<div dir="auto"><div dir="auto"><br></div><div dir="auto">That's because I was trying to illustrate the <br>difference between the abstract mathematical definition and an implementation suitable for computer graphics. I had just asked Glen if he grokked the difference and he said no.<br><div data-smartmail="gmail_signature" dir="auto">---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM</div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jul 23, 2020, 4:27 PM Angel Edward <<a href="mailto:edward.angel@gmail.com">edward.angel@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word;line-break:after-white-space">You keep talking in terms of implementations rather than the abstract object. <div><br></div><div>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><br></div><div>Ed<br><div>
<div>__________<br><br>Ed Angel<br><br>Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)<br>Professor Emeritus of Computer Science, University of New Mexico<br><br>1017 Sierra Pinon<br>Santa Fe, NM 87501<br>505-984-0136 (home)<span style="white-space:pre-wrap"> </span> <span style="white-space:pre-wrap"> </span><a href="mailto:edward.angel@gmail.com" target="_blank" rel="noreferrer">edward.angel@gmail.com</a><br>505-453-4944 (cell) <span style="white-space:pre-wrap"> </span><span style="white-space:pre-wrap"> </span><a href="http://www.cs.unm.edu/~angel" target="_blank" rel="noreferrer">http://www.cs.unm.edu/~angel</a><br></div>
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<div><br><blockquote type="cite"><div>On Jul 23, 2020, at 4:09 PM, Frank Wimberly <<a href="mailto:wimberly3@gmail.com" target="_blank" rel="noreferrer">wimberly3@gmail.com</a>> wrote:</div><br><div><div dir="auto">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"><br></div><div dir="auto">If I were writing a Square class for a graphics application I would include two member variables:</div><div dir="auto"><br></div><div dir="auto"> LocationOfLowerLeft point;</div><div dir="auto"> LengthOfSide double;</div><div dir="auto"><br></div><div dir="auto">I haven't written code for years so beware.<br><br><div data-smartmail="gmail_signature" dir="auto">---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM</div></div></div><br><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" target="_blank" rel="noreferrer">gepropella@gmail.com</a>> wrote:<br></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>
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On 7/23/20 2:46 PM, Frank Wimberly wrote:<br>
> OK. As long as you grok the difference between the mathematical concept and the OO concept.<br>
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-- <br>
↙↙↙ uǝlƃ<br>
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