3d orthogonal projection on a plane

abcdefg · September 27th, 2011, 12:39 AM

hi,
I have a point in 3d P(x,y,z) and a plane of view Ax+By+Cz+d=0 . A point in plane is E.Now i want to project that 3d point to that plane and get 2d coordinates of the projected point relative to the point E.

P = 3d point

p.s. what i am doing right now is to get nearest point in plane from point P.then i subtract that point to E.I suspect that this is right ???

please help me.
Thanks.

ZardoZ · September 27th, 2011, 05:35 AM

[color=#000000]The vector $\vec{u}=\left<A,B,C\right=>=$ is perpendicular to the plane $\epsilon:Ax+By+Cz+D=0$ , use the equation of the parametric line $\sigma(t)=t\left<A,B,C\right=>+\vec{P}=$ and compute where this line intersects the ? plane.[/color]

September 27th, 2011, 12:39 AM	#1
abcdefg Newbie Joined: Sep 2011 Posts: 1 Thanks: 0	3d orthogonal projection on a plane hi, I have a point in 3d P(x,y,z) and a plane of view Ax+By+Cz+d=0 . A point in plane is E.Now i want to project that 3d point to that plane and get 2d coordinates of the projected point relative to the point E. P = 3d point p.s. what i am doing right now is to get nearest point in plane from point P.then i subtract that point to E.I suspect that this is right ??? please help me. Thanks.
$abcdefg is offline$

September 27th, 2011, 05:35 AM	#2
ZardoZ Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus	Re: 3d orthogonal projection on a plane [color=#000000]The vector $\vec{u}=\left<A,B,C\right=>=$ is perpendicular to the plane $\epsilon:Ax+By+Cz+D=0$ , use the equation of the parametric line $\sigma(t)=t\left<A,B,C\right=>+\vec{P}=$ and compute where this line intersects the ? plane.[/color]
$ZardoZ is offline$

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