Intersection Between Two Planes Math
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Lines of intersection between planes sometimes we want to calculate the line at which two planes intersect each other.
Intersection between two planes math. Where p is the point of intersection t can go from inf inf and d is the direction vector that is the cross product of the normals of the two original planes. It s all standard linear algebra geometry in three dimensions. A point in the 3d coordinate plane contains the ordered triple of numbers x y z as opposed to an ordered pair in 2d. 3 x y 4 2x 4y solve it and you will get the equation of the intersection line.
Next we nd the direction vector d for the line of intersection by computing d n. First find the equation of the line of intersection of the planes determined by the two triangles. The normal vector n 1 of x 1 5x 2 3x 3 11 is 2 4 1 5 3 3 5 and the normal vector n 2 of 3x 1 2x 2 2x 3 7 is 2 4 3 2 2 3 5. Find a vector equation of the line of intersections of the two planes x 1 5x 2 3x 3 11 and 3x 1 2x 2 2x 3 7.
This is found by noticing that the line must be perpendicular to both plane normals and so parallel to their cross product this cross product is zero if and only if the planes are parallel and are therefore non intersecting or. Note that this will result in a system with parameters from which we can determine parametric equations from. And. Then find the at most four points where that line meets the edges of the triangles.
We can accomplish this with a system of equations to determine where these two planes intersect. Two intersecting planes always form a line if two planes intersect each other the intersection will always be a line. The line of intersection between two planes. The vector equation for the line of intersection is given by r r 0 tv r r.
First we read o the normal vectors of the planes. Where are normalized is given by where. The following equation results from setting z1 z2.
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