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

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1answer
482 views

Point projection on curve

Point projection on Bézier curves can be easily accomplished using Newton Iteration to try to minimize the dot product between the vector connecting the point P and its projection on curve C and the ...
1
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1answer
135 views

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 $6$ ...
2
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1answer
828 views

Equation for control point distance for fixed-length cubic Bézier path (with specific constraints)

A particular Stack Overflow question asks how to construct a specific cubic Bézier path of constant length. I have experimentally determined the ideal distances of the control points from the nearest ...
3
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0answers
221 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 ...
2
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1answer
494 views

Determining the result of Boolean shape operations on closed Bézier shapes

Given two closed shapes made up of Bézier curves (and/or straight lines), I'm looking for an efficient way of calculating the resulting shape of the following Boolean operations: union difference ...
0
votes
1answer
307 views

Calculating points on the curve

I want to get the x and y coordinates of a curve..How can i do that... In the above image.Is it possible to calculate the intermediate points(one side) by knowing starting and ending point
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1answer
286 views

Frenet frame formula misunderstanding

The Frenet frame formula says that the first derivation of the equation $q(t)$ is my view: $$q'(t) = \verb|vec_view|$$ the cross product of derivation one and two $q' \times q''$ is ...
2
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4answers
804 views

Changing a bezier curve by dragging a point on the curve itself rather than a control point

I'm developing an iPhone app that allows users to cut out part of an image from its background. In order to do this, they'll connect a bunch of bezier curves together to form the clipping path. Rather ...
1
vote
1answer
106 views

Control points are off for “negative” vectors in a poly-line Bézier curve

I need to calculate the control points of a Bézier curve passing through N points where N > 2. I have been able to use the equations in this post to get close... but when "negative vectors" (the only ...
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1answer
596 views

Finding two Bézier control points given three points

My apologies if this is asked in the wrong spot, I believe that this problem has a fairly simple solution... but it is beyond me. Given three points (A,B,C) drawn at random, how do you figure out the ...
0
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1answer
51 views

How can I count waypoints between a curve?

I have curve that is drawn between point A and B. I want to divide this curve to 100 smaller waypoints. How can I determine what these 100 waypoints are as coordinates, when I only know points A and ...
1
vote
2answers
550 views

How can I learn de casteljau algorithm? (from calculus)

I'm an highschool graduate who is currently waiting for college. Meanwhile, I'm trying to do a little project by myself. (Computer stuff) And yesterday, I found that I needed to deal with something ...
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4answers
5k views

Casteljau's algorithm - practical example

I have a dataset with about 50 points (x,y) and I would like to draw a smooth curve that can pass as closer as possible on those points. I have heard about Casteljau's algorithm for splines but after ...
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2answers
976 views

Control Points of Bézier Curve?

Could someone give me a reason/proof why the control points do not lie on the Bézier Curve? Perhaps involving Bernstein Polynomials, if possible? Thanks!
1
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2answers
267 views

creating the smoothest curve

I have this iPhone app that has an array containing around 50 to 100 points. How do I calculate the smoothest curve that will fit the points? It can be bezier, cubic, quadratic, whatever. It just have ...
1
vote
1answer
241 views

Bézier Curve and Gravitational Pull

Okay, so I'm trying to manipulate an object programmatically. When it gets near another object, lets say a globe. I want the globe to have a gravitational pull on the original object. This isn't so ...
2
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4answers
1k views

Find control point on piecewise quadratic Bézier curve

I need to write an OpenGL program to generate and display a piecewise quadratic Bézier curve that interpolates each set of data points: $$(0.1, 0), (0, 0), (0, 5), (0.25, 5), (0.25, 0), (5, 0), (5, ...
2
votes
0answers
130 views

Turning real roots into curves (for visualisation)

One can obviously map a set of real numbers $x_1, x_2, \ldots x_N$ to a curve in 2-D via $y=(x-x_1)(x-x_2)\ldots(x-x_N)$. Thinking about data visualisation, one can portray a set of $N$ observations ...
5
votes
3answers
431 views

Find sagitta of a cubic Bézier-described arc

I have a situation where I have an arc that was mangled (irrelevant: by c#'s GraphicsPath.AddArc() function). The original arc is guaranteed to be circular, and the new data I have describes the ...
1
vote
1answer
265 views

How do I restore implied on-curve points in TTF Fonts?

