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math: Clarify scalar multiples must be the same for D too

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eggy 2021-06-08 14:17:03 -04:00
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@ -605,7 +605,7 @@ $$d=\frac{|D_1-D_2|}{\sqrt{A^2+B^2+C^2}}$$
Two planes are parallel if their direction vectors are scalar multiples of each other:
$$\vec n_1 = k\vec n_2$$
If they are also coincident, the D-values will also be identical:
If they are also coincident, the D-values will also be identical or equal to the same scalar multiple as the normal:
$$D_1=D_2$$
Otherwise, the planes intersect, the line along which is equal to the cross product between the two direction vectors.
@ -619,7 +619,7 @@ When looking at three planes:
If all three normals are scalar multiples:
- If all three $D$-values are scalar multiples, the planes are parallel and coincident and they have infinite points of intersection along the plane equation.
- If all three $D$-values are those same scalar multiples, the planes are parallel and coincident and they have infinite points of intersection along the plane equation.
- Otherwise, there are no solutions and the planes are parallel and distinct and/or parallel and coincident for two.
If two normals are scalar multiples: