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Questions tagged [bezier-curve]

Questions on Bézier curves, which are used for numerical analysis with applications in computer graphics.

Bézier curves are widely used in computer graphics to model smooth curves by using control points. Affine transformations of the curve correspond to affine transformations of the control points. The curve is contained in the convex hull of its control points. On computers, these points are often graphically displayed and used to manipulate the curve by dragging the control points.

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How to create cubic bezier curve using control points?

How can I create the cubic bezier curve to (6,2) using control points (2,3.8) and (3.8,2)? What I have tried: I considered all the points as the control points P0=(2,3.8) P2=(6,2) P1=(3.8,2) Consider the below equation: ∑ pi Bi,n (u) where B…
Ankur_009
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Calculating number of bezier curve graph points

I want to paint a smooth bezier curve in a 2D pane. The number of control points is probably irrelevant to my question. The question is, in the loop of $B(t)$ calculation, https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Explicit_definition, how can…
k_kaz
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Get value of control point if weight is zero.

In a rational Bezier curve, the weighted control points are given as $$\mathbf{P}^w=(wx, wy, wz, w)=(X,Y,Z,W).$$ We can extract the control point $\mathbf{P}$ from $\mathbf{P}^w$ by dividing each of the coordinates in $\mathbf{P}^w$ by the last…
nonremovable
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Calculate intermediary control points in Cubic Bezier Curves

I need to programatically generate two-dimensional circles of various dimensions, knowing only their radius and position. The circles will be drawn by employing 4 cubic Bezier curves. How should I calculate the Cartesian coordinates of the two…
A Dwarf
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Solve for y(x) from y(t, u) and x(t, u) where $ u = 1 - t$

I've been trying to get wolfram alpha to solve these equations and leave the coefficients alone (Bezier control points), but I can't figure it out! I want to eliminate t and u, but leave all other coefficients alone u = t - 1 y = A*u^3 + 3*B*u^2*t +…
neaumusic
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Bezier curve, change of parametrized variable

From the NURBS book (pg 48 B-spline basis functions), given that we have a Bezier curve $C_1(u)$, the following condition holds: $\frac{1}{u_1 - u_0} C'_1(v = 1) = C'_1 (u_1)$ for $u_0
c0der
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What are pieces or sections in Bezier curves?

What are pieces or sections in Bezier curves? Specifically I'm doing this computer assignment: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-837-computer-graphics-fall-2012/assignments/MIT6_837F12_assn1.pdf Where in the…
mavavilj
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Cubic Bezier Curves - Calculate Y for any given X

Possible Duplicate: Is there an explicit form for cubic Bézier curves? I want to calculate Y for any given X of a bezier to help me chart a graph. X represents time and Y represents distance from an object. I got this formula for cubic…
Beakie
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Compute intersection between bezier curve and a line

Is there ready analytical solution of a set of two equations describes intersection between bezier curve and line
Andrey Nekrasov
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Are there any cubic bezier curve that cannot imitate by multiple quadratic bezier curve?

I want to make a line curve system with bezier curve. And I want to use only quadratic bezier curve so it can be extend and control easily, it can add control point anywhere and more intuitive But I'm curious that it might not be cover some kind of…
Thaina
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Bezier Curve Problem, finding missing control point

Given the two sets of control points: A: $(1, 2)$, $(2, 3)$, $(a, b)$, $(4, 2)$. B: $(4, 2)$, $(c, d)$, $(5, 5)$, $(6, 4)$. Find values for the control points $(a, b)$ and $(c, d)$ so that the resulting composite Bezier curve is smooth at the…
Hannah
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Control vertices of nonparametric Bézier curve $y = 2x –2x^2$

My teacher solved this problem, but I don't know how he get that the: $$y_0-2y_1+y_2 = -2$$ $$-2y_0 + 2y_1 = 2$$ $$y_0 = 0$$ Here is the full example with solution, step by step: $$y=2x-2x^2$$ $$y=2t-2t^2$$ $$y(t)=y_0 (1-t)^2+ y_1 2(1-t)t+y_2…
Runtime Terror
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Power Function as a Cubic Bezier Curve

With: A Power Function $f(x)=x^n$, where $x\in[0,1]$ and $n\ge0$. A Cubic Bezier with points $P_0, P_1, P_2, P_3$ such that $P_0=(0,0)$ and $P_3=(1,1)$. The Cubic Bezier function is $B(t)=(1-t)^3P_0+3(1-t)^2tP_1+3(1-t)t^2P_2+t^3P_3$. Given: The $n$…
Yay295
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getting angle between tangent of Bézier curve and an y axis

(sorry for the draw) I try to get the blue angle , i thought it was easy but... the curve is a Bézier curve. the black dot shows the tangent of D I know position of A B C D. I tried to get the angle by addition of angle a and angle b the point F…
eephyne
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A function that can smooth out line joining three points

I want to know if there is a function with which we can smooth out line joining two( or more )points . I've read we can do it with Quad and cubic splines or something but I am not clear with them. i want a simple function which can be computed…
Rahul Verma
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