Questions on Bézier curves, curves that are frequently used in computer graphics.

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Bézier curve limits

Can be any curve of any shape (without sharp edges) described by Bézier curve with unlimited (but finite) number of control points? The answer to the question above would probably be no, because I ...
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2answers
40 views

Is it possible to generate a circle with a Bezier curve?

I am designing an algorithm that generates shapes of bezier curves. Each output are control points for a single curve. In some cases, it should return a circle. Which control points does the ...
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0answers
10 views

geometric modelling-bezier curves [closed]

homework: please help to solve this- Let P0(1,3), P1(4,6), P2(5,1) and P3(2,1) are the four control points of a cubic Bezier curve. Determine the end tangent vector.
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1answer
15 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 ...
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1answer
19 views

Intersect Ray (Line) vs Quadratic Bezier Triangle

I'm trying to find the intersection between a line segment and a quadratic bezier triangle for my OpenCL real time raytracer. The main recomendations I've seen are to try subdivision, or tensor ...
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1answer
35 views

What are some alternative ways of describing n-dimensional surfaces using control points other than Bezier surfaces?

I'm interested in problems involving geometric constraints and curve subdivision. I noticed that most of these problems describe the curves/surfaces using the Bezier form. I wanted to know if there ...
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1answer
37 views

Bézier curves and optimization

I have a very peculiar problem. Assuming that you know how B-Splines or Bézier Curves work, you may also know that if we assume the result of the function, let's say tri-dimmensional, as a position in ...
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1answer
20 views

keeping c1 continuity in joining several bezier curve

I have some complex curves, I separate the long curves to smallest one to be able to fit them with Bezier curve. However, my Bezier curve has no C1 continuously, if I force C1 continuously, my curves ...
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1answer
27 views

Reparametrize of cubic bezier curve in arclength

I am looking for a way to re-parametrize the cubic Bezier curve in t domain to cubic bezier curve in S (arclength) domain. Thanks
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1answer
49 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 ...
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1answer
80 views

Gradient of a rational Bezier curve

I'd appreciate help working out the gradient of a rational Bezier curve $C = (\,x(t) \,, \,C_y(t) \,)$. I know that the gradient $g$ of a the parametric curve is $$ g(t) = \left( \frac{dy(t)}{dt} ...
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0answers
64 views

How To Calculate Control Points of a Cubic Bezier Curve from Boundary Conditions

I need to calculate the control points $P_1$ and $P_2$ of a cubic bezier curve such that the enclosed area of the resulting curve equals zero (see picture). The points $P_1$ and $P_2$ must be located ...
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2answers
46 views

How to create a nice sky route

I'm trying to find a nice algorithm to trace a sky route between 2 points of a planet. Here is where I am : https://dl.dropboxusercontent.com/u/17657227/migrationGlobe/index.html (or here ...
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0answers
31 views

Is there anything interesting about this figure constructed from a set of points and their barycentre?

Playing with the TikZ package for (La)TeX, I made a nice figure. Well, I think it is nice, anyway. You can ignore the distracting colours and the concentric circles, they are not important for this ...
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1answer
23 views

Degree elevation of weighted Bezier curve to an arbitrary degree

Following on from a past question about degree elevation of a rational Bezier curve, of degree $n$ by one to $n + 1$, I am now looking to derive a single expression for degree elevation by an ...
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0answers
17 views

How to find new co-ordinates for points on a line dragged as a bezier curve.

I have a line with a set of points. I captured the start point and the end point of the line and found two control points for a bezier curve using the linear parametric equation. I construct the ...
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0answers
17 views

Draw a parallel bezier curve [duplicate]

This may be a duplicate of Control points of offset bezier curve but I am not quite able to say so. Also, the answers linked there are just one level more abstract than is helpful to my limited ...
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1answer
45 views

How to apply perspective transform to Bezier curve?

I found that both Bezier curves and B-splines are described with a formula $p(t)=\sum\limits_{i=0}^d B^i_m p_i$ but in the case of B-splines $B^i_m$ are B-spline blending functions, while for Bezier ...
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0answers
37 views

Spline interpolation problem akin to Bezier spline

Given three pairwise distinct points $p_1, p_2, p_3 \in \mathbb{R}^2$, I'd like to find a function $f: \mathbb{R} \to \mathbb{R}^2$ with at least $f \in C^1$ such that $f(0) = p_1, f(1) = p_3, f'(1) ...
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1answer
219 views

Find value of '$t$' at a point on a cubic Bezier curve

I have a cubic Bezier curve, and I need to divide it and create same curve between point on the original curve and the end point of the original curve. From my research, I found the DeCasteljau ...
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1answer
36 views

Showing that Bezier curve length is less than its control polygon

This is a homework and pardon me for the huge gap of my Mathematics knowledge. After thinking and referencing for a few days I came up with something like following, appreciate help to comment whether ...
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1answer
432 views

how to calculate the normal vector for a bezier curve

Say we have a cubic Bezier curve (so 4 control points) named Q. I understand how to calculate the tangent at by taking the derivative of Q and substituting but i'm not sure how to calculate the normal ...
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1answer
100 views

Degree elevation of weighted Bezier curve

I'm having difficulty understanding the derivation of the formula for degree elevation of a weighted Bezier curve given here. The only information that's given is to project a Bezier curve info affine ...
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5answers
231 views

