On 23 April 2014 13:17, Henrik Johansen <[hidden email]> wrote:

On 22 Apr 2014, at 2:23 , Igor Stasenko <[hidden email]> wrote:

> as for why there's 4 arc segments instead of one, its because
> of bad approximation, when drawing more that 90 degree arcs.
>
> also, in athens, arc segment is defined with following inputs:
> - end point of previous segment (implicit)
> - angle
> - direction (clockwise/counterclockwise)
> - end point
>
> the radius, therefore calculated automatically, because with given set of parameters there's only one way to draw an arc connecting given points.
>
> Now if you put angle of 360 degrees, you cannot draw arc without specifying radius,
> because your end points will coincide, which means there's infinite number of ways to draw full circle passing through a single point, with any radius.
>
> cairo using different inputs for specifying arc segments..
> - center, radius, start angle, end angle
>
> the problem with such parametrization is that it is completely separate from rest of commands (line/move/bezier etc).. and you will be very lucky if your arc will be connected with rest of your path.. because arc's starting point depends on start angle, instead of last point of previous path segment.
>
> this was the main reason to use more appropriate parametrization to get rid of inconsistency.. while losing ability to draw full circle with single command..

AFAICT, still doesn’t explain how to draw an ellipse with constant stroke path width, which was the original question :)

Right, what is missing is elliptical arc segment type. And there's no direct support for it in Cairo.. so it can be only approximated by other segment types, like lines or bezier curves.

There's a work started on calculating path geometry using approximation with line segments.. it can be used to represent any kind of curves defined parametrically.

But it is not yet plugged into the API.

One way is to not use a transformed circle path altogether, but draw the actual ellipsis path using cubic beziers:
http://www.charlespetzold.com/blog/2012/12/Bezier-Circles-and-Bezier-Ellipses.html

ellipsisOfExtent := [:builder :anExtent | | halfX halfY |
                halfX := anExtent x / 2.
                halfY := anExtent y / 2.
                “We expect relative builder, and start the ellipsis at anExtent x / 2 @ 0"
                builder
                        curveVia: 0@(halfY negated * 0.55) and: (0.45 * halfX)@halfY negated to: halfX@ halfY negated;
                        curveVia: halfX* 0.55 @ 0 and: halfX@ (0.45 * halfY) to: halfX @ halfY;
                        curveVia: 0 @ (halfY * 0.55 ) and: (0.45 * halfX negated @ halfY) to: halfX negated @ halfY;
                        curveVia: (halfX negated * 0.55) @ 0 and: halfX negated @ (halfY negated * 0.45) to: halfX negated @ halfY negated;
                        close].

AthensSceneView new
        scene: [ :can |
                | path |

        path := can
                                createPath: [ :builder |

                                        builder moveTo: 10@60.
                                        ellipsisOfExtent value: builder value: 200@100 ].
        (can

                setStrokePaint: Color red)
                width: 8 asFloat.
        can drawShape:  path ] ;
        openInWindow

 

quite nice approximation. What is an error measure comparing to true ellipse?

We provide a surprisingly simple cubic Bézier curve which gives a very accurate approximation to a segment of a circle. Joining the Bézier segments we obtain an approximation to the circle with continuous tangent and curvature. For 45° segments the error is approximately 2·10^-6, and in general the approximation is sixth order accurate.

Considering the code simply stretches a bezier circle’s control points, I’d say quite. In fact, I’d be surprised if the arc primitive in cairo is implemented using a different method.

(Of course, even less error using the actual value of the formula for 90 degrees, instead of approximate values .55 / 1- 0.55.)

Cheers,
Henry