<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">You keep talking in terms of implementations rather than the abstract object. <div class=""><br class=""></div><div class="">Here you say a square does not include information about its location but then you add the location in the class definition. In coordinate-free geometry, you have only three basic entities: scalars, points and vectors. You can use them to define all the standard geometric objects and write code purely in terms of these entities.</div><div class=""><br class=""></div><div class="">Ed<br class=""><div class="">
<div>__________<br class=""><br class="">Ed Angel<br class=""><br class="">Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)<br class="">Professor Emeritus of Computer Science, University of New Mexico<br class=""><br class="">1017 Sierra Pinon<br class="">Santa Fe, NM 87501<br class="">505-984-0136 (home)<span class="Apple-tab-span" style="white-space: pre;"> </span> <span class="Apple-tab-span" style="white-space: pre;"> </span><a href="mailto:edward.angel@gmail.com" class="">edward.angel@gmail.com</a><br class="">505-453-4944 (cell) <span class="Apple-tab-span" style="white-space: pre;"> </span><span class="Apple-tab-span" style="white-space: pre;"> </span>http://www.cs.unm.edu/~angel<br class=""></div>
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<div><br class=""><blockquote type="cite" class=""><div class="">On Jul 23, 2020, at 4:09 PM, Frank Wimberly <<a href="mailto:wimberly3@gmail.com" class="">wimberly3@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="auto" class="">The mathematical concept of a point in R^2 is that a it is completely determined by the values of its coordinates. Same coordinates, same point. A square per se Is determined by the length of its side(s). There is no information about it's location.<div dir="auto" class=""><br class=""></div><div dir="auto" class="">If I were writing a Square class for a graphics application I would include two member variables:</div><div dir="auto" class=""><br class=""></div><div dir="auto" class=""> LocationOfLowerLeft point;</div><div dir="auto" class=""> LengthOfSide double;</div><div dir="auto" class=""><br class=""></div><div dir="auto" class="">I haven't written code for years so beware.<br class=""><br class=""><div data-smartmail="gmail_signature" dir="auto" class="">---<br class="">Frank C. Wimberly<br class="">140 Calle Ojo Feliz, <br class="">Santa Fe, NM 87505<br class=""><br class="">505 670-9918<br class="">Santa Fe, NM</div></div></div><br class=""><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jul 23, 2020, 3:58 PM uǝlƃ ↙↙↙ <<a href="mailto:gepropella@gmail.com" class="">gepropella@gmail.com</a>> wrote:<br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">No, I don't. What's the difference?<br class="">
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On 7/23/20 2:46 PM, Frank Wimberly wrote:<br class="">
> OK. As long as you grok the difference between the mathematical concept and the OO concept.<br class="">
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↙↙↙ uǝlƃ<br class="">
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