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 [6] 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.