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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)
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Fu-Kwun Hwang
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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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