And because of the Q point in the saddle-shaped space curve
, according to (3), we have
Analogously, osculating curves in the Minkowski space-time are defined in  as the space curves
whose position vector (with respect to some chosen origin) always lies in its osculating space, which represents the orthogonal complement of the first binormal or second binormal vector field of the curve.
The birational mappings of implicitly defined space curves
find numerous applications in geometric modeling and computer graphics since they provide an efficient way of manipulating curves in space by processing curves in the plane.
If [alpha]is a spacelike space curve
with a spacelike principal normal N, then the following Frenet formulas hold
Chen, When does the position vector of a space curve
always lie in its rectifying plane?, Amer.
They cover vector representation of geometric entities, two-dimensional and three-dimensional transformation, the parametric representation of planar curves and space curves
, the parametric representation of surfaces, windowing and clipping, generating a three-dimensional model, projections, graphic programs in C language, OpenGL with computer graphics, and programming graphics using OpenGL.
The research on the curvature-based energy for space curves
began with Bernoulli and Euler's studies on elastic thin beams and rods.
Wang, "Mathematical model and simulation of pump turbine with characteristic space curves
," Journal of Hydroelectric Engineering, vol.
In the study of fundamental theory and the characterizations of space curves
, the corresponding relations between the curves are a very fascinating problem.
Fujivara, On Space Curves
of Constant Breadth, Tohoku Math.
But what dominates the apartment is an enormous pillar, around which the L-shaped living space curves
with John's own little studio tucked away in the space beneath the mezzanine.