# Tagged Questions

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

278 views

### Continuity of composite Bézier curves

The composite curve S with pieces where c0 = (−1, 1), c1 = (−1, 0), c2 = (0, 0), and d0 = (0, 0), d1 = (1, 0), d2 = (2, 1). What is the order of continuity of s at (0, 0)?
130 views

### Number of Curvature Maxima of a 2D Cubic Bezier curve

I am trying to prove that a standard cubic Bezier curve can only have at most 2 curvature maxima over $t \in [0,1]$. Assuming that no 3 adjacent control points are colinear, the curvature will either ...
1k views

### How to find the N control point of a bezier curve with N+1 points on the curve

I have a the set of points my curve has to pass through, 2 of those are the start and end points. I'm looking for a way to find the control points of my bezier curve (mostly quadratic and cubic) by ...
446 views

### B-spline: compute control points given equations and knots?

Assuming a cubic or higher-order 2-D B-spline: if all piecewise polynomial equations for the final spline (and thus the knot vector as well) are already known, is there a relatively "streamlined" ...
87 views

### Calculating bezier path when target is moving. (And calculate total travel time)

As a response to another question I asked here (2d spaceship movement + eta) someone suggested to use a bezier curve. This is not answering the question, but it can provide the effect I am looking for....
231 views

### Distance from point to parabola (quadratic bezier)

I'm trying to draw quadratic bezier curve (as line). I approximate quadratic bezier curve as parabola ($y=x^2$), according to this document http://http.developer.nvidia.com/GPUGems3/gpugems3_ch25....
358 views

### How to clip Bézier curves using Casteljau's algorithm?

I am attempting to approximate intersections of Bézier curves using iterative clipping. This common method is described here and here. It basically works like this: Find bounding lines outside one ...
249 views

### inflection point of cubic bezier with restrictions

Say you have this type of cubic Bézier curve: The 4 control points A,B,C,D have restrictions: A & B have the same Y-axis coordinate C & D have the same Y-axis coordinate B & C have ...
33 views

350 views

### Intersect Ray (Line) vs Quadratic Bezier Triangle

I'm trying to find the intersection between a line segment and a quadratic bezier triangle for my OpenCL real time raytracer. The main recomendations I've seen are to try subdivision, or tensor ...
115 views

### What are some alternative ways of describing n-dimensional surfaces using control points other than Bezier surfaces?

I'm interested in problems involving geometric constraints and curve subdivision. I noticed that most of these problems describe the curves/surfaces using the Bezier form. I wanted to know if there ...
281 views

### Bézier curves and optimization

I have a very peculiar problem. Assuming that you know how B-Splines or Bézier Curves work, you may also know that if we assume the result of the function, let's say tri-dimmensional, as a position in ...
217 views

### keeping c1 continuity in joining several bezier curve

I have some complex curves, I separate the long curves to smallest one to be able to fit them with Bezier curve. However, my Bezier curve has no C1 continuously, if I force C1 continuously, my curves ...
99 views

### Reparametrize of cubic bezier curve in arclength

I am looking for a way to re-parametrize the cubic Bezier curve in t domain to cubic bezier curve in S (arclength) domain. Thanks
255 views

### Given a control polygon, how do you find a tangent vector at a given point (CAGD, Bezier Curve)?

I am having a hard time with my Computer Aided Graphic Design class. I am presented with the bezier control polygon (in a Mathematica statement): P = Table[{x^2, x^3, 0}, {x, 4,7}] And the ...
256 views

### Gradient of a rational Bezier curve

I'd appreciate help working out the gradient of a rational Bezier curve $C = (\,x(t) \,, \,C_y(t) \,)$. I know that the gradient $g$ of a the parametric curve is  g(t) = \left( \frac{dy(t)}{dt} \...
74 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 http://...
79 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 ...
32 views

### Degree elevation of weighted Bezier curve to an arbitrary degree

Following on from a past question about degree elevation of a rational Bezier curve, of degree $n$ by one to $n + 1$, I am now looking to derive a single expression for degree elevation by an ...
20 views

### Draw a parallel bezier curve [duplicate]

This may be a duplicate of Control points of offset bezier curve but I am not quite able to say so. Also, the answers linked there are just one level more abstract than is helpful to my limited ...
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 ...