Thank you, Max. The angle function doesn't appear to provide the same calculation as my atantwo in all cases. https://pdfhost.io/v/Oqj7XmibJ_scaled The shorter line segment should be directed towards the vertex closest to the longer line segment. I tried using both: theta := angle( dx, dy ); theta := angle( dy, dx ); Neither made a difference, in some cases the angle differs from what I'd expect. My implementation is based on the first version given here: https://en.wikipedia.org/wiki/Atan2#Definition_and_computation I have something that works, so this is more of a curiosity as to there being a difference between my implementation of atantwo and the angle function. Here's an example with many lines and the angle function: https://pdfhost.io/v/1T4jgBnxh_scaled On Wed, Oct 12, 2022 at 11:42 PM Max Chernoff wrote:

Hi,

...

How is atan2 called? I rolled my own as follows:

...

Is atan with two parameters supposed to behave like atan2?

At mp-math.mpxl:167 there is:

vardef atan primary x = angle(1,x) enddef ;

The MetaPost manual says:

The angle operator takes a pair and computes the two-argument arctangent; i.e., angle is the inverse of the dir operator

So it looks like "angle" is the function that you want for "atan2".

Thanks, -- Max

On 10/14/2022 2:35 AM, Max Chernoff via ntg-context wrote:

Hi,

...

The angle function doesn't appear to provide the same calculation as my atantwo in all cases.

They both give the same results, but "angle" gives a result in degrees while "atantwo" gives a result in radians. This demo:

\startMPpage vardef atantwo( expr dy, dx ) = save theta;

numeric theta;

theta := 0;

if (dx > 0): theta := atan( dy / dx ); elseif (dx < 0) and (dy >= 0): theta := atan( dy / dx ) + pi; elseif (dx < 0) and (dy < 0): theta := atan( dy / dx ) - pi; elseif (dx == 0) and (dy > 0): theta := pi / 2; elseif (dx == 0) and (dy < 0): theta := -pi / 2; fi;

theta enddef;

def showangles(expr dx, dy) = message "---------------" message "atantwo " & decimal atantwo(dy, dx) message "angle " & decimal (angle(dx, dy) * pi / 180) message "angle " & decimal angle(dx, dy) message "(" & decimal dx & ", " & decimal dy & ")" enddef;

showangles(1, 0); showangles(1, 1); showangles(0, 1); showangles(-1, 1); showangles(-1, 0); showangles(-1, -1); showangles(0, -1); showangles(1, -1); \stopMPpage

So you suggest to add atantwo? As side note, you can redure your definition to: vardef atantwo( expr dy, dx ) = if (dx > 0): atan( dy / dx ) elseif (dx < 0) and (dy >= 0): atan( dy / dx ) + pi elseif (dx < 0) and (dy < 0): atan( dy / dx ) - pi elseif (dx == 0) and (dy > 0): pi / 2 elseif (dx == 0) and (dy < 0): -pi / 2 else : 0 fi enddef ; and then vardef atantwo(expr dy, dx) = if dx == 0 : if dy < 0 : - fi pi / 2 else : atan(dy/dx) if dx > 0 : if dy < 0 : - else : + fi pi fi fi enddef ; going further makes us end up in an one-line obscurity Hans ----------------------------------------------------------------- Hans Hagen | PRAGMA ADE Ridderstraat 27 | 8061 GH Hasselt | The Netherlands tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl -----------------------------------------------------------------

I don't think an atantwo is needed. I *thought* I had read somewhere that atan( y, x ) was equivalent to calling atan2 in Lua. Ensuring there's no breakage when x == y would be nice, though. It was a little surprising to see angle return degrees rather than radians, but it does simplify my code: dc := vbc - vac; dr := vbr - var; vi := 0; if not( dc == dr ): vi := round( angle( dc, dr ) / 60 ); fi; % Compute the direction towards the first segment (to vertex of an edge). vangle := vi * 60 * pi / 180; Even simpler would be: dc := vbc - vac; dr := vbr - var; vi := round( angle( dc, dr ) / 60 ); % returns 0 when dc == dr % Compute the direction towards the first segment (to vertex of an edge). vangle := vi * 60 * pi / 180; Or accepting a third argument as the return value in the special case: vi := round( angle( dc, dr, 0 ) / 60 ); % returns 0 when dc == dr Cheers!

