Spherical splines and orientation interpolation

Constructing spherical curves by interpolation

“…With those methods one can construct C 1 -continuous curve on sphere. Literature [2] described a method to design C 1 -continuous interpolation on sphere by two weighted spatial rotations. However, in geometric modeling, Geometric continuity is more popular then algebraic continuity.…”

“…He extended de Casteljau's algorithm to sphere, replacing straight line segments by geodesic circle and replacing ratios of Euclidean distances by the ratios of geodesic distances. Pobegailo proposed an approach for C 1 interpolation and blending 0965 on a sphere [2]. Crouch et al [3,4] reported generalization of splines curves on sphere.…”

Generation of spherical non-uniform rational basis spline curves and its application in five-axis machining

“…Generating smooth spherical curves on unit sphere can be applied in many situations, such as designing spherical curve, generating smooth rigid motion in computer animation, and tool path generation of multi-axis machining. 1–4 Since B-spline has many good properties, it has already been widely used in curves and surface designs. 5–9 Therefore, much effort has been made to extend B-spline curve in Euclidean space to the construction of spherical B-spline curves.…”

“…The interpolation spherical curve has C 1 continuity at the curve joint. In 1994, Pobegailo 2 proposed a method for designing spherical curves by two weighted spatial rotations. The generated curve has C 1 continuity, local control, and invariance orthogonal transformations of coordinate system.…”