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Athens and ellipse drawing

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Juraj Kubelka-5

Apr 11, 2014; 7:33pm

Athens and ellipse drawing

CONTENTS DELETED

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Igor Stasenko

Apr 11, 2014; 8:35pm

Re: Athens and ellipse drawing

yes, you using stroke for 2nd ellipse,

but stroke width is also subject of scaling, that's why it has different width, because

of non-uniform scaling (x/y).

instead you can first, draw a filled ellipse (blue) and then draw green one over it.

On 11 April 2014 21:33, Juraj Kubelka <[hidden email]> wrote:

Hi Igor, hi all!

I am not sure how to properly draw ellipse. Right now I draw a path like this:

The path is created that way:
-=-=-=-=-
computePath
path := self athensCanvas
createPath: [ :builder |

builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;

ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ]

-=-=-=-=-

And draw it like this:
-=-=-=-=-
drawOn: athensCanvas
athensCanvas pathTransform
restoreAfter: [

athensCanvas pathTransform
scaleBy: rectangle extent asFloatPoint
athensCanvas

setPaint: color;
drawShape: self path.
(athensCanvas setStrokePaint: strokePaint)

width: (self strokeWidth / self scale) asFloat.
athensCanvas drawShape: self path ]
-=-=-=-=-

But with a different shapes, the border does not have same width all around the ellipse. See the image:

Is there better way to draw it?
Thank you,
Jura

... [show rest of quote]

--
Best regards,
Igor Stasenko.

Juraj Kubelka-5

Apr 11, 2014; 11:37pm

Re: Athens and ellipse drawing

CONTENTS DELETED

The author has deleted this message.

Igor Stasenko

Apr 11, 2014; 11:56pm

Re: Athens and ellipse drawing

On 12 April 2014 01:37, Juraj Kubelka <[hidden email]> wrote:

Thank you Igor,

I suspect there is no better solution. But anyway I am surprised, every simple drawing application manages ellipses.

Athens is not an application, it is framework.

And why you think that every framework supports drawing ellipses as a basic command/primitive..for instance? I know of at least one, which doesn't - try drawing it with OpenGL.
;)

Thank you anyway.
Juraj

El 11-04-2014, a las 17:35, Igor Stasenko <[hidden email]> escribió:

yes, you using stroke for 2nd ellipse,
but stroke width is also subject of scaling, that's why it has different width, because
of non-uniform scaling (x/y).
instead you can first, draw a filled ellipse (blue) and then draw green one over it.

On 11 April 2014 21:33, Juraj Kubelka <[hidden email]> wrote:

Hi Igor, hi all!

I am not sure how to properly draw ellipse. Right now I draw a path like this:

The path is created that way:
-=-=-=-=-
computePath
path := self athensCanvas
createPath: [ :builder |

builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;

ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ]

-=-=-=-=-

And draw it like this:
-=-=-=-=-
drawOn: athensCanvas
athensCanvas pathTransform
restoreAfter: [

athensCanvas pathTransform
scaleBy: rectangle extent asFloatPoint
athensCanvas

setPaint: color;
drawShape: self path.
(athensCanvas setStrokePaint: strokePaint)

width: (self strokeWidth / self scale) asFloat.
athensCanvas drawShape: self path ]
-=-=-=-=-

But with a different shapes, the border does not have same width all around the ellipse. See the image:

<Captura de pantalla 2014-04-11 a la(s) 16.29.13.png>

Is there better way to draw it?
Thank you,
Jura
... [show rest of quote]

--
Best regards,
Igor Stasenko.

... [show rest of quote]

... [show rest of quote]

--
Best regards,
Igor Stasenko.

Juraj Kubelka-5

Apr 12, 2014; 12:06am

Re: Athens and ellipse drawing

CONTENTS DELETED

The author has deleted this message.

