Which projection originates from a point on the surface of the sphere onto the plane?

Which projection originates from a point on the surface of the sphere onto the plane?

• A. Gnomonic Projection
• B. Orthographic Projection
• C. Stereographic Projection
• D. Lambert Conformal Projection

Answer: (C)

The key idea is where the projection rays come from. In stereographic projection, you project from a point that lies on the surface of the sphere onto a plane. Imagine a line starting at a specific point on the sphere and extending to intersect a plane; every other point on the sphere maps to a unique point on that plane along such a line. This setup—origin on the sphere—distinguishes stereographic projection from the others: gnomonic uses the sphere’s center as the projection origin, orthographic uses rays from infinity, and Lambert conformal describes a type of projection chosen for conformality rather than a specific origin point on the sphere. An added note: stereographic projection typically takes the plane to be tangent to the sphere opposite the projection point, making the projection point map to infinity while preserving angles locally, which helps explain why it’s the correct choice for this description.

The key idea is where the projection rays come from. In stereographic projection, you project from a point that lies on the surface of the sphere onto a plane. Imagine a line starting at a specific point on the sphere and extending to intersect a plane; every other point on the sphere maps to a unique point on that plane along such a line. This setup—origin on the sphere—distinguishes stereographic projection from the others: gnomonic uses the sphere’s center as the projection origin, orthographic uses rays from infinity, and Lambert conformal describes a type of projection chosen for conformality rather than a specific origin point on the sphere. An added note: stereographic projection typically takes the plane to be tangent to the sphere opposite the projection point, making the projection point map to infinity while preserving angles locally, which helps explain why it’s the correct choice for this description.