Mumbai University > Mechanical Engineering > Sem 7 > CAD CAM CAE

Marks: 5 Marks

Year: Dec 2016

The Different types of curve equation used are

1. Bezier curves equations

2. B spline curves equations

3. Hermite curves splines equations

A. Bezier Curves Equations

The No. of Control Points = 4

$\therefore \text{The Degree of the curve one - The No. of Points} \\ =4-1 \\ =3 \\ \therefore \text{Degree of the Curve} = 3$

Bezier Matrix

$M_B=\begin{bmatrix}-1 & 3 & -3 & 1 \\ 3 & -6 & 3 & 0 \\ -3 & 3 & 0 & 0 \\ 1 & 0 & 0& 0 \end{bmatrix} G_B=\begin{bmatrix}P_1 \\ P_2 \\ P_3 \\ P_4 \end{bmatrix} \\ P(u)=u . M_B \times G_B \\ P(u) = (1-4)^3 P_1 + 3u(1-u)^2+3u^2(1-u)P_3+P_4 \times u^4$

Properties of Beizier Curve

1. The entire curve lies in the comes hall

2. The number of control points 5 more that the degree of the curve.

   i.e for No. of points = 4, degree of the curve= 3

3. the curve passes throught the 1st and last point

4. The curve is always tangential to 1st and last point.