Juraj Kubelka-5

Apr 12, 2014; 3:13am

Re: Athens and ellipse drawing

In reply to this post by Igor Stasenko

CONTENTS DELETED

The author has deleted this message.

pharo4Stef@free.fr

Apr 12, 2014; 7:01am

Re: Athens and ellipse drawing

AthensSceneView new
scene: [ :can |
| path |
path := can
createPath: [ :builder |
builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ].

can pathTransform
restoreAfter: [
can pathTransform scaleBy: 200 .
can
setPaint: Color red ;
drawShape: path.
"(athensCanvas setStrokePaint: strokePaint)
width: (self strokeWidth / self scale) asFloat."
can drawShape: path.].
can pathTransform
restoreAfter: [
can pathTransform scaleBy: 190 .
can
setPaint: Color blue ;
drawShape: path.
"(athensCanvas setStrokePaint: strokePaint)
width: (self strokeWidth / self scale) asFloat."
can drawShape: path

]
] ;
openInWindow

Screen Shot 2014-04-12 at 09.01.09.pdf (24K) Download Attachment

Juraj Kubelka-5

Apr 14, 2014; 11:21am

Re: Athens and ellipse drawing

CONTENTS DELETED

The author has deleted this message.

Juraj Kubelka-5

Apr 14, 2014; 11:53am

Re: Athens and ellipse drawing

CONTENTS DELETED

The author has deleted this message.

Igor Stasenko

Apr 22, 2014; 12:05pm

Re: Athens and ellipse drawing

On 14 April 2014 13:53, Juraj Kubelka <[hidden email]> wrote:

El 14-04-2014, a las 8:21, Juraj Kubelka <[hidden email]> escribió:

Thank you Stef,

the example helped me a lot to understand how to play with Athens.

The solution is not what I am looking for. If someone starts to play with alpha canal, s/he will get unexpected results.

I have finally found an example in C language. It look like this:
-=-=-=-=-
cairo_set_line_width (cr, 0.1);
cairo_save (cr);

cairo_scale (cr, 1, 0.2);
cairo_arc (cr, 1.5, 1.5, 1, 0, 2 * M_PI);
cairo_restore (cr);

cairo_set_source_rgba (cr, 0, 1, 0, 0.50);
cairo_stroke (cr);
-=-=-=-=-
<tips-ellipse.png>

I do not know how to write the same instructions with Athens.

First, they draw one arc (cairo_arc (cr, 1.5, 1.5, 1, 0, 2 * M_PI);), I draw 4 arcs:
-=-=-=-=-
canvas
createPath: [ :builder |
builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ].

-=-=-=-=-
... [show rest of quote]

OK, now I can draw ellipse with just one arc:
-=-=-=-
canvas
createPath: [ :builder |
builder
absolute;
moveTo: 0.5 @ 0;
arcCenterX: 0 centerY: 0 radius: 0.5 startAngle: 0 endAngle: Float twoPi

-=-=-=-

Why is this method in private protocol? Why I should not use it?

... [show rest of quote]

because its private.. and implementation specific.
other implementations may not have this method at all, and your code will simply throw DNU.
And that's why you got the horizontal line btw.. because of using private protocol bypassing coordinate tracking.

Why I have to use “moveTo:”? In C-example they do not use it. But I have to, otherwise there is an extra line on the canvas:

Well, I see in AthensCairoPathBuilder>>createPath:, there is call of "self moveToX: 0 Y: 0.”. If I remove it, I do not have to write “moveTo: 0.5@0”. So, I understand why I have to write it in my code. The question is what is the purpose of "self moveToX: 0 Y: 0.”? I guess it simplify some situations, am I right? Which one?

the initial moveTo: command lets you set the origin (starting point) of your path.

if you don't start path with moveTo: command, it is implicitly set to 0@0.

There is actual Athens example:
-=-=-=-
AthensSceneView new scene: [ :can |
| path |
path := can createPath: [ :builder |
builder
absolute;

moveTo: 0.5 @ 0;
arcCenterX: 0 centerY: 0 radius: 0.5 startAngle: 0 endAngle: Float twoPi ].
can pathTransform restoreAfter: [
can pathTransform scaleBy: 200 @ 50.

(can setStrokePaint: Color red) width: 0.1.
can drawShape: path.

].
] ;
openInWindow
-=-=-=-

Thank you,
Juraj

Second, they set line width, before any other action (like cairo_save). I do:

-=-=-=-=-
canvas pathTransform scaleBy: 200 @ 50.
(can setStrokePaint: Color red) width: 0.1.
can drawShape: path.
-=-=-=-=-

So, my result in Athens is like this:

<Captura de pantalla 2014-04-14 a la(s) 8.18.38.png>

Any idea? The example is explained here, C source code is here (by clicking on the image in the page).

