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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 ...
• 8,437

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 ...
• 348
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 ...
• 901
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 <...
• 166
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 ...
• 3,636

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 ...
• 8,437

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 ...
• 3,421

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 ...
• 6,830