 '17 at 9:56






  • 2




    $begingroup$
    Geometric algebra for computer science, by Dorst, Fontijne, and Mann covers all these intersection topics. amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/…
    $endgroup$
    – Peeter Joot
    Jun 27 '17 at 0:58
















$begingroup$
There are some references listed in the Wikipedia page on Geometric algebra, which you might find interesting.
$endgroup$
– Jose Arnaldo Bebita Dris
Jun 23 '17 at 9:52




$begingroup$
There are some references listed in the Wikipedia page on Geometric algebra, which you might find interesting.
$endgroup$
– Jose Arnaldo Bebita Dris
Jun 23 '17 at 9:52












$begingroup$
You want to study line-plane intersections using Clifford algebras? Really?
$endgroup$
– Gerry Myerson
Jun 23 '17 at 9:53




$begingroup$
You want to study line-plane intersections using Clifford algebras? Really?
$endgroup$
– Gerry Myerson
Jun 23 '17 at 9:53




2




2




$begingroup$
@GerryMyerson what's wrong with that? Can't I just be curious?
$endgroup$
– user8469759
Jun 23 '17 at 9:55




$begingroup$
@GerryMyerson what's wrong with that? Can't I just be curious?
$endgroup$
– user8469759
Jun 23 '17 at 9:55












$begingroup$
Sure. Go for it.
$endgroup$
– Gerry Myerson
Jun 23 '17 at 9:56




$begingroup$
Sure. Go for it.
$endgroup$
– Gerry Myerson
Jun 23 '17 at 9:56




2




2




$begingroup$
Geometric algebra for computer science, by Dorst, Fontijne, and Mann covers all these intersection topics. amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/…
$endgroup$
– Peeter Joot
Jun 27 '17 at 0:58




$begingroup$
Geometric algebra for computer science, by Dorst, Fontijne, and Mann covers all these intersection topics. amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/…
$endgroup$
– Peeter Joot
Jun 27 '17 at 0:58










1 Answer
1






active

oldest

votes


















1












$begingroup$

For a thorough introduction to Geometric Algebras have a look at:
Geometric Algebra for Physicists by Chris Doran and Anthony Lasenby



For a thorough look at the conformal model:
Geometric Algebra for Computer Scientists by Dorst,Fontijne and Mann.
This book contains a lot of very useful practical information on implementing and using geometric algebra in practice.



For a handy reference for the conformal model look at:
A Covariant Approach to Geometry using Geometric Algebra by Anthony Lasenby, Joan Lasenby and Rich Wareham (this is a very nice one, I work a lot with geometric primitive intersection and have this open most of the time. Full disclaimer: Joan Lasenby is my PhD supervisor so I am probably biased towards liking her papers as we use the same notation and think about GA in a similar way)



A very good collection of useful material comes from Guide to Geometric Algebra in Practice edited again by Leo Dorst and Joan Lasenby. This one contains a lot of good papers from one year of the AGACSE conference.



The big reference text for a GA is Clifford Algebra to Geometric Calculus. A Unified Language for Mathematics and Physics by David Hestenes and Garret Sobczyk, this contains a huge amount of stuff but is fairly heavy going if you are just starting the subject.



If you are interested in playing around with an interactive environment for GA then ganja.js has a lot of examples and good visualisation capabilities (Disclaimer: Steven De Keninck, the author of this library, is a friend of mine)






share|cite|improve this answer









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    1 Answer
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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    For a thorough introduction to Geometric Algebras have a look at:
    Geometric Algebra for Physicists by Chris Doran and Anthony Lasenby



    For a thorough look at the conformal model:
    Geometric Algebra for Computer Scientists by Dorst,Fontijne and Mann.
    This book contains a lot of very useful practical information on implementing and using geometric algebra in practice.



    For a handy reference for the conformal model look at:
    A Covariant Approach to Geometry using Geometric Algebra by Anthony Lasenby, Joan Lasenby and Rich Wareham (this is a very nice one, I work a lot with geometric primitive intersection and have this open most of the time. Full disclaimer: Joan Lasenby is my PhD supervisor so I am probably biased towards liking her papers as we use the same notation and think about GA in a similar way)



    A very good collection of useful material comes from Guide to Geometric Algebra in Practice edited again by Leo Dorst and Joan Lasenby. This one contains a lot of good papers from one year of the AGACSE conference.



    The big reference text for a GA is Clifford Algebra to Geometric Calculus. A Unified Language for Mathematics and Physics by David Hestenes and Garret Sobczyk, this contains a huge amount of stuff but is fairly heavy going if you are just starting the subject.