Thank you,
Jura

El 12-04-2014, a las 4:01, Pharo4Stef <[hidden email]> escribió:

AthensSceneView new
scene: [ :can |
| path |
path := can
createPath: [ :builder |
builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ].

can pathTransform
restoreAfter: [
can pathTransform scaleBy: 200 .
can
setPaint: Color red ;
drawShape: path.
"(athensCanvas setStrokePaint: strokePaint)
width: (self strokeWidth / self scale) asFloat."
can drawShape: path.].
can pathTransform
restoreAfter: [
can pathTransform scaleBy: 190 .
can
setPaint: Color blue ;
drawShape: path.
"(athensCanvas setStrokePaint: strokePaint)
width: (self strokeWidth / self scale) asFloat."
can drawShape: path

]
] ;
openInWindow

<Screen Shot 2014-04-12 at 09.01.09.pdf>
... [show rest of quote]

... [show rest of quote]

... [show rest of quote]

--
Best regards,
Igor Stasenko.

Igor Stasenko

Apr 22, 2014; 12:23pm

Re: Athens and ellipse drawing

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..

On 22 April 2014 14:05, Igor Stasenko <[hidden email]> wrote:

On 14 April 2014 13:53, Juraj Kubelka <[hidden email]> wrote:

El 14-04-2014, a las 8:21, Juraj Kubelka <[hidden email]> escribió:

Thank you Stef,

the example helped me a lot to understand how to play with Athens.

The solution is not what I am looking for. If someone starts to play with alpha canal, s/he will get unexpected results.

I have finally found an example in C language. It look like this:
-=-=-=-=-
cairo_set_line_width (cr, 0.1);
cairo_save (cr);

cairo_scale (cr, 1, 0.2);
cairo_arc (cr, 1.5, 1.5, 1, 0, 2 * M_PI);
cairo_restore (cr);

cairo_set_source_rgba (cr, 0, 1, 0, 0.50);
cairo_stroke (cr);
-=-=-=-=-
<tips-ellipse.png>

I do not know how to write the same instructions with Athens.

First, they draw one arc (cairo_arc (cr, 1.5, 1.5, 1, 0, 2 * M_PI);), I draw 4 arcs:
-=-=-=-=-
canvas
createPath: [ :builder |
builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ].

-=-=-=-=-
... [show rest of quote]

OK, now I can draw ellipse with just one arc:
-=-=-=-
canvas
createPath: [ :builder |
builder
absolute;
moveTo: 0.5 @ 0;
arcCenterX: 0 centerY: 0 radius: 0.5 startAngle: 0 endAngle: Float twoPi

-=-=-=-

Why is this method in private protocol? Why I should not use it?

... [show rest of quote]

because its private.. and implementation specific.
other implementations may not have this method at all, and your code will simply throw DNU.
And that's why you got the horizontal line btw.. because of using private protocol bypassing coordinate tracking.

Why I have to use “moveTo:”? In C-example they do not use it. But I have to, otherwise there is an extra line on the canvas:

Well, I see in AthensCairoPathBuilder>>createPath:, there is call of "self moveToX: 0 Y: 0.”. If I remove it, I do not have to write “moveTo: 0.5@0”. So, I understand why I have to write it in my code. The question is what is the purpose of "self moveToX: 0 Y: 0.”? I guess it simplify some situations, am I right? Which one?

the initial moveTo: command lets you set the origin (starting point) of your path.
if you don't start path with moveTo: command, it is implicitly set to 0@0.

There is actual Athens example:

-=-=-=-
AthensSceneView new scene: [ :can |
| path |
path := can createPath: [ :builder |
builder
absolute;

moveTo: 0.5 @ 0;
arcCenterX: 0 centerY: 0 radius: 0.5 startAngle: 0 endAngle: Float twoPi ].
can pathTransform restoreAfter: [
can pathTransform scaleBy: 200 @ 50.

(can setStrokePaint: Color red) width: 0.1.
can drawShape: path.

].
] ;
openInWindow
-=-=-=-

Thank you,
Juraj

Second, they set line width, before any other action (like cairo_save). I do:

-=-=-=-=-
canvas pathTransform scaleBy: 200 @ 50.
(can setStrokePaint: Color red) width: 0.1.
can drawShape: path.
-=-=-=-=-

So, my result in Athens is like this:

<Captura de pantalla 2014-04-14 a la(s) 8.18.38.png>

Any idea? The example is explained here, C source code is here (by clicking on the image in the page).

