We’re rewarding the question askers & reputations are being recalculated! Read more.

# Questions tagged [bezier-curve]

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

473 questions
Filter by
Sorted by
Tagged with
42 views

### Is there a relationship between the length of the inner and outer edges of a curve with a given width?

If you have an arbitrary line, say a bezier curve, that has a width, is there a relationship between the length of the curve at the inner and outer edges? Given the width of the curve at the ...
12 views

### Finding the length of control points to obtain a specific curve length

I want to begin by letting you know that my math skills don't go far beyond basic Algebra. I can understand most concepts after a walk-through, but this one is, so far, beyond my capabilities. What ...
34 views

### Sample points between two Bezier curves

I am looking for a way to randomly pick points between two Bezier curves (red and greenhttps://drive.google.com/file/d/1aRIOFf6-zzInadZg3yusyAroXGsAGz4P/view?usp=sharing). I also have a set of points ...
13 views

### balistic: aiming at a point on a bezier curve, given velocity of the bullet and velocity of the moving target

Given a moving point E with know velocity and no acceleration moving on a Bezier spline composed of a set of bezier path, joined continuously, which are approximated by line segments. a static point ...
33 views

### How to manipulate the $x$-Axis of a Cubic-Bézier-Curve?

I have a Cubic Bézier-Curve a la: $$f(x) = A (1-x)^3 + 3 B (1-x)^2 x + 3 C (1-x) x^2 +D x^3$$ with my control constant A,B,C,D which are just constants. x ist running from 0 to 1. What I ...
20 views

### Find continuous curvature approximation for going from a straight line into a half circle

I have the problem that I want to steer a 4 wheel robot. It should move on a straight line, and for turning to go on a circle with a defined radius, as in this picture: The problem I have is that if ...
34 views

### Adjust a one dimensional Bezier-Curve?

I really need to adjust my one dimensional Bezier-Curve, but I don't know how. I got this equation: $$y = A(1-x)^3 + 3B(1-x)^2x + 3C(1-x)x^2 + Dx^3$$ with the constants A,B,C,D which represent ...
10 views

### Why Are Cubic Bezier Curves Used In Animation Transitions On The Web?

CSS allows defining animations using a timing function along a cubic bezier curve. In this case the curve is defined by four control points P0, P1, P2, and P3, where P0 and P3 are fixed as [0,0] and [...
38 views

### Cubic Bezier curve - how to make height always the same as a given vertical line

I have a cubic bezier curve that is always drawn from a source to a destination. but its not always drawn on a horizontal line. anyway ideally it looks like this: but the PEEK of the curve should ...
46 views

76 views

### Cubic Bézier radius of curvature calculation

I modelled a racetrack using cubic Bézier curves. I understand that the representation is parametric: x and y vary with t. I have successfully created the cartesian coordinates thanks to this: https://...
31 views

### How to prove axis of symmetry for Bezier-Bernstein curve?

I have a planar bezier curve of degree $\ n=3$ with the control points: $\ p_{o}=[0, 0]^T$ $\ p_{1}=[1, 1]^T$ $\ p_{2}=[2, 1]^T$ $\ p_{3}=[3, 0]^T$ Suppose I have the bernstein polynomials. ...
25 views

### How to prove if all points of Bezier-Bernstein belong to the same plane?

I have a deggree $\ n=3$ Bezier - Bernstein curve with the following control points: $\ p_{o} = [0, 0, 1]^T$ $\ p_{1} = [1,2, 2]^T$ $\ p_{2} = [2,2,3]^T$ $\ p_{3}=[3,4,4]^T$ I have found the ...
26 views

### Algorithm to Identify if B-spline Surface is a Surface of Revolution

I'm trying to reach an algorithm to determine if a given a general B-spline/Bezier surface (could be rational) is a surface of revolution around the Z axis. I tried to solve it analytically and ...
31 views

### Confusion on the formula of Rational Bezier curve in Duncan's book

Duncan Marsh's book Applied Geometry for Computer Graphics and CAD stated I'm really confused about this formula. First of all, why do we replace $w_i\mathbf{b_i}$ with $\mathbf{b_i}$ when $w_i=0$? ...
52 views

### How do I produce a Bézier curve with 4 points and without just using a website?

I have these for points, (1,-2), (4,3), (12,3) and (15,-3), and I was wondering how do I make a model out of this, and how would this relate to polynomials and Pascal's triangle? I have this formula: ...
43 views

### approximating a b-spline with a single bezier curve of any degree

suppose we have b-spline composed of several bezier curves with known control points and nodes and is not necessarily smooth. Is there a way to create a single bezier curve of any degree that will ...
25 views

62 views

### How can I create a seam for an ellipse?

I want to create a seam for an ellipse. (Mathematically I think this means that there are constant-length normal lines between the ellipse and the curve that creates the seam, but I'm not 100% sure ...
86 views

### Algorithm to calculate the positions of bezier curve control point handles to transform from circle to straight line

From the image linked below (in A, I don't have enough points to add it directly) I have approximated two bezier cubic curve segments to a circle. I know how to move the anchor points AP1 and AP3 ...
147 views

### Bounding rectangle of ellipse

In a stale branch of the code base I'm working on, I found an interesting algorithm to go from the SVG definition of an elliptical arc, to Bézier curves. This is a question about a small but crucial ...
41 views

### Bézier with fewest inflection points

I have an algorithm to automatically generate control points for smooth Bezier curves which pass through given nodes. It's inspired by what Inkscape appears to do when you make nodes "auto-smooth". In ...
31 views

### How to find shortest bezier curve with N control points passing though N target points?

I'm working on a pattern making software (clothing). I have a set of N target points and I need to find the shortest bezier curve with N target points that goes through all the N target points. My ...
388 views

### How to perfectly split a bezier curve into two curves of unequal length

I couldn't find a title that didn't seem duplicate, but my question is very different from every other I could find on this site. I have a Bezier curve, defined by 4 points. Two of those points (...
121 views

### The good pseudo-half-circle-like curves that quadratic bezier curves can create

Since quadratic bezier curves can only approximate circles, I'm wondering what they can actually do well. That is, the sort of half-circle-like shapes that quadratic curves can make. For instance, in ...
205 views

### Understanding Bezier Curves vs. Circular/Elliptical/Other Arcs

From what I've read, you cannot construct an elliptical or circular arc with a single bezier curve (though I read maybe you can if the arc is less than 1/4 of a circle or something small like that, or ...