A class of quasi Bézier curves based on hyperbolic polynomials

Adjustable Bézier Curves with Simple Geometric Continuity Conditions

“…. , m , are defined by (13), and the intermediate points R l i are defined recursively by Recursive evaluation process of an adjustable Bézier curve. The red circles, green triangles, blue stars, black stars, yellow triangles, purple rhombuses represent the points received in step 1 to step 6 of the recurrence, respectively.…”

“…To overcome this shortcoming, many attempts have been made to incorporate shape parameters into the Bézier model [2][3][4][5][6][7][8][9][10][11][12][13]. These models are constructed on different spaces, such as polynomial function space [2][3][4][5][6][7][8], trigonometric function space [9][10][11][12], and hyperbolical function space [13]. All the curves constructed in [2][3][4][5][6][7][8][9][10][11][12][13] are extensions of the classical Bézier curves.…”

“…These models are constructed on different spaces, such as polynomial function space [2][3][4][5][6][7][8], trigonometric function space [9][10][11][12], and hyperbolical function space [13]. All the curves constructed in [2][3][4][5][6][7][8][9][10][11][12][13] are extensions of the classical Bézier curves. They inherit most of the properties of the Bézier method and enjoy other properties ideal for modeling.…”

“…In general, the higher the requirement for smoothness is, the more complex the smooth joining condition is. Most of the new methods [2][3][4][5][6][8][9][10][11][12][13] in the literature have not reduced the difficulty of this problem. Yan and Liang present a special family of Bézier curves that have the same structure as the quadratic Bézier curves [7].…”

Geometric shapes of C-Bézier curves

“…They include the p-Bézier [2], the quasi Bézier [3], the C-Bézier [4,5], the AH-Bézier [6], the AHT-Bézier [7], the Bézier-like models using complex numbers [8][9][10], and so on.…”