General formula for generating a cubic fuzzy elliptical arc?

Question

How could I implement in C a simple way to generate 2 missing control points for an elliptical arc given by a start and end point? I don't need a fancy error score, just something that can take points A and D and generate breakpoints B and C for an elliptical arc, where I can use the cubic bezier interpolation algorithm to generate the curve.

sort of

void GetArcControlPoints(Point a, Point &b, Point &c, Point d)
{

.....
b = ...
c = ....
}

thank

Answer 1

There are some drawbacks to your question in mathematics:

• t [0; 1]. , , , , . , ( , n). , . , , , " " . : .

• , . , , , . , , , , "" , (100% = ), radians (2 * pi = ), . : () , .

, ().

---

EDIT:

• , Bézier .

• , "" . , "" , , , 90 , "" , voilà, , "90 ". .

Answer 2

:

http://www.whizkidtech.redprince.net/bezier/circle/kappa/

.

Answer 3

. 4- : 8 ( , , ), .

, , "" ( 1 ), , ( , , , , "" "" , , , , 8 , ).

Such an incremental algorithm approximating elliptical arcs is completely different from those used for Bezier splines, but it is very efficient (and actually even faster than when drawing arbitrary Bezier splines).