Intersection of vector and plane

p0 Is the intersection of a vector and a plane

p Is a point on the plane （ Any point can take the center point of the plane ）

n Is the plane normal vector

d Is the distance from the starting point of the vector to the intersection point

L Is the vector direction

LP As a starting point （ Any point on a straight line ）

* Multiplication

· Point multiplication

type 1：(p0-p)·n =0; The vector on the plane is perpendicular to the normal vector

type 2：p0=LP+d*L;// Vector starting point + Vector direction *（ The distance between the intersection and the starting point is the intersection ）

deduction ：

Will type 2 Bring in 1 have to

(LP+d*L-P)·n=0;

Dot product satisfies commutative law have to

(LP-P)·n+d*L·n=0

0-(p-LP)·n=dL·n

(0-p+LP)·n=dL·n

(p-LP)·n=dL·n

Dot multiplication satisfies the law of association have to

type 3： d=(p-LP)·n/L·n

p It is known that LP It is known that n It is known that L It is known that

Bring in the calculated distance

take type 3 The calculated result is carried into the formula 2 Get intersection