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Main Forums => Homework Help => Topic started by: Probie on March 26, 2009, 11:02:08 AM

Title: Planes, Distances and nonzero origins
Post by: Probie on March 26, 2009, 11:02:08 AM: If I have a plane equation Ax + By + Cz + D = 0 where A B and C are the normal of the plane and D is the distance from the 0,0,0, and I also have the real origin of the object in a 3D world which is nonzero (say for example something like -150, -150, -150 or there abouts) then is it possible to work out the distance from the nonzero origin? And if so can anyone explain it to me.

I have a page of rearranged equations and frankly its melting my brain. I think what i need to do is quite simple

1. work out the closest point of the plane along the normal from the origin.

2. use the origin and the point on the normal to work out the length of the 3D hypotenuse.

Any help would be very greatly appriciated. Even if its just a site that explains it in idiot for me.

Thank you.
Title: Re: Planes, Distances and nonzero origins
Post by: ivan on March 26, 2009, 11:09:35 AM: This page over here (http://softsurfer.com/Archive/algorithm_0104/algorithm_0104.htm) has a point-to-plane formula (scroll down to "Distance of a Point to a Plane").

It's pretty gnarly.
Title: Re: Planes, Distances and nonzero origins
Post by: Probie on March 26, 2009, 11:38:48 AM: Cheers, I'll try and smush that together with the wolfram stuff. I'm definitely over complicating it.
Title: Re: Planes, Distances and nonzero origins
Post by: ivan on March 26, 2009, 11:51:07 AM: What the hell is a "unit normal"?

Whatever it is, it makes the formula a lot shorter.
Title: Re: Planes, Distances and nonzero origins
Post by: Probie on March 26, 2009, 11:58:15 AM: a unit normal is a vector of values with the magnitude of 1.

So you could have 15, 5, 10 and normal is it so that the values would be rally small and have a magnitude of 1.

Disclaimer: this could be worded completely wrong :P
Title: Re: Planes, Distances and nonzero origins
Post by: ivan on March 26, 2009, 12:06:55 PM: Well, if you can manage to deal only with unit normals, then your life will be easier.
Title: Re: Planes, Distances and nonzero origins
Post by: Probie on March 26, 2009, 12:09:47 PM: yeah I think what i need to do is project the origin into the plane and then work out the distance from there.
Title: Re: Planes, Distances and nonzero origins
Post by: Probie on March 26, 2009, 12:37:57 PM: I think i am onto something. If i crack it I will post a write up in extreme idiot terms for anyone who is like me and needs cutting a break!