Questions on Bézier curves, curves that are frequently used in computer graphics.
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0answers
58 views
How can I calculate all possible Bézier handle points in order to make the curve to a given length?
Given two anchor points and a handle point of a cubic Bézier curve, how can I calculate the other handle point in order to make the curve length to a fixed value?
What kind of orbit will it be?
...
0
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0answers
41 views
Convert a quadratic bezier curve to an f(x) function [duplicate]
Possible Duplicate:
Is there an explicit form for cubic Bézier curves?
Specifically, on http://matthewlein.com/ceaser/, the ease-out curve. How would I go about getting the f(x) for ...
1
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1answer
158 views
Finding point of inflection on a Bézier Curve
I need to determine the first point of inflection on a Bézier curve, if it exists, for a computer graphics application. My original idea was to iteratively walk the curve, evaluating 2nd derivatives ...
1
vote
0answers
130 views
Motion on a parametric surface
Please excuse what will surely turn into a long rambling question, full of incorrect terminology.
I'm trying to figure out the mathematics of moving on a parametric surface - that is, for some ...
2
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1answer
199 views
Finding Y given X on a Cubic Bezier Curve?
I just asked this in the Computing sections but they sent me here:
"So I've been looking around for some sort of method to allow me to find the Y-coordinate on a Cubic Bezier Curve, given an ...
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1answer
95 views
How can a Bézier curve be periodic?
As I know it, a periodic function is a function that repeats its values in regular intervals or period. However Bézier curves can also be periodic which means closed as opposed to non-periodic which ...
3
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1answer
553 views
How to derive the equation for a bézier curve
So, I remember a while back there was a maths competition and we were given a curve that we needed to write an equation for. I just skipped the question since I didn't even know where to begin. I ...
0
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1answer
224 views
A function that can smooth out line joining three points
I want to know if there is a function with which we can smooth out line joining two( or more )points . I've read we can do it with Quad and cubic splines or something but I am not clear with them. i ...
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2answers
204 views
Shifting a quadratic Bézier curve
I have a quadratic Bézier curve.
I want to make a path that runs along that curve, whose width is 'w'. (So at any point in time along the exact center of that path, you will be also on the original ...
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vote
1answer
302 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
votes
1answer
239 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 ...
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1answer
111 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 ...
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vote
1answer
135 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: ...
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0answers
261 views
Subdividing a cubic Bezier curve at an arbitrary point
I want to subdivide a cubic Bezier curve at a point which may not be the curve's midpoint. I'm using the plain and slow incremental method to plot the curve from its parametric equations.
4
votes
4answers
603 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), ...
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2answers
366 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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1answer
209 views
Application to draw/edit/export 2d bezier-curve over image
I am searching for an application (window preferred but linux, mac are possible too).
The application would be used to redraw a bezier-curve over an hand-drawn image.
I have multiple images with 2 ...
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0answers
69 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.
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0answers
149 views
How to use the cspline formula?
I learned here that cspline is possibly suitable for my problem. Using the formula bellow for a paticular curve I have a problem and let me ask it.
$p(t)=(2t^3-3t^2+1)\cdot p(0)+(t^3-2t^2+t)\cdot ...
1
vote
1answer
209 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
votes
1answer
149 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 ...
4
votes
1answer
1k 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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vote
1answer
172 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
votes
2answers
176 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 ...
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1answer
274 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
92 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
1answer
457 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
votes
0answers
164 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 ...
0
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0answers
59 views
Fit a smooth curve to 2 functions spliced together
I have a function
if x<=const1 then
y=x*const2
if x>const1 then
y= x * const2 + x * x * const3
but Id like it to be continuous , ie to apply some form of smoothing, does anybody have a ...
1
vote
1answer
309 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
188 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
212 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 ...
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2answers
452 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
66 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
371 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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votes
1answer
46 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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vote
2answers
493 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
2k 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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vote
2answers
724 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
vote
2answers
243 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
168 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
524 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
123 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
300 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 ...
0
votes
1answer
167 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
148 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
315 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 ...
5
votes
6answers
2k 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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vote
2answers
279 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 ...
6
votes
0answers
436 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, ...
