scholarly journals Bézier Triangles with G2 Continuity across Boundaries

Symmetry ◽  
2016 ◽  
Vol 8 (3) ◽  
pp. 13 ◽  
Author(s):  
Chang-Ki Lee ◽  
Hae-Do Hwang ◽  
Seung-Hyun Yoon
Keyword(s):  
G2 Continuity ◽  
Bézier Triangles

G1 and G2 Continuity Between (SBR) Surfaces

1991 ◽  
pp. 33-36 ◽  
Author(s):  
J.L. Bauchat ◽  
J.C. Fiorot ◽  
P. Jeannin
Keyword(s):  
G2 Continuity

Gregory-type patches bounded by low degree intergral curves for G2 continuity

1996 ◽  
Vol 13 (9) ◽  
pp. 793-810
Author(s):  
Kenjiro Takai Miura ◽  
Kuo-King Wang
Keyword(s):  
Low Degree ◽  
G2 Continuity

scholarly journals Repairing the cerebral vascular through blending Ball B-Spline curves with G2 continuity

2016 ◽  
Vol 173 ◽  
pp. 768-777 ◽  
Author(s):  
Xingce Wang ◽  
Zhongke Wu ◽  
Juncheng Shen ◽  
Ting Zhang ◽  
Xiao Mou ◽  
...  
Keyword(s):  
B Spline ◽  
Spline Curves ◽  
G2 Continuity ◽  
Cerebral Vascular

Smoothness of C-Bezier Curves

2000 ◽  
Author(s):  
Manhong Wen ◽  
Kwun-Lon Ting
Keyword(s):  
Shape Control ◽  
Control Point ◽  
Design Procedure ◽  
Design Parameters ◽  
Control Points ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Point Distribution ◽  
G1 Continuity ◽  
G2 Continuity

Abstract This paper presents G1 and G2 continuity conditions of c-Bezier curves. It shows that the collinear condition for G1 continuity of Bezier curves is generally no longer necessary for c-Bezier curves. Such a relaxation of constraints on control points is beneficial from the structure of c-Bezier curves. By using vector weights, each control point has two extra free design parameters, which offer the probability of obtaining G1 and G2 continuity by only adjusting the weights if the control points are properly distributed. The enlargement of control point distribution region greatly simplifies the design procedure to and enhances the shape control on constructing composite curves.

scholarly journals Optimization of Tooth Root Profile Using Bezier Curve with G2 Continuity to Reduce Bending Stress of Asymmetric Spur Gear Tooth

2018 ◽  
Vol 237 ◽  
pp. 03010 ◽  
Author(s):  
Priyakant Vaghela ◽  
Jagdish Prajapati
Keyword(s):  
Stress Concentration ◽  
Gear Tooth ◽  
Spur Gear ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Tooth Root ◽  
Geometric Continuity ◽  
Bending Stress ◽  
Gear Design ◽  
G2 Continuity

This research describes simple and innovative approach to reduce bending stress at tooth root of asymmetric spur gear tooth which is desire for improve high load carrying capacity. In gear design at root of tooth circular-filleted is widely used. Blending of the involute profile of tooth and circular fillet creates discontinuity at root of tooth causes stress concentration occurs. In order to minimize stress concentration, geometric continuity of order 2 at the blending of gear tooth plays very important role. Bezier curve is used with geometric continuity of order 2 at tooth root of asymmetric spur gear to reduce bending stress.

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