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

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1answer
756 views

How to merge two poly Bézier curves?

I am battling with a programming problem. Given two or more overlapping and interacting Bézier polygons, how can I perform merge (union) operations on a list of input Bézier polygons so as to produce ...
0
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1answer
742 views

Newton's Method, and approximating parameters for Bézier curves.

I've been wanting, for quite a while now, to polish up some source code I wrote for approximating arbitrary Bézier curves to given series of points. I managed to accomplish quite a bit, but I hit a ...
0
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1answer
191 views

How to fly a curve from one heading to another using only roll and pitch.

I have 3 perpendicular vectors representing an object in 3d space... Heading Right Up ...and I would like to be able to 'fly' this object so that it ends up at a ...
1
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1answer
283 views

Detect “Kinks” in Parallel Lines to Bezier Curves [x-post]

I feel like this is just as much a mathematics question as it is a programming question so I figured it couldn't hurt to cross post my question here. Original Post: ...
5
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4answers
3k views

Why is the Convex Hull property (e..g of Bézier curves) so important?

Recently I read some course notes and articles on Bézier curves. They all sum up the properties of Bézier curves, like the partition-of-unity property of the basis functions (Bernstein polynomials), ...
2
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3answers
2k views

Can a rational Bézier curve take exactly the same shape as a part of the sine function?

I'm wondering whether a rational Bézier curve could take exactly the same shape as a part of the sine function. The best way to check this seems like this: Find a part of the sine function such that ...
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0answers
80 views

How to approximate a trigonometric curve by Bezier curves?

Let me ask how to approximate a trigonometric curve by Bezier curves? Is there any known algorithm? Thank you in advance.
1
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1answer
290 views

How to draw a smooth curve between 2 points given the 2 tangents at them?

Let me ask a question , given 2 points on the XY plane and given the 2 tangents at them, how to compute an arbitrary chosen smooth curve passing the 2 given points. For details, traveling along the ...
2
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1answer
217 views

Cubic curve software that generates equation

Is there a free / open-source program that would allow me to drag and drop points of a cubic curve and displays the equation? There are a number of equations that I could use in my game project and ...
9
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1answer
6k views

What is the difference between natural cubic spline, Hermite spline, Bézier spline and B-spline?

I am reading a book about computer graphics. It is confusing about the various splines and their algorithms. What is the difference between natural cubic spline, Hermite spline, Bézier spline and ...
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1answer
395 views

Find the arc-distance between the start and end points of a Bézier curve

Given that I have the start, end and control points for a linear Bézier curve, I am trying to find the arc-distance between the start and end points. Google seems to be failing me this morning; can ...
4
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2answers
285 views

Get $t$ of ascending Bézier curve from $x$

I have an ascending cubic Bézier curve. ($x_0 \leq x_1 \leq x_2 \leq x_3$) Considering this property, there is always one and only one $y$ value per $x$ value. The point ($x, y$) along the curve is ...
0
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1answer
557 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
vote
1answer
140 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
votes
2answers
916 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
242 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
votes
1answer
572 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 ...
-1
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1answer
374 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
294 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
902 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
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1answer
115 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 ...
0
votes
1answer
638 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 ...
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1answer
52 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 ...
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2answers
555 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
6k 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
1k 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!
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2answers
270 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
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1answer
270 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
votes
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
131 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
464 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
280 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
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1answer
169 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
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1answer
643 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 ...
10
votes
6answers
6k 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 ...
1
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2answers
546 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
843 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
2k 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
550 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 ...
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1answer
164 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
631 views

Given a radius, calculate Bezier curve

For a given radius, theta, and position, can you calculate a Bezier curve?
7
votes
3answers
8k 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
316 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?
1
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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
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1answer
391 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 ...
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1answer
303 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
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2answers
805 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
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3answers
846 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. ...