Thank you,
Jura

El 12-04-2014, a las 4:01, Pharo4Stef <[hidden email]> escribió:

AthensSceneView new
scene: [ :can |
| path |
path := can
createPath: [ :builder |
builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ].

can pathTransform
restoreAfter: [
can pathTransform scaleBy: 200 .
can
setPaint: Color red ;
drawShape: path.
"(athensCanvas setStrokePaint: strokePaint)
width: (self strokeWidth / self scale) asFloat."
can drawShape: path.].
can pathTransform
restoreAfter: [
can pathTransform scaleBy: 190 .
can
setPaint: Color blue ;
drawShape: path.
"(athensCanvas setStrokePaint: strokePaint)
width: (self strokeWidth / self scale) asFloat."
can drawShape: path

]
] ;
openInWindow

<Screen Shot 2014-04-12 at 09.01.09.pdf>
... [show rest of quote]

... [show rest of quote]

... [show rest of quote]

--
Best regards,
Igor Stasenko.

... [show rest of quote]

--
Best regards,
Igor Stasenko.

stepharo

Apr 22, 2014; 7:50pm

Re: Athens and ellipse drawing

In reply to this post by Igor Stasenko

Thanks for the explanation I will add them to the chapter.

On 22/4/14 14:05, Igor Stasenko wrote:

On 14 April 2014 13:53, Juraj Kubelka <[hidden email]> wrote:

El 14-04-2014, a las 8:21, Juraj Kubelka <[hidden email]> escribió:

Thank you Stef,

the example helped me a lot to understand how to play with Athens.

The solution is not what I am looking for. If someone starts to play with alpha canal, s/he will get unexpected results.

I have finally found an example in C language. It look like this:

-=-=-=-=-

cairo_set_line_width (cr, 0.1);

cairo_save (cr);

cairo_scale (cr, 1, 0.2);

cairo_arc (cr, 1.5, 1.5, 1, 0, 2 * M_PI);

cairo_restore (cr);

cairo_set_source_rgba (cr, 0, 1, 0, 0.50);

cairo_stroke (cr);

-=-=-=-=-

<tips-ellipse.png>

I do not know how to write the same instructions with Athens.

First, they draw one arc (cairo_arc (cr, 1.5, 1.5, 1, 0, 2 * M_PI);), I draw 4 arcs:

-=-=-=-=-

canvas
createPath: [ :builder |
builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ].

-=-=-=-=-

... [show rest of quote]

OK, now I can draw ellipse with just one arc:

-=-=-=-

canvas

createPath: [ :builder |
builder
absolute;

moveTo: 0.5 @ 0;

arcCenterX: 0 centerY: 0 radius: 0.5 startAngle: 0 endAngle: Float twoPi

-=-=-=-

Why is this method in private protocol? Why I should not use it?

... [show rest of quote]

because its private.. and implementation specific.
other implementations may not have this method at all, and your code will simply throw DNU.
And that's why you got the horizontal line btw.. because of using private protocol bypassing coordinate tracking.

Why I have to use “moveTo:”? In C-example they do not use it. But I have to, otherwise there is an extra line on the canvas:

Well, I see in AthensCairoPathBuilder>>createPath:, there is call of "self moveToX: 0 Y: 0.”. If I remove it, I do not have to write “moveTo: 0.5@0”. So, I understand why I have to write it in my code. The question is what is the purpose of "self moveToX: 0 Y: 0.”? I guess it simplify some situations, am I right? Which one?

the initial moveTo: command lets you set the origin (starting point) of your path.

if you don't start path with moveTo: command, it is implicitly set to 0@0.

There is actual Athens example:

-=-=-=-

AthensSceneView new scene: [ :can |
| path |
path := can createPath: [ :builder |
builder
absolute;

moveTo: 0.5 @ 0;
arcCenterX: 0 centerY: 0 radius: 0.5 startAngle: 0 endAngle: Float twoPi ].
can pathTransform restoreAfter: [
can pathTransform scaleBy: 200 @ 50.

(can setStrokePaint: Color red) width: 0.1.
can drawShape: path.

