I am having a few problems understanding some of the notation in my text book. For example the following equation is used for finding the intersection between a line and a plane : N.P(t) + D = 0 What does the ''=0'' part mean? Surely this equation does not always yield zero no matter what value of t you plug into it. This =0 thing crops up a lot and i is causing me trouble (i know i probably look like a dumbass now

If the equality were always meant to be true, it would be called an "identity". An "equation" is usually a condition that will be false for some values of the variables involved and true for others. In the context of the intersection of a line and a plane, the variable is probably a parameter of the line (t). You find the value of t for which the equation holds, and you find the intersection point substituting that value in the parametrization of the line.



[edited by - alvaro on December 5, 2002 2:11:30 PM]

so does the =0 actually mean ''false'' and would be specific to the context in which the equation was being refered to?

No, it should mean that if you substitute the parameters needed into the equation and it works out, then the line intersects the plane.

---
Brent Gunning | My Site

it means that when "N.P(t) + D = 0", intersection has occured. when it equals a number other than 0 then it hasn''t. The zero doesn''t mean true or false as such, it''s just what it has to
evaluate to to be true.

3 + t = 5

plug in 1 and you''ll end up with 4, which is the wrong (false)answer. put in 2 and you''ll get five, so the equation becomes "true"

I don''t know what the mathematical notation for a boolean equivalency test is, but the "=" assign generally means that the equation asserts both sides are equal.

Put another way, the "=" sign means you have an algebra problem to solve. And if there is no solution, the equation just isn''t valid for the given situation.

In C++ notation (and Java, C# I guess), the "==" notation means do a boolean test to see if the two sides are equal. Thus,

3 + t = 5 is only meaningful when t = 2.

But,

3 + t == 5 will return true if t = 2, and false if t is anything else.

Now, for the N.P(t) + D = 0 equation, N and D are fixed (defining the plane) and P varies according to t. The equation implies that you may be able to find a value of t for which the equation is satisfied. It''s an algebra problem and you have to solve for t.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.