### Author Topic: Faces  (Read 7022 times)

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#### annikk.exe

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##### Re: Faces
« Reply #60 on: June 18, 2011, 04:59:07 PM »
Here's what I have:

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` -- for a plane defined by coordinates (Px1, Py1, Pz1), (Px2, Py2, Pz2), and (Px3, Py3, Pz3) -- and a line defined by coordinates (Lx1, Ly1, Lz1), (Lx2, Ly2, Lz2) -- find the X, Y, and Z coordinates at which they intersect -- first get 2 vectors along the plane -- ("PV1x" stands for Plane Vector #1, X-coordinate) PV1x = Px2 - Px1 PV1y = Py2 - Py1 PV1z = Pz2 - Pz1 PV2x = Px3 - Px1 PV2y = Py3 - Py1 PV2z = Pz3 - Pz1 -- now find the cross product -- PV1 X PV2 = normal vector! i = (PV1y * PV2z) - (PV1z * PV2y) j = (PV1z * PV2x) - (PV1x * PV2z) k = (PV1x * PV2y) - (PV1y * PV2x) -- define d planex = i planey = j planek = k d = (i * PV1x) + (j * PV1y) + (k * PV1z) -- for the line, calculate tx, ty, tz tx = Lx2 - Lx1 ty = Ly2 - Ly1 tz = Lz2 - Lz1 -- calculate t t = (i * (tx + PV1x)) + (j * (ty + PV1y)) + (k * (tz + PV1z)) -- calculate intersection coordinates intersectX = t * tx intersectY = t * ty intersectZ = t * tz`

It doesn't work perfectly.  There's something wrong.  But what..? :>

#### Aino

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##### Re: Faces
« Reply #61 on: June 18, 2011, 05:07:57 PM »
Sudden crash for me D:

Edit: If it is dependand of dividing with camerax or y then that mi9ght be it... I got no real idea, but not recreateable :/
« Last Edit: June 18, 2011, 05:11:00 PM by Aino »

#### annikk.exe

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##### Re: Faces
« Reply #62 on: June 18, 2011, 05:12:35 PM »
Fixed it, I think.  I was calculating "t" using the normal vector instead of the vertex coordinate.  :P  And I needed to subtract "d".

#### annikk.exe

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##### Re: Faces
« Reply #63 on: June 18, 2011, 05:14:12 PM »
Oh, wait.. no...  it's still broken. :<

#### Aino

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##### Re: Faces
« Reply #64 on: June 18, 2011, 05:14:57 PM »
Talking stuff that I don't have much idea of... By the way annikk; what is "t" for you?

Just asking, I have a sense that it might mean temporarily

And what is the problem, I don't see any... or is it that the lines ain't disapearing?

#### annikk.exe

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##### Re: Faces
« Reply #65 on: June 19, 2011, 01:18:48 AM »
It's "t" from the parametric equation of a line.  It's a maths convention that I just copied for the variable name.

#### annikk.exe

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##### Re: Faces
« Reply #66 on: June 20, 2011, 01:42:45 PM »
No further forward with this..

I'm having a lot of difficulty translating this from maths into code.
A lot of the programming examples out there use facilities available in the language in which they are written to represent things like vectors, and there are shortcut commands such as cross() for the cross product...  the rest all seem to be written in complex mathematical notation, or substitute in coordinates at some point in order to solve something.  Argh...

#### Aino

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##### Re: Faces
« Reply #67 on: June 20, 2011, 03:32:15 PM »
What?!

The great Annikk can't be in vain D:

Well, I'm no good at that, so I'm to no help yet again -.-'

#### annikk.exe

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##### Re: Faces
« Reply #68 on: June 20, 2011, 04:45:08 PM »
Hmm, for the "great Annikk" standing on the shoulders of giants is one thing, balancing is another...

#### Bonobo

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##### Re: Faces
« Reply #69 on: June 20, 2011, 05:55:27 PM »
Youze folks are a luvable bunch!

Just sayin’.
Do you play Go? (aka iGo aka Baduk aka Weiqi)

#### annikk.exe

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##### Re: Faces
« Reply #70 on: June 21, 2011, 12:07:43 AM »
With some help, I have identified a possible algebra problem.

I have this:

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`0 = (i * ((t * tx) + Lx1) - Px1)) + (j * ((t * ty) + Ly1) - Py1)) + (k * ((t * tz) + Lz1) - Pz1))`
t is the unknown, and the value i need to calculate.  The equation has to be reshuffled to have t on the left side, and all the other terms on the right side.

#### Bonobo

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##### Re: Faces
« Reply #71 on: June 21, 2011, 12:36:05 AM »
I can’t do such things, but I know that something’s wrong with your parentheses here. Two or three closing ones too many.
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#### Sniped50

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##### Re: Faces
« Reply #72 on: June 21, 2011, 08:44:31 AM »
My advice would be (don't know if this would work) splitting the equation into three equal parts (so they contain 1 t each), then working out t = ? for each of them. Once you've done that, I think you can just add them together so you get 3t = ? + ? + ?, and then just divide by 3, t = (? + ? + ?)/3.

Would that work, Annikk?

PS: Bonobo is right. You do actually have too many closing parentheses. By my count, 9 opening ones and 12 closing ones.
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#### annikk.exe

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##### Re: Faces
« Reply #73 on: June 21, 2011, 10:26:14 AM »
Ah, well-spotted.  It should be like this, I think:

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`0 = (i * (((t * tx) + Lx1) - Px1)) + (j * (((t * ty) + Ly1) - Py1)) + (k * (((t * tz) + Lz1) - Pz1))`

#### annikk.exe

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`t = ((i * (Px1 - Lx1)) + (j * (Py1 - Ly1)) + (k * (Pz1 - Lz1))) / ((i * (Lx2 - Lx1)) + (j * (Ly2 - Ly1)) + (k * (Lz2 - Lz1)))`