In geometry, an octant of a sphere is a spherical triangle with three right angles and three right sides. It is one face of a spherical octahedron.
For a sphere embedded in three-dimensional Euclidean space, the vectors from the sphere's center to each vertex of an octant are the basis vectors of a Cartesian coordinate system relative to which the sphere is a unit sphere. The spherical octant itself is the intersection of the sphere with one octant of space.
Uniquely among spherical triangles, the octant is its own polar triangle.[1]
The octant can be parametrized using a rational quartic Bézier triangle.[2]
^Coxeter, H. S. M. (1982). "Rational spherical triangles". The Mathematical Gazette. 66 (436): 145–147.
^Farin, G.; Piper, B.; Worsey, Andrew J. (1987). "The octant of a sphere as a non-degenerate triangular Bézier patch". Computer Aided Geometric Design. 4 (4): 329–332.
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