Equation of Plane in a unit cube given the normal and volume enclosed
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I know the normal and volume enclosed by the plane. I am interested in finding out the equation of the plane. The volume enclosed is with respect to origin. The plane can have any random orientation.How should I approach this problem ?
$ n_xx+n_yy+n_zz + d =0 $
How can I calculate the 'd' ?
geometry
asked Dec 7 '18 at 5:19
Some_guySome_guy
213
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add a comment |
$begingroup$
I know the normal and volume enclosed by the plane. I am interested in finding out the equation of the plane. The volume enclosed is with respect to origin. The plane can have any random orientation.How should I approach this problem ?
$ n_xx+n_yy+n_zz + d =0 $
How can I calculate the 'd' ?
geometry
asked Dec 7 '18 at 5:19
Some_guySome_guy
213
$endgroup$
$begingroup$
You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
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– John Wayland Bales
Dec 7 '18 at 6:11
$begingroup$
@JohnWaylandBales Thanks for this... Will check it out
$endgroup$
– Some_guy
Dec 7 '18 at 6:17
add a comment |
$begingroup$
I know the normal and volume enclosed by the plane. I am interested in finding out the equation of the plane. The volume enclosed is with respect to origin. The plane can have any random orientation.How should I approach this problem ?
$ n_xx+n_yy+n_zz + d =0 $
How can I calculate the 'd' ?
geometry
asked Dec 7 '18 at 5:19
Some_guySome_guy
213
$endgroup$
I know the normal and volume enclosed by the plane. I am interested in finding out the equation of the plane. The volume enclosed is with respect to origin. The plane can have any random orientation.How should I approach this problem ?
$ n_xx+n_yy+n_zz + d =0 $
How can I calculate the 'd' ?
geometry
geometry
asked Dec 7 '18 at 5:19
Some_guySome_guy
213
asked Dec 7 '18 at 5:19
Some_guySome_guy
213
asked Dec 7 '18 at 5:19
Some_guySome_guy
213
asked Dec 7 '18 at 5:19
Some_guySome_guy
213
asked Dec 7 '18 at 5:19
Some_guySome_guy
213
213
$begingroup$
You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
$endgroup$
– John Wayland Bales
Dec 7 '18 at 6:11
$begingroup$
@JohnWaylandBales Thanks for this... Will check it out
$endgroup$
– Some_guy
Dec 7 '18 at 6:17
add a comment |
$begingroup$
You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
$endgroup$
– John Wayland Bales
Dec 7 '18 at 6:11
$begingroup$
@JohnWaylandBales Thanks for this... Will check it out
$endgroup$
– Some_guy
Dec 7 '18 at 6:17
$begingroup$
You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
$endgroup$
– John Wayland Bales
Dec 7 '18 at 6:11
$begingroup$
You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
$endgroup$
– John Wayland Bales
Dec 7 '18 at 6:11
$begingroup$
@JohnWaylandBales Thanks for this... Will check it out
$endgroup$
– Some_guy
Dec 7 '18 at 6:17
$begingroup$
@JohnWaylandBales Thanks for this... Will check it out
$endgroup$
– Some_guy
Dec 7 '18 at 6:17
add a comment |
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$begingroup$
You can integrate the cross-sectional areas of the intersections of parallel planes, but that is not a trivial exercise since the cross-sections of the cube parallel to a given plane can be triangles, rectangles, pentagons or hexagons. youtube.com/watch?v=aSokFEpoJFM
$endgroup$
– John Wayland Bales
Dec 7 '18 at 6:11
$begingroup$
@JohnWaylandBales Thanks for this... Will check it out
$endgroup$
– Some_guy
Dec 7 '18 at 6:17