Remove dot points add waffles

[ipdf/sam.git] / chapters / Background_Lines.tex

diff --git a/chapters/Background_Lines.tex b/chapters/Background_Lines.tex
index 4752a21..581a653 100644 (file)
--- a/chapters/Background_Lines.tex
+++ b/chapters/Background_Lines.tex
@@ -1,8 +1,8 @@
 It is well known that in cartesian coordinates, a line between points $(x_1, y_1)$ and $(x_2, y_2)$, can be described by:
 \begin{align}
-       y(x) &= m x + b\label{eqn_line} \quad \text{ on $x \in [x_1, x_2]$}  \\
-       \text{ for } & m = (y_2 - y_1)/(x_2 - x_1) \\
-       \text{ and } & b
+       y(x) &= m x + c\label{eqn_line} \quad \text{ on $x \in [x_1, x_2]$} 
+       \text{ for } & m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \\
+       \text{ and } & c = 
 \end{align}
 
 On a raster display, only points $(x,y)$ with integer coordinates can be displayed; however $m$ will generally not be an integer. Thus a straight forward use of Equation \ref{eqn_line} will require costly floating point operations and rounding (See Section\ref{}). Modifications based on computing steps $\delta x$ and $\delta y$ eliminate the multiplication but are still less than ideal in terms of performance\cite{computergraphics2}.