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 Author Topic: Equation for a plane: a*x+b*y+c*z+d=0 what those coefficients (a,b,c,d) means  (Read 10907 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
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 « Embed this message on: June 19, 2009, 02:23:08 pm » posted from:Taipei,T\'ai-pei,Taiwan

A plane in 3D can be represented by $a*x+b*y+c*z+d=0$;
It can be viewed as the inner product between two vectors : $(a,b,c)\cdot (x,y,z)=-d$

Let r to be length of vector (a,b,c). i.e. r=|(a,b,c)|= Math.sqrt{a*a+b*b+c*c}.
Then the equation can be re-writted as $\hat{a}*x+\hat{b}*y+\hat{c}*z+d/r=0$,
where $\hat{a}=a/r,$hat{b}=b/r, hat{c}=c/r\$.

If d=0, the origin (0,0,0) is on the plane.
Otherwise, the shortest distance between (0,0,0) and the plane is d/r.

You can drag the vector (a,b,c) with mouse or change their values with sliders.

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"The mind is its own place, and in itself, can make heaven of Hell, and a hell of Heaven." ..."John Milton(1608-1674, English Poet)"

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