I'm trying to find the coordinates of the implied point p2 using the control points p1 and p3. See here: In the TTF spec they say: Connected quadratic curves have first degree continuity and ...
0
votes
1answer
168 views

Find whether n closed curves intersect

I have a number of closed curves (contours) which I want split into groups of mutually intersecting curves. The contours are made of straight lines and bezier curves. How could I do that? Thanks!
1
vote
1answer
589 views

Finding the parameter of a quadratic Bézier curve for which the tangent passes through a point

I am currently working on a program that requires me to deal with quadratic Bézier curves (basically, I have to take a curve and draw it with a specified thickness). In order to do so, I create two ...
9
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6answers
5k views

Is there an explicit form for cubic Bézier curves?

(See edits at the bottom) I'm trying to use Bézier curves as an animation tool. Here's an image of what I'm talking about: Basically, the value axis can represent anything that can be animated ...
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2answers
469 views

Finding a quadratic Bézier curve of length $l$ between two points

I have two points $P_1$ and $P_2$ in the plane. For each of the points, I have two vectors $v_1$ and $v_2$. I want to find a quadratic Bézier curve from $P_1$ to $P_2$ of length $l$ leaving $P_1$ in ...
7
votes
0answers
760 views

How can I tell when two cubic Bézier curves intersect?

I'm working a little program that converges on vector-based approximations of raster images, inspired by Roger Alsing's genetic Mona Lisa. (I started on this after his first blog post two years ago, ...
8
votes
1answer
1k views

Find points along a Bézier curve that are equal distance from one another

I'm trying to figure out a generic way of determining a series of points on a Bézier curve where all the points are the same distance from their neighboring points. By distance I mean direct distance ...
0
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1answer
515 views

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 ...
1
vote
1answer
159 views

Continuous curve interpolating a list of points

I need a function (a curve -- preferably a simple one) that, given $n$ points of a 2D space ($R^2$) passes (interpolates) through all points in a smooth/continuous way. Found out that what I need is ...
1
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1answer
576 views

Given a radius, calculate Bezier curve

For a given radius, theta, and position, can you calculate a Bezier curve?
7
votes
3answers
7k views

Arc Length of Bézier Curves

I posted this on gamedev.stackexchange.com earlier, but I didn't get any answers... and only a few views. EDIT: I've got two answers there (as of now), and I'm investigating them now. How can I find ...
2
votes
0answers
309 views

Can elliptic arc be represented by quadratic Bezier curve?

Can elliptic arc (defined as part of an ellipse, with extent not bigger than 90 degrees) be represented by quadratic Bezier curve?
3
votes
2answers
3k views

How elliptic arc can be represented by cubic Bézier curve?

If I have an arc (which comes as part of an ellipse), can I represent it (or at least closely approximate) by cubic Bézier curve? And if yes, how can I calculate control points for that Bézier curve?
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2answers
2k views

Moving along a bezier curve in time T, factoring in acceleration from X to Y

OK, so I got my ships moving along the bezier in time T, now I need to factor in acceleration, but I don't really know how to do it. I'm using the DeCasteljau Algorithm, that's what my code looks ...
1
vote
1answer
372 views

How to calculate a Bézier curve with only start and end points?

This animation from Wikipedia shows basically what I want to accomplish, however - I'm hoping to have it flipped around, where it starts progressing more towards the destination and "up" (in this ...
1
vote
1answer
297 views

Parabola attributes - custom curve?

UPDATE: I feel like my original question was too vague and didn't provide enough information (as others have mentioned). So I'm going to restate it. Purpose: I want to find an equation in order to ...
1
vote
2answers
722 views

bézier to f(x) polynomial function

I've got a 2D quadratic Bézier curve which, by construction, is a f(x) function : no loops, a single solution for each defined x. Is there a common mean to convert this curve to a 3rd degree ...
5
votes
2answers
2k views

algorithm to calculate the control points of a cubic Bezier curve

I have all points where my curve pass through, but I need to get the coordinates of the control points to be able to draw the curve. How can I do to calculate this points?
1
vote
3answers
839 views

Bezier curves algorithm complex yet simple

I've got a path that is made up of multiple points - i.e. 0,0 0,50 50,50 70,20 If I just draw this line on the screen it looks quite harsh as it puts a sharp angle at the joining of each point. ...
6
votes
3answers
1k views

How to approximate/connect two continuous cubic Bézier curves with/to a single one?

I subdivide a cubic Bézier curve at a given t value using de Casteljau’s algorithm, which yields two cubic Bézier curves. Afterwards I “scale” the second curve (proportionally). I’d like to reconnect ...
2
votes
1answer
131 views

Generating bezier handles based on constraints

I want to try to emulate what this application can do: Given the red round dots (from the mouse) it is able to solve for the bezier handles given that the tension of the curve is set to $0.6$. How ...