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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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Continuity of composite Bézier curves

The composite curve S with pieces where c0 = (−1, 1), c1 = (−1, 0), c2 = (0, 0), and d0 = (0, 0), d1 = (1, 0), d2 = (2, 1). What is the order of continuity of s at (0, 0)?
Hanna
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Calculating bezier path when target is moving. (And calculate total travel time)

As a response to another question I asked here (https://math.stackexchange.com/questions/945593/2d-spaceship-movement-eta) someone suggested to use a bezier curve. This is not answering the question, but it can provide the effect I am looking…
Jasper
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Approximate $n$ grade Bézier through cubic and/or quadratic Bézier curves

I'm trying to draw a $6$ grade (start point, $4$ control points, end point) Bézier curve but the API offers me only cubic and quadratic curves methods. Is there a way to split or approximate the $6$ (or $n$) grade curve only through cubic or…
Alex
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Formula to derive angle and radius from Bezier circular curve control points

I know the x,y coordinates for the 2 endpoints and the 2 control points for a Bezier circular curve that is less than 180 degrees. I do not know the radius of the circle or the angle of the curve. Could someone give me a formula--or two--where I…
djstooks
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Computing the coordinates of a Bezier Curve

I just started messing with Bezier Curves over the past couple days and I'm trying to get some of the basics down. I have this problem. Consider a quadratic Bezier curve with control points (0, 0), (2, 2), and (4, 0). What are the coordinates of…
user41931
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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 product bezier patches. I've read in a few places that…
Alan Wolfe
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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 are will not be fitted enough to my real data. Do…
Mahsa Ghaffari
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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 arbitrary number, say $m$, to $n + m$. I'd appreciate…
Olumide
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Draw a parallel bezier curve

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 understanding. I have a bezier curve. I want to give…
Michael
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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 this is already correct: By observing the…
dresden
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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 vector. Thank you for the help!
user1217222
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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 space in order to obtain the desired expression.…
Olumide
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Combining multiple Bézier curves

Consider the situation where we have two [cubic] Bézier curves with the following properties: They share one common point (end of curve 1 = start of curve 2) They have the same direction at the point where they meet (a smooth join) We suspect that…
OJW
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Aligning Cubic Bezier Curves (with a width)

I have a cubic Bezier curve which has a width, and I am trying to align another cubic Bezier curve around the outside of it. This is hard to explain in text, so please see the following image: Clearly, just translating the curve doesn't work (this…
alex
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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 point to the missing control point C (blue) what…
bub
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