I have a set of (X,Y,Z) points representing different planar features. I need to calculate the slope of each plane and their aspect angle using normal vectors.
For the slope, I want to compute angle between normal vector (NV) of each plane and NV of imaginary horizontal plane. Assume, the plane equation that I use is; Ax+By+c=z. The normal vector of my plane is (a,b, -1). For my plane equation, what should be the equation of imaginary horizontal plane? I think equation of horizontal plane is z=c. (where c is height of the plane from xy plane). Hence, the normal vector is (0,0,-1). Is this correct?
Then the angle between my plane and the horizontal plane is;
cos^(-1)??(a.0+b.0+(-1).1)/(?(?a1?^2+?b1?^2+?c1?^2 ).?(0^2+0^2+1^2 ))?
Is that correct?
Also, I want to know the equation of planes which is parallel (1) to xz plane (2) to yz plane and (3) any vertical plane not oriented to xz or yz planes (i.e. not parallel to xz or yz planes) with their corresponding normal vectors.
After that, I want to compute the aspect angle by using the projected NV of (a,b, -1) to the XY plane. But, I do not know how to get the projected NV. Then, from the NV of xz plane and projected one, I’ll compute aspect angle. So, I would like to know whether this concept is correct or wrong.
Also, please let me know the equation of getting aspect angle for my case as I confused with that Projected normal vectors.
I hope, anyone can help me to solve this. Thank you.
For the slope, I want to compute angle between normal vector (NV) of each plane and NV of imaginary horizontal plane. Assume, the plane equation that I use is; Ax+By+c=z. The normal vector of my plane is (a,b, -1). For my plane equation, what should be the equation of imaginary horizontal plane? I think equation of horizontal plane is z=c. (where c is height of the plane from xy plane). Hence, the normal vector is (0,0,-1). Is this correct?
Then the angle between my plane and the horizontal plane is;
cos^(-1)??(a.0+b.0+(-1).1)/(?(?a1?^2+?b1?^2+?c1?^2 ).?(0^2+0^2+1^2 ))?
Is that correct?
Also, I want to know the equation of planes which is parallel (1) to xz plane (2) to yz plane and (3) any vertical plane not oriented to xz or yz planes (i.e. not parallel to xz or yz planes) with their corresponding normal vectors.
After that, I want to compute the aspect angle by using the projected NV of (a,b, -1) to the XY plane. But, I do not know how to get the projected NV. Then, from the NV of xz plane and projected one, I’ll compute aspect angle. So, I would like to know whether this concept is correct or wrong.
Also, please let me know the equation of getting aspect angle for my case as I confused with that Projected normal vectors.
I hope, anyone can help me to solve this. Thank you.