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I''ve asked this question ones but I didn''t get any good answer.
I have a plane - a triangle, and I know the coordinates of it''s vertices. How do I found the Y (Height) of any given x,z on this plane?
Sorry for my English.
Thanks.
Extract the plane equation:
ax + by + cz + d = 0
Rearrange:
y = (- d - ax - cz) / b
To get the plane eqn:
(v1,v2,v3 is triangle verts)
e1 = v2 - v1
e2 = v3 - v1
normal = normalize( cross(e1,e2) )
where cross takes two vectors and returns the cross product, normalize takes a vector and returns the normalized (unit) version.
then in the above equation:
a = normal.x
b = normal.y
c = normal.z
d = -dot(normal,v1)
ax + by + cz + d = 0
Rearrange:
y = (- d - ax - cz) / b
To get the plane eqn:
(v1,v2,v3 is triangle verts)
e1 = v2 - v1
e2 = v3 - v1
normal = normalize( cross(e1,e2) )
where cross takes two vectors and returns the cross product, normalize takes a vector and returns the normalized (unit) version.
then in the above equation:
a = normal.x
b = normal.y
c = normal.z
d = -dot(normal,v1)
quote:Original post by JuNC
...
normal = normalize( cross(e1,e2) )
...
a = normal.x
b = normal.y
c = normal.z
d = -dot(normal,v1)
Right! However you dont need do normalize the normal if you dont need the ''normal'' explicitly (ie.: light).
So, given 3 points P0, P1, P2
simply
vector3 normal = (P2-P0)^(P1-P0) = (a, b, c)
and float d = - normal * P0
-> y = -(a*x + c*z + d)/b
guys, dont talk so complicated. If he ask this question, its probably he dont know VECTOR ALGEBRA.
What you want to do is to find intersection point between a plane and a line?
What you want to do is to find intersection point between a plane and a line?
quote:Original post by Daivuk
guys, dont talk so complicated.
If someone find this math complicated...leave 3D graphics...it''s better! I''ve studied these topics at school when I was 14...(a lot of time ago...
)quote:
What you want to do is to find intersection point between a plane and a line?
No!
14 ?!!!!!!!?
Damn, where did you go at school??
Me I learned it at 19 at college.
long time ago too
Damn, where did you go at school??
Me I learned it at 19 at college.
long time ago too
Author
quote:Original post by Daivuk
guys, dont talk so complicated. If he ask this question, its probably he dont know VECTOR ALGEBRA.
What you want to do is to find intersection point between a plane and a line?
I understood what he was saying and I have already done something similiar. My mistake was using "-" instead of "+"
so I have solved my problem. Thank you.
Author
quote:Original post by blizzard999
If someone find this math complicated...leave 3D graphics...it''s better! I''ve studied these topics at school when I was 14...(a lot of time ago...
I have studied it at the age of 13 by myself. :D
quote:
I have studied it at the age of 13 by myself. :D
I was obliged of course...at 13 I had other things in my head
Seriously...geometry is a lot simpler than linear algebra or other ''math topics''
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