How do you find the intersection between a line and a sphere?

How do you find the intersection between a line and a sphere?

Intersection of a Line and a Sphere (or circle) If it equals 0 then the line is a tangent to the sphere intersecting it at one point, namely at u = -b/2a. If it is greater then 0 the line intersects the sphere at two points.

How do you know if a sphere intersects?

Given two spheres of equal radii, they will intersect if and only if the distance between their centers is less than or equal to two times their common radius.

What is the intersection of a plane and a sphere through its center?

A circle of a sphere is a circle that lies on a sphere. Such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. A circle on a sphere whose plane passes through the center of the sphere is called a great circle; otherwise it is a small circle.

What is a line segment on a sphere?

The radius of a sphere is a line segment whose one endpoint lies on the sphere and whose other endpoint is the center. A great circle of a sphere is the intersection of a plane that contains the center of the sphere with the sphere. Its diameter is called an axis and the endpoint of the axes are called poles.

Can parametric curves self intersect?

If the iso-parametric curves S(u, t0), t0 constant, are all planar, S(u, t) holds self-intersecting iso-parametric curves.

What is the number of possible intersections between a line and a circle?

A line can intersect a circle in three possible ways, as shown below: 1. We obtain two points of the intersection if a line intersects or cuts through the circle, as shown in the diagram below. We can see that in the above figure, the line meets the circle at two points.

What is a line that intersects a circle at one point?

A line that intersects a circle at exactly one point is called a tangent line.

Do spheres intersect?

Intersection of two spheres A sphere intersects the plane at infinity in a conic, which is called the absolute conic of the space. The intersection curve of two sphere always degenerates into the absolute conic and a circle. Therefore, the real intersection of two spheres is a circle.

How do you describe the intersection of a sphere and a plane?

Such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. A circle on a sphere whose plane passes through the center of the sphere is called a great circle; otherwise it is a small circle.