1
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2answers
53 views

Fastest way to obtain the parametric value t of a bezier curve, for a given set x coordinates.

The problem is the following: Having a bezier curve B(t) we have coordinate x from the curve, and we need to obtain the y values from it, hence we need to compute the t values. What is the fastest ...
1
vote
1answer
28 views

How can I apply Newton's method with boundaries?

I am trying to use Newton's method to minimize the distance between a line segment and a bezier curve. The distance function $f(x, t)$ that I'm minimizing is only defined for $x_1 \le x \le x_2$ and ...
0
votes
1answer
80 views

Given a control polygon, how do you find a tangent vector at a given point (CAGD, Bezier Curve)?

I am having a hard time with my Computer Aided Graphic Design class. I am presented with the bezier control polygon (in a Mathematica statement): P = Table[{x^2, x^3, 0}, {x, 4,7}] And the ...
0
votes
1answer
37 views

Subdividing a Bézier patch

I have a tensor-product Bézier patch and I want to subidivide this adding a curve inside the patch, which creates two rectangular subpatches. I found that the following statement holds: "if we ...
1
vote
1answer
630 views

Finding a point on a bezier surface using De Casteljau's algorithm

Given $16$ control points $(x,y,z)$ of a bicubic bezier patch, how do I use De Casteljau's algorithm to generate a point $(s,t) = (0.5, 0.2)$ on the surface? As far as I understand, this kind of ...
1
vote
0answers
321 views

Relation between Hermite interpolation and Bezier curve

I will really appreciate if someone can explain me the relation between Hermite interpolation and Bezier Curve. For example, $p(0)=1,p(3)=2,p'(0)=1,p'(3)=1$, how do we do the Hermite interpolation? ...
1
vote
0answers
57 views

I came across a paradoxical situation when applying Casteljau algorithm

The example is like this: Given 3 points $p(0)=2,p(1)=1,p(3)=1$.The question asks us to apply the Casteljau algorithm to evaluate the Bezier curve b(u) for the given Bezier polygon at $u=2$. I did the ...
1
vote
1answer
242 views

Relation between Bezier Curve, Bernstein polynomial and control polygon

I am currently learning numerical method and I am somehow confused about the Bezier Curve, Bernstein polynomial and control polygon. For example, if we have a curve $p(u)=-12u^2+12u+1$,and we want to ...
3
votes
0answers
212 views

Approximating a system of differential equations as a Bézier curve

I am looking for a general transform to approximate the solution to an n-dimensional system of differential equations and initial conditions as a cubic or quadratic Bézier curve. Sorry if my ...