2.5.1 Brute Force

cf. [FvDFH90, 3.12.2]

To clip a point $(x,y)$ against a rectangle $[x_{\min},x_{\max}]\times [y_{\min},y_{\max}]$ means to draw the point exactly if the following condition is satisfied:

$$(x_{\min}\leq x\leq x_{\max})$$    and $$(y_{\min}\leq y\leq y_{\max}).$$

Clipping a line against a rectangle can lead to one of the following cases:

• Both endpoints lie inside. Hence the whole segment is inside and is to be drawn completely.
• Exactly one endpoint lies inside. Hence the line hits boundary exactly once and we have to determine the corresponding intersection point and clip the line there.
• Both endpoints lie outside. Then it is not clear whether the line hits the rectangle or not. So we intersect this line with each of the 4 sides (i.e. the infinite lines) and check whether some intersection points lies on the boundary of the rectangle. This is best done in parametric form

  $$x=x_0+t(x_1-x_0)\quad y=y_0+t(y_1-y_0).$$

  
  

But this is still an inefficient method.