    If you are interested in playing around with an interactive environment for GA then ganja.js has a lot of examples and good visualisation capabilities (Disclaimer: Steven De Keninck, the author of this library, is a friend of mine)






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      For a thorough introduction to Geometric Algebras have a look at:
      Geometric Algebra for Physicists by Chris Doran and Anthony Lasenby



      For a thorough look at the conformal model:
      Geometric Algebra for Computer Scientists by Dorst,Fontijne and Mann.
      This book contains a lot of very useful practical information on implementing and using geometric algebra in practice.



      For a handy reference for the conformal model look at:
      A Covariant Approach to Geometry using Geometric Algebra by Anthony Lasenby, Joan Lasenby and Rich Wareham (this is a very nice one, I work a lot with geometric primitive intersection and have this open most of the time. Full disclaimer: Joan Lasenby is my PhD supervisor so I am probably biased towards liking her papers as we use the same notation and think about GA in a similar way)



      A very good collection of useful material comes from Guide to Geometric Algebra in Practice edited again by Leo Dorst and Joan Lasenby. This one contains a lot of good papers from one year of the AGACSE conference.



      The big reference text for a GA is Clifford Algebra to Geometric Calculus. A Unified Language for Mathematics and Physics by David Hestenes and Garret Sobczyk, this contains a huge amount of stuff but is fairly heavy going if you are just starting the subject.



      If you are interested in playing around with an interactive environment for GA then ganja.js has a lot of examples and good visualisation capabilities (Disclaimer: Steven De Keninck, the author of this library, is a friend of mine)






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        For a thorough introduction to Geometric Algebras have a look at:
        Geometric Algebra for Physicists by Chris Doran and Anthony Lasenby



        For a thorough look at the conformal model:
        Geometric Algebra for Computer Scientists by Dorst,Fontijne and Mann.
        This book contains a lot of very useful practical information on implementing and using geometric algebra in practice.



        For a handy reference for the conformal model look at:
        A Covariant Approach to Geometry using Geometric Algebra by Anthony Lasenby, Joan Lasenby and Rich Wareham (this is a very nice one, I work a lot with geometric primitive intersection and have this open most of the time. Full disclaimer: Joan Lasenby is my PhD supervisor so I am probably biased towards liking her papers as we use the same notation and think about GA in a similar way)



        A very good collection of useful material comes from Guide to Geometric Algebra in Practice edited again by Leo Dorst and Joan Lasenby. This one contains a lot of good papers from one year of the AGACSE conference.



        The big reference text for a GA is Clifford Algebra to Geometric Calculus. A Unified Language for Mathematics and Physics by David Hestenes and Garret Sobczyk, this contains a huge amount of stuff but is fairly heavy going if you are just starting the subject.



        If you are interested in playing around with an interactive environment for GA then ganja.js has a lot of examples and good visualisation capabilities (Disclaimer: Steven De Keninck, the author of this library, is a friend of mine)






        share|cite|improve this answer









        $endgroup$



        For a thorough introduction to Geometric Algebras have a look at:
        Geometric Algebra for Physicists by Chris Doran and Anthony Lasenby



        For a thorough look at the conformal model:
        Geometric Algebra for Computer Scientists by Dorst,Fontijne and Mann.
        This book contains a lot of very useful practical information on implementing and using geometric algebra in practice.



        For a handy reference for the conformal model look at:
        A Covariant Approach to Geometry using Geometric Algebra by Anthony Lasenby, Joan Lasenby and Rich Wareham (this is a very nice one, I work a lot with geometric primitive intersection and have this open most of the time. Full disclaimer: Joan Lasenby is my PhD supervisor so I am probably biased towards liking her papers as we use the same notation and think about GA in a similar way)



        A very good collection of useful material comes from Guide to Geometric Algebra in Practice edited again by Leo Dorst and Joan Lasenby. This one contains a lot of good papers from one year of the AGACSE conference.



        The big reference text for a GA is Clifford Algebra to Geometric Calculus. A Unified Language for Mathematics and Physics by David Hestenes and Garret Sobczyk, this contains a huge amount of stuff but is fairly heavy going if you are just starting the subject.



        If you are interested in playing around with an interactive environment for GA then ganja.js has a lot of examples and good visualisation capabilities (Disclaimer: Steven De Keninck, the author of this library, is a friend of mine)







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 10 '18 at 18:10









        Hugo HadfieldHugo Hadfield

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