1
vote
2answers
74 views

Retrieve the initial cubic Bézier curve subdivided in two Bézier curves

I have a cubic Bezier curve subdivided to two cubic Bezier: Assuming that "t_cut" is the t value where this initial Bezier is cut: example of function subdivision(BezierCurve initialCurve, ...
1
vote
1answer
34 views

Resample Bézier Curve with curvature and number of points constraints

I have an algorithm that implements an uniform resample process throughout a Bézier curve. This is done using a chord parametrization process. However, the results achieved do not accomplish my ...
0
votes
1answer
56 views

Bézier curve limits

Can be any curve of any shape (without sharp edges) described by Bézier curve with unlimited (but finite) number of control points? The answer to the question above would probably be no, because I ...
0
votes
2answers
53 views

How to create a nice sky route

I'm trying to find a nice algorithm to trace a sky route between 2 points of a planet. Here is where I am : https://dl.dropboxusercontent.com/u/17657227/migrationGlobe/index.html (or here ...
2
votes
0answers
38 views

Is there anything interesting about this figure constructed from a set of points and their barycentre?

Playing with the TikZ package for (La)TeX, I made a nice figure. Well, I think it is nice, anyway. You can ignore the distracting colours and the concentric circles, they are not important for this ...
1
vote
1answer
72 views

How to apply perspective transform to Bezier curve?

I found that both Bezier curves and B-splines are described with a formula $p(t)=\sum\limits_{i=0}^d B^i_m p_i$ but in the case of B-splines $B^i_m$ are B-spline blending functions, while for Bezier ...
6
votes
5answers
239 views

Parabolas through three points

We can draw an infinite number of parabolas that pass through three given points $A$, $B$, $C$ (in that order). For each such parabola, we take the tangent lines at $A$ and $C$, and intersect them to ...
0
votes
1answer
214 views

Find angle at point on bezier curve

I have two end points and two control points. I am using these points and this link. i have found a point on bezier curve. Now i would like to find angle at this point on bezier curve. Is there any ...
2
votes
1answer
421 views

Intersect a line with a bicubic Bezier Surface Patch.

This question mentions Bezier surfaces, but doesn't go into any detail. How do you going about finding the intersection between a line, $E_{pos} + E_{dir}*t$ and a Bezier surface patch, $P = $ ...
2
votes
2answers
97 views

Duplicate quadratic Bézier curve with new start point?

I have Bézier curve as shown by the wikipedia gif here: I would like to create a new curve that is a segment of the old one. For example, in this gif (from the same article): .. if I wanted B to ...
2
votes
1answer
909 views

Approximate arc length of cubic bezier curve?

I want to divide a cubic bezier curve, with 4 points, start, end and 2 control points, into segments that are not bigger then a certain distance. So, am looking for a computationally quick way to ...
2
votes
2answers
456 views

Offseting a Bezier curve

I searched this site and I read that in general it is not possible to calculate offset of a Bezier curve. But is it possible to calculate the offset in some special cases? Obviously, if the Bezier ...
0
votes
1answer
49 views

What $t$ coefficient should I choose for a Bezier curve?

For a cubic Bezier curve, I have this formula: $$\mathrm{B}(t)=\mathrm{P}_0(1-t)^3+3\mathrm{P}_1t(1-t)^2+3\mathrm{P}_2t^2(1-t)+\mathrm{P}_3t^3,\ t\in[0,1]$$ Now about $t$ I only know that is ...
15
votes
5answers
1k views

Polynomial approximation of circle or ellipse

Trying again, with a somewhat simpler sounding question, since my previous one (Generalizations of equi-oscillation criterion) got zero response: Let $F:[0,1] \to R^2$ be a parametric polynomial ...
3
votes
1answer
789 views

Bézier approximation of archimedes spiral?

As part of an iOS app I’m making, I want to draw a decent approximation of an Archimedes spiral. The drawing library I’m using (CGPath in Quartz 2D, which is C-based) supports arcs as well as cubic ...
1
vote
2answers
385 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 ...
1
vote
1answer
565 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 ...
1
vote
1answer
314 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 ...
0
votes
1answer
435 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 ...
2
votes
1answer
776 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 ...
2
votes
1answer
441 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
258 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
2
votes
3answers
703 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 ...
0
votes
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
545 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 ...
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, ...
5
votes
3answers
397 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
247 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 ...
1
vote
1answer
556 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 ...
1
vote
2answers
418 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
677 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 ...
1
vote
1answer
517 views

Given a radius, calculate Bezier curve

For a given radius, theta, and position, can you calculate a Bezier curve?
2
votes
0answers
300 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
2k 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
vote
1answer
352 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 ...
4
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
833 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. ...
2
votes
1answer
130 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 ...