<p>I am going through one of the most basic line drawing algorithms and stuck with the following mathematical explanations. The implicit function of line equation is:</p>

<pre><code>f(x,y) = ax + by + c
</code></pre>

<p>The Book(Computer Graphics , Principles  and practice) mentions that</p>

<pre><code>f(x,y) = 0 , when any point m is on line
f(x,y) &lt; 0, when any point m is above the line, and 
f(x,y) &gt; 0, when any point m is below the line.
</code></pre>

<p>It would be great to have some explanation of the claim above. I tried to figure out the first one with the following example:</p>

<pre><code>3x + 2y = 1
=&gt; 3x + 2y -1 = 0, where a = 3, b = 2 and c = -1
</code></pre>

<p>All I figure out that I need to plug in a (x,y) coordinate so that 3x + 2y - 1 = 0. I am not sure how to choose this coordinate value .</p>

<p>And I am clueless about the next two cases. An example demonstrating all the three cases would be fantastic !</p>

<p>Thanks </p>

CC BY-SA 3.0
2016-05-30T21:59:39.150Z
I am unsure what you are asking here. What you posted as quote from the book is just the definition of a line, your title sounds unrelated. Are you asking how to find point on a line of which you have an implicit form like the one you posted?
cifz
CC BY-SA 3.0
2016-05-30T23:51:27.607Z
The midpoint algorithm uses the implicit equation of the line and I am looking forward to some proofs of the three cases mentioned in my initial post.
sajis997
<midpoint>
Midpoint algorithm
sajis997
# Midpoint algorithm

(Asked by: username_0 on 2016-05-30)

I am going through one of the most basic line drawing algorithms and stuck with the following mathematical explanations. The implicit function of line equation is:

```
f(x,y) = ax + by + c

```

The Book(Computer Graphics , Principles and practice) mentions that

```
f(x,y) = 0 , when any point m is on line
f(x,y) < 0, when any point m is above the line, and 
f(x,y) > 0, when any point m is below the line.

```

It would be great to have some explanation of the claim above. I tried to figure out the first one with the following example:

```
3x + 2y = 1
=> 3x + 2y -1 = 0, where a = 3, b = 2 and c = -1

```

All I figure out that I need to plug in a (x,y) coordinate so that 3x + 2y - 1 = 0. I am not sure how to choose this coordinate value .

And I am clueless about the next two cases. An example demonstrating all the three cases would be fantastic !

Thanks

**Tags:** midpoint

> **Comments:**
> **username_1**: I am unsure what you are asking here. What you posted as quote from the book is just the definition of a line, your title sounds unrelated. Are you asking how to find point on a line of which you have an implicit form like the one you posted?  
> **username_0**: The midpoint algorithm uses the implicit equation of the line and I am looking forward to some proofs of the three cases mentioned in my initial post.  

---

## 0 answers

