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2. Plane–plane intersection - Wikipedia

   en.wikipedia.org/wiki/Plane–plane_intersection

   Download as PDF; Printable version ... (i.e. on their intersection), so insert this equation into each of the equations of the planes to get two simultaneous ...

3. Intersection (geometry) - Wikipedia

   en.wikipedia.org/wiki/Intersection_(geometry)

   There are two possibilities: if =, the spheres coincide, and the intersection is the entire sphere; if , the spheres are disjoint and the intersection is empty. When a is nonzero, the intersection lies in a vertical plane with this x-coordinate, which may intersect both of the spheres, be tangent to both spheres, or external to both spheres.

4. Line–sphere intersection - Wikipedia

   en.wikipedia.org/wiki/Line–sphere_intersection

   Intersection in two points. Methods for distinguishing these cases, and determining the coordinates for the points in the latter cases, are useful in a number of circumstances. For example, it is a common calculation to perform during ray tracing .

5. Line–plane intersection - Wikipedia

   en.wikipedia.org/wiki/Line–plane_intersection

   The three possible plane-line relationships in three dimensions. (Shown in each case is only a portion of the plane, which extends infinitely far.) 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. It is the entire line if that line is embedded in the plane, and is ...

6. Intersection curve - Wikipedia

   en.wikipedia.org/wiki/Intersection_curve

   The intersection of two planes. The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a) the intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc.), c) intersection of two quadrics in special cases. For the general case, literature provides algorithms ...

7. Sphere - Wikipedia

   en.wikipedia.org/wiki/Spheres

   The set of all spheres satisfying this equation is called a pencil of spheres determined by the original two spheres. In this definition a sphere is allowed to be a plane (infinite radius, center at infinity) and if both the original spheres are planes then all the spheres of the pencil are planes, otherwise there is only one plane (the radical ...

8. Great circle - Wikipedia

   en.wikipedia.org/wiki/Great_circle

   The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space R n + 1.

9. Spherical geometry - Wikipedia

   en.wikipedia.org/wiki/Spherical_geometry

   This is more than an analogy; spherical and plane geometry and others can all be unified under the umbrella of geometry built from distance measurement, where "lines" are defined to mean shortest paths (geodesics). Many statements about the geometry of points and such "lines" are equally true in all those geometries provided lines are defined ...