].
] ;
openInWindow

-=-=-=-

Thank you,

Juraj

Second, they set line width, before any other action (like cairo_save). I do:

-=-=-=-=-

canvas pathTransform scaleBy: 200 @ 50.

(can setStrokePaint: Color red) width: 0.1.

can drawShape: path.

-=-=-=-=-

So, my result in Athens is like this:

<Captura de pantalla 2014-04-14 a la(s) 8.18.38.png>

Any idea? The example is explained here, C source code is here (by clicking on the image in the page).

Thank you,

Jura

El 12-04-2014, a las 4:01, Pharo4Stef <[hidden email]> escribió:

AthensSceneView new
scene: [ :can |
| path |
path := can
createPath: [ :builder |
builder
absolute;
moveTo: 0 @ 0.5;
ccwArcTo: 0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0.0 @ -0.5 angle: 90 degreesToRadians;
ccwArcTo: -0.5 @ 0.0 angle: 90 degreesToRadians;
ccwArcTo: 0 @ 0.5 angle: 90 degreesToRadians ].

can pathTransform
restoreAfter: [
can pathTransform scaleBy: 200 .
can
setPaint: Color red ;
drawShape: path.
"(athensCanvas setStrokePaint: strokePaint)
width: (self strokeWidth / self scale) asFloat."
can drawShape: path.].
can pathTransform
restoreAfter: [
can pathTransform scaleBy: 190 .
can
setPaint: Color blue ;
drawShape: path.
"(athensCanvas setStrokePaint: strokePaint)
width: (self strokeWidth / self scale) asFloat."
can drawShape: path

]
] ;
openInWindow

<Screen Shot 2014-04-12 at 09.01.09.pdf>
... [show rest of quote]

... [show rest of quote]

... [show rest of quote]

--
Best regards,
Igor Stasenko.

... [show rest of quote]

Henrik Sperre Johansen

Apr 23, 2014; 11:17am

Re: Athens and ellipse drawing

In reply to this post by Igor Stasenko

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..

... [show rest of quote]

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

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

Cheers,
Henry

signature.asc (859 bytes) Download Attachment

Igor Stasenko

Apr 23, 2014; 12:31pm

Re: Athens and ellipse drawing

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 :)

... [show rest of quote]

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?

Cheers,
Henry

--
Best regards,
Igor Stasenko.

Henrik Sperre Johansen

Apr 23, 2014; 12:54pm

Re: Athens and ellipse drawing

On 23 Apr 2014, at 2:31 , Igor Stasenko <[hidden email]> wrote:

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 :)

... [show rest of quote]

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?

... [show rest of quote]

From the abstract of the paper cited in the linked site:

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

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Nicolai Hess

Jun 22, 2014; 10:34pm

Re: Athens and ellipse drawing

in (pure) cairo it is possible to stroke a path, after restoring
the current state/transformation:

cairo_set_line_width (cr, 0.1);

cairo_save (cr);
cairo_scale (cr, 0.5, 1);
cairo_arc (cr, 0.5, 0.5, 0.40, 0, 2 * M_PI);
cairo_restore (cr);

cairo_stroke (cr);

So we can scale the circle arc to an elliptic one, without
scaling the stroke width.

From my observation, this is not possible with the current athens rendering scheme:

steps in AthensCanvas draw->
setPathTransform
loadpath
stroke/fill

Igor, did I miss something, is it possible with the Athens API ?

nicolai

2014-04-23 14:54 GMT+02:00 Henrik Johansen <[hidden email]>:

On 23 Apr 2014, at 2:31 , Igor Stasenko <[hidden email]> wrote:

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 :)

... [show rest of quote]

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?
... [show rest of quote]

From the abstract of the paper cited in the linked site:

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

... [show rest of quote]

Juraj Kubelka-5

Jun 25, 2014; 7:35pm

Re: Athens and ellipse drawing

CONTENTS DELETED

The author has deleted this message.

Nicolai Hess

Jun 30, 2014; 6:44am

Re: Athens and ellipse drawing

Igor, what do you think. Is it possible or should it
be possible to draw a non-uniform scaled path with
an unscaled (stroke-)paint?

Nicolai

2014-06-25 21:35 GMT+02:00 Juraj Kubelka <[hidden email]>:

I have understood it is not possible.

Cheers,
Juraj

--
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