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## [epsilon-devel] Learning to write I/O actions: paint_line

 From: Luca Saiu Subject: [epsilon-devel] Learning to write I/O actions: paint_line Date: Thu, 20 Nov 2003 23:03:14 +0100 User-agent: Mozilla/5.0 (X11; U; Linux i586; en-US; rv:1.3a) Gecko/20021212

Ok Matteo, I am giving you some hints to write a function paint_line, with type
```  integer -> integer -> integer -> integer -> color -> i/o of void
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The function takes the coordinates of two points and a color, and returns an action which, when executed, paints a segment on the screen:
```  x1 |--> y1 |--> x2 |--> y2 |--> color |--> action

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The function should *not* be named draw_line, since in the CVS version a function with that name is already present.
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We want to draw a segment on the screen. A segment is a subset of a straight line, which can be described by one of the following equations:
```  y = m x + q  // Case 1: a non-vertical straight line
x = k        // Case 2: a vertical straight line

Let's exclude case 2 by now. So we are in case 1.

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It's easy to compute m and q; we want to force the line to include (x1, y1) and (x2, y2). So we solve the following linear system in m and q:
``` / y1 = m x1 + q
\ y2 = m x2 + q

The solution is
/ m = (y2 - y1) / (x2 - x1)
\ q = (x2 y1 - x1 y2) / (x2 - x1)

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Note that there is no solution when x1 = x2, i.e. when the line is vertical. This is correct.
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Let's say that we want to draw one pixel for each integer value of x. Later I'm going to justify this siplification. So we are going to recur on x, and *only* on x, to make the computation faster; we are going to start from the minimum between x1 and x2 and we are going to stop at the maximum (it is useful to define two auxiliary functions min and max, both with type integer -> integer -> integer). For each x it's easy to compute y, since y = m x + q. Remember to compute m as a float, since it will be much more precise (this shouldn't be needed for q). You'll need integer_to_float and float_to_integer.
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We want to make our program fast, so we'll compute min_x, max_x, m and q just *once*. It's convenient to have a function which computes them (you can use a let) and then calls the recursive function with the computed values (and the color, and anything else which may be needed) as arguments. The convenience function (the non-recursive one) will be paint_line itself.
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Ok, you can start and send the result here; we are going to finish the next time; if what you do now is correct it will be very easy. This list supports attachments, you can attach the .epb file. Use 'reply all'.
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Bye,

--
Luca Saiu, maintainer of GNU epsilon
http://www.gnu.org/software/epsilon

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