# Tag Info

### Algorithm to find the center of a Bezier curve

Bézier curves are mathematical entities and have no clearly defined center. One can in fact define many different things as the center of the Bézier curve. I have tried to depict some of the possible ...

### How to raytrace Bezier surfaces?

is it a total pipe dream to hope to solve the Ray/Bezier-surface intersection algebraically Yes, it's a pipe dream. A bicubic Bezier patch is an algebraic surface of degree 18. To intersect a ray ...
Accepted

### How to calculate matching roundness of two offset rectangles?

What you (probably) want to achieve is something like this: When having a closer look at one of the corners and add a few lines, we see this: The black lines indicate that the center points of the ...
Accepted

### Determining Rational Quadratic Bezier Curve Weights for Circle

Check out the section on Circular Arcs and Circles, from Ching-Kuang Shene's excellent computational geometry course notes: [G]iven three control points P0, P1 and P2 such that P0P1 = P1P2 holds, if ...

### Reliable test for intersection of two Bezier curves

An alternative way to formulate the problem is to define a function that gives the distance between points on the two curves, as a function of the curves' parameters. Then attempt to find the global ...

### Reliable test for intersection of two Bezier curves

[Disclaimer: I think the following should work but have not actually coded it myself] I couldn't think of a "trivial" method of producing a yes/no answer but the following would be a reasonable ...
Accepted

### Apply distortion to Bézier surface

Edit: changed the answer according to new images and clarification. for every control point p(k, n) p'(k, n) = ( p(k, n) - p(k) ) * d * l(k) + p(k, n) where <...
Accepted

### Bezier Curve Tool Controlled by Mouse

Instead of using cubic Bezier spline, you should use cubic Hermite spline. For cubic Hermite curve you specify the segment end points and tangents, which is what you then control in the tool. Hermite ...

### Does this 3D rendering method exist? How is it called? Is there any C++ algorithm for it?

Yes, such rendering exists. It is called a parametric surface and there are several methods you can render such entities. In this case you are talking of bezier patches. Turn the object into enough ...

### Does this 3D rendering method exist? How is it called? Is there any C++ algorithm for it?

The 1994 game Ecstatica and its 1997 sequel rendered ellipsoid segments instead of triangles, but I don't think anyone else has ever used this exact technique. Direct raytracing of Bézier patches was ...

### Join two bezier curves so that the result is two-times continuously differentiable

For 2 bezier curves to connect and be continuous at all, the last control point of the first curve (C in your case) must be the same as the first control point of the next curve (D). So c3 has to ...

### Bicubic bezier surface from 4 bezier curves

Yes, its pretty standard stuff. Most 3D applications our there can do this. Since the nomenclature of 3d applications is not standardized, the tool has different names in different applications: Loft (...

1 vote
Accepted

### Cubic Bezier Curve - General Questions

Regarding the first question: a bezier curve is defined as linear combinations of control points and basis function (Bernstein polynomials). Although usually one considers a unit interval as ...
1 vote

### Spline interpolation library in cpp

So you have a series of points and, at each point, a supplied derivative? Is a piecewise cubic sufficient or does it need higher derivative continuity? If the former is ok, then Cubic Hermite Splines ...
1 vote
Accepted

### LoopBlinn Cubic Curve Rendering - Serpentine arteffect

found the problem, it was the shader. I am using following shader, that works fine ...
1 vote

### Simple Intersection Algorithm for Ray and 3D Bézier Curves of Varying Thickness

You say that you don't need the fastest possible algorithm, so instead of solving it analytically, you might try considering the numeric alternatives, which in this case could mean ray marching. How ...
1 vote
Accepted

### How does the Lane Riesenfeld algorithm work?

What you're looking for is called de Boor's algorithm. It lets you compute a point on a b-spline curve by doing a series of linear interpolation (LERP) calculations. So, it works very much like the de ...
1 vote

### First steps towards CAD standard curve fitting

As far as I know, there are no standard shapes for (physical) French curves. The folks who manufacture them are free to choose any shapes they like. Of course, they choose shapes that look "nice", ...
1 vote

### Checking the correct offset direction for Bezier curve offset

For a two dimensional spline it is possible to define a left and a right side, or let us call the directions counterclockwise and clockwise side (or maybe port and starboard would be appropriate). The ...

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