Unlock the power of 3D modeling with our free Quadratic Bezier Curve Surface Points Calculator. This essential tool helps designers and developers easily compute specific (X, Y, Z) coordinates on a complex Bezier surface. Simply input your 9 control points and the desired U and V parameters to generate precise surface points for your projects, from CAD design to advanced computer graphics.
Formula:
A point P(u,v) on a Quadratic Bezier Surface is defined by a 3x3 grid of 9 control points Pi,j and two parameters u, v (where 0 ≤ u,v ≤ 1). The formula is:
P(u,v) = ∑i=02 ∑j=02 Bi,2(u) Bj,2(v) Pi,j
Where Bk,2(t) are the quadratic Bernstein polynomials:
- B0,2(t) = (1-t)2
- B1,2(t) = 2t(1-t)
- B2,2(t) = t2
Variables Explained:
- u, v: Surface parameters, ranging from 0 to 1 (e.g., 0.5, 0.3).
- Pi,j: The X, Y, Z coordinates of the 9 control points that define the surface (e.g., P00x, P00y, P00z).