Suppose you have a 3D object made of polygons and you want to determine the pixel on the screen (a plane in 3D space) where a particular vertex with position vector ** a** should be plotted. The camera has position vector

the line joining A and B, with

the plane through C with normal vector

We know

for some t that we would like to know - if we found t we'd just plug it into the above equation and we'd have

We also know

(

because

Putting the two together is enough to find the value of t:

(

=>

=> t (

=> t = ( (

Found it! So plugging t into

gives us

Add a little programming and this is our pixel. All the vector applets in this site (eg this one) use this exact method, though good programmers can do some impressive stuff with their knowledge of vectors.

The point of intersection of a line with a plane is also needed in the process known as clipping - truncating the edge of a polygon that is intersecting a plane of what is known as the viewing frustrum.

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