Can the intersection of a plane and line segment be a line segment?

Can the intersection of a plane and line segment be a line segment?

In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. Otherwise, the line cuts through the plane at a single point.

Can a segment intersect a plane?

Represent the plane by the equation ax+by+cz+d=0 and plug the coordinates of the end points of the line segment into the left-hand side. If the resulting values have opposite signs, then the segment intersects the plane. If you get zero for either endpoint, then that point of course lies on the plane.

Can the intersection of a plane and a ray can be a line?

7) Opposite Rays are collinear, share a common endpoint and extend in ::opposite directions. 8) . The intersection of a plane and a line lying within the plane itself, is the line itself. A Postulate is an accepted statement of fact based upon observations.

Where does a ray intersect a plane?

Ray-Disk Intersection A disk is generally defined by a position (the disk center’s position), a normal and a radius. First we can test if the ray intersects the plane in which lies the disk.

Does a line extend forever?

A point is an exact location in space. A line is infinitely many points that extend forever in both directions. A plane is infinitely many intersecting lines that extend forever in all directions.

Can three planes be a ray?

To answer the original question, 3 planes can intersect in a point, but cannot intersect in a ray.

Can two planes intersect at a ray?

The intersection of two planes is a line. If the planes do not intersect, they are parallel. They cannot intersect at only one point because planes are infinite.

Do line segments go on forever in both directions?

A line is a straight path on a plane that extends forever in both directions with no endpoints. A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.

What do you call the points lying on the same line?

Three or more points that lie on the same line are collinear points . Example : The points A , B and C lie on the line m . They are collinear.

What happens when a line does not intersect on a plane?

It also will return the contact point on the plane where the line intersects, if the line does not intersect, the function should still return the intersection point had the line segmenent had been a ray. I used the information and code from Christer Ericson’s Real-time Collision Detection but I don’t think im implementing it correctly.

How to test line segment and plane intersection?

I’m trying to implement a line segment and plane intersection test that will return true or false depending on whether or not it intersects the plane.

Are there any other cases where there is an intersection?

In all other cases there will be an intersection. On to the intersection computation : All points X of a plane follow the equation Where N is the normal and d can be found by putting a known point of the plane in the equation. Onto the ray, all points s of a line can be expressed as a point p and a vector giving the direction D :

Why do you use dot product in plane intersection?

Note that you’re computing the dot product between the plane’s normal vector (a vector) and the ray’s origin point (a point in space). This seems weird because it means that depending on where the ray originates in space, the scaling factor you use for the ray changes.