Hello Thanasis,
Here is the equation in the computer notation:
x(t) = (1-t)*(1-t)*p0.x + 2*t*(1-t)*p1.x + t*t*p2.x
y(t) = (1-t)*(1-t)*p0.y + 2*t*(1-t)*p1.y + t*t*p2.y
p0, p1, p2 - control points
Best Regards,
Alexey
Pete wrote:
Hello Thanasis,
don't really know if this belongs here...
In general the equation of a (non-rational) bezier segment is
b(t) = \sum_{i=0}^n b_i \cdot B_i^n( t ),
b_i your n+1 control points,
B_i^n the Bernstein-Polynomials of degree n,
t \in [0,1].
You can search wikipedia for the properties of bernstein polynomials. They are
defined as:
b_k^n(t) := \frac{n!}{k! (n-k)!} t^k (1-t)^{(n-k)},
t\in R, k=0, ..., n.
Just put this all together for n=2 and you should be fine. Of course you can
also search the web for the algorithm of de Casteljau or an algorithm
following the bezier-horner-schema.
Grüße Pete
On Friday 31 March 2006 12:57, Thanasis (Hotmail) wrote:
| Hello to everyone,
|
| i have illustrated a quadratic bevier curve from point P1 to point P2 using
| a control point C. What is the equation of the quadratic curve in order to
| find some other points on it?
|
|
| Thanks in advance
| Thanasis
|
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