Question

What is a Bezier curve? Explain the Mathematical expression Bezier Curves. Derive all the properties of Bezier curves. A Cubic Bezier curve has control points P0 (0, 0); P1 (5, 40); P2 (40, 5); P3 (50, 15). Determine 2 more points on the same Bezier curve. Also, discuss the Parametric Continuities and Geometric Continuities of Bezier Curves, with suitable expressions, equations and examples

16 Sep 2022
Answer :
Word Count : 868

Bezier curves are mathematical curves that are widely used in computer graphics, animation, and industrial design. They are named after Pierre Bézier, a French engineer who developed the mathematical basis for these curves in the 1960s.

A Bezier curve is defined by a set of control points, which are used to determine the shape of the curve. The simplest form of a Bezier curve is a straight line, which is defined by two control points. A cubic Bezier curve is defined by four control points and can have a more complex shape.

Mathematically, a cubic Bezier curve is defined by the following equation:

B(t) = (1-t)^3 P0 + 3(1-t)^2 t P1 + 3(1-t) t^2 P2 + t^3 P3

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