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

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7
votes
0answers
678 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
votes
1answer
500 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
154 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
vote
1answer
519 views

Given a radius, calculate Bezier curve

For a given radius, theta, and position, can you calculate a Bezier curve?
7
votes
2answers
5k 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
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
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
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 ...
1
vote
1answer
293 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
680 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 ...
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. ...
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
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 ...