Parabolas through three points

We can draw an infinite number of parabolas that pass through three given points $A$, $B$, $C$ (in that order). For each such parabola, we take the tangent lines at $A$ and $C$, and intersect them to ...
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3answers
273 views

Formula to get a control point closest for a given point what belongs to this quadratic curve

We have a quadratic bezier curve, with control point A (red start), control point B (red end), and yellow point X what belongs to the curve and what you actually "drag" - so it should be the closest ...
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1answer
147 views

Find angle at point on bezier curve

I have two end points and two control points. I am using these points and this link. i have found a point on bezier curve. Now i would like to find angle at this point on bezier curve. Is there any ...
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1answer
110 views

X-axis coordinates of outer control points (only) for a Quadratic Bézier curve through 3 points

I am interested in the distance between the 2 outer (left & right: P0 & P2) control-points of a quadratic Bézier curve that goes through 3 data points. The curve's non-equidistant control ...
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1answer
27 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 ...
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1answer
97 views

How to calculate and curved line from given parameters.

Given the distance from the start to the end of an arc $d$, the maximum height of the arc $h$ and some control point to define the type of curve $c$ How might one calculate points on a curve? E.G. ...
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2answers
579 views

Control points of offset bezier curve

If I have a cubic Bezier segment specified by two endpoints and two control points, how can I find an offset curve which is "parallel" to the original at some given distance, after i have determined ...
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1answer
35 views

I have a function which depends on four parameters and a target value, how can I discover the value for the four parameters that hits my target value?

So I have an equation: $$F(s,t,u,v)=A$$ Where $A$ is some given value. Is there an iterative method to discover the four parameters that will obtain my given $A$? If it helps, my function $F$ is a ...
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5answers
1k views

Is it possible to build a circle with quadratic Bézier curves?

i'm searching for a curve type with a minimum of functionality and maximum of usability. I run into quadratic Bézier curves and i wonder, if its possible to draw a circle with it.
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1answer
46 views

algorithm for Bezier curve with eleven control points

I would like to know the algorithm/ polynomial equation for a Bezier curve with eleven control points. Thanks in advance.
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1answer
183 views

Intersection of cubic bezier curve and circle

Let $B$ be a cubic Bézier curve with control points $P_0,P_1,P_2,P_3 \in \mathbb{R}^2$, and $C$ be a circle with center $P_C$ and radius $r$. How can I find all intersections of $B$ and $C$? Is ...
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2answers
130 views

What's the best way to calculate all of the points for a curve given only a few points?

I've been reading up on curves, polynomials, splines, knots, etc., and I could definitely use some help. (I'm writing open source code, if that makes a difference.) Given two end points and any ...
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1answer
75 views

Link points on a bicubic bezier patch

A bicubic bezier patch is defined by 16 control points. Given two points both lying on the patch boundaries, I think that if you link the two points you will end up with a cubic bezier curve in 3D. Is ...
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0answers
28 views

Bézier curves as portions of algebraic curves

Can every Bézier curve of any degree be defined as the algebraic (polynomial) curve of which it is a part and it's endpoints? If some Bézier's (such as those of degree $n$ or greater) cannot be ...
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1answer
599 views

Convert a B-Spline into Bezier curves

I have a B-Spline curve. I have all the knots, and the x,y coordinates of the Control Points. I need to convert the B-Spline curve into Bezier curves. My end goal is to be able to draw the shape on ...
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1answer
116 views

What is the general formula for NURBS curves?

Give me the general mathematical formula for NURBS curves, with special cases (B-spline and Bézier curves)
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1answer
88 views

Solving a Cubic Function

Can someone help me find my solution(s) to this cubic equation? x = a(1-t)^3 + 3bt(1-t)^2 + 3c(1-t)t^2 + dt^3 Where: ...
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1answer
51 views

Bezier curve, X position of reference points outside [Xstart, Xend]

Not quite sure whether this belongs here or on stackoverflow, but considering it's about the formula itself and not the implementation I'm placing it here. I'm required to implement bezier curves in ...
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1answer
449 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 ...
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1answer
186 views

Curve through four points — simple algebra??

The motivation for this is Bezier curves. But, if you don't know what these are, you can skip down to the last paragraph, where the problem is described in purely algebraic terms. Suppose I want to ...
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2answers
392 views

Forcing Bezier Interpolation

I found this very informative site that discusses forcing bezier interpolation and the site gives formulae for calculating the control points so that the curve goes through a set of four points, y0, ...
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0answers
33 views

Equation for bezier curve [duplicate]

I have a cubic bezier curve ; whose 1st anchor-point is (a,b) 1st control-point is (c,d) , 2nd control point is (e,f) and 2nd anchor-point is ( g,h ); Now I want an equation in x and y format; so ...
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1answer
828 views

Is it possible to convert a B-Spline into a Bezier curve?

If so, do I lose any feature of the curve?
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0answers
284 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? ...
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0answers
49 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 ...
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1answer
201 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 ...
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1answer
166 views

Understanding the Spiro Spline

My name's Wray. This is my first time here. Firstly, I like curves. I've been keeping a pet project for a long time that would implement a delightful new curve-interpolation algorithm named the Spiro ...