Visualization of Infinitesimal Bending of Curves

Curvebend graphical tool for presentation of infinitesimal bending of curves

“…Infinitesimal bending of curves at E 3 was studied at [8], [20], [21] and [22]. This work presents a follow up of the results given at [20].…”

Ruled surfaces obtained by bending of curves

“…Theorem 3.2 [10] The necessary and sufficient condition for z(u) to be an infinitesimal bending field of a curve r is to be…”

“…Theorem 3.3 [10] Infinitesimal bending field for a regular curve r is We now want to visualize the ruled surface obtained by bending (see Figure 1):…”

“…The bending of curves and surfaces is related to biology and medicine [12,13]. A few suggestions for further reading about bending of curves and surfaces are [7,8,10,11]. The relation between ruled surfaces and bending of curves has motivated us to conduct this study.…”

Characterization of dual curves using the theory of infinitesimal bending

“…Infinitesimal bending theory has numerous applications in mathematics and mechanics, especially in the theory of thin shells. Some recent papers on this topic are [8][9][10][11][12][13][14][15][16][17] It is interesting to study the influence of infinitesimal bending on ruled surfaces and their flexibility. As is well known, a surface is said to be ruled if at every point of the surface there is a straight line lying on the surface.…”