That's certainly tighter, thank you, Alan. Would making the conditional part of the API be useful to others? Cheers! On Fri, Oct 14, 2022 at 3:42 PM Alan Braslau wrote:

On Fri, 14 Oct 2022 11:59:49 -0700 Thangalin wrote:

...

I don't think an atantwo is needed. I *thought* I had read somewhere that atan( y, x ) was equivalent to calling atan2 in Lua. Ensuring there's no breakage when x == y would be nice, though. It was a little surprising to see angle return degrees rather than radians, but it does simplify my code:

dc := vbc - vac; dr := vbr - var; vi := 0;

if not( dc == dr ): vi := round( angle( dc, dr ) / 60 ); fi;

% Compute the direction towards the first segment (to vertex of an edge). vangle := vi * 60 * pi / 180;

Even simpler would be:

dc := vbc - vac; dr := vbr - var; vi := round( angle( dc, dr ) / 60 ); % returns 0 when dc == dr

% Compute the direction towards the first segment (to vertex of an edge). vangle := vi * 60 * pi / 180;

Or accepting a third argument as the return value in the special case:

vi := round( angle( dc, dr, 0 ) / 60 ); % returns 0 when dc == dr

Cheers!

vi := if (dc = dr) : 0 else : round (angle(dc,dr)/60) fi ;

Alan

Are you using MP in scaled integer or in doubleprecision mode? I have not looked into the MP angle operator code, but my suspicion is that it is based on some super-clever John Hobby scheme optimized for scaled integer calculations. Hans has integrated the entire math library (and more) into lmtx. On 13/10/22 13/10/22, 13:51, Thangalin via ntg-context wrote:

Thank you, Max.

The angle function doesn't appear to provide the same calculation as my atantwo in all cases.

https://pdfhost.io/v/Oqj7XmibJ_scaled

The shorter line segment should be directed towards the vertex closest to the longer line segment. I tried using both:

theta := angle( dx, dy ); theta := angle( dy, dx );

Neither made a difference, in some cases the angle differs from what I'd expect.

My implementation is based on the first version given here:

https://en.wikipedia.org/wiki/Atan2#Definition_and_computation

I have something that works, so this is more of a curiosity as to there being a difference between my implementation of atantwo and the angle function.

Here's an example with many lines and the angle function: https://pdfhost.io/v/1T4jgBnxh_scaled

On Wed, Oct 12, 2022 at 11:42 PM Max Chernoff wrote:

...

Hi,

...

How is atan2 called? I rolled my own as follows:

...

Is atan with two parameters supposed to behave like atan2?

At mp-math.mpxl:167 there is:

vardef atan primary x = angle(1,x) enddef ;

The MetaPost manual says:

The angle operator takes a pair and computes the two-argument arctangent; i.e., angle is the inverse of the dir operator

So it looks like "angle" is the function that you want for "atan2".

Thanks, -- Max

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On Fri, 14 Oct 2022 at 14:58, Taco Hoekwater via ntg-context < ntg-context@ntg.nl> wrote:

...

On 14 Oct 2022, at 14:26, Alan Braslau via ntg-context < ntg-context@ntg.nl> wrote:

Are you using MP in scaled integer or in doubleprecision mode?

I have not looked into the MP angle operator code, but my suspicion is that it is based on some super-clever John Hobby scheme optimized for scaled integer calculations.

The scaled version of “angle” is a handwritten approximation in web, not using any math library. I really doubt that that code is faster than calling atan2() on a modern machine, but I’ve kept it in because using a lib might give slightly different results.

iirc, in metapost the whole scaled number system has no dependency from any external math library (I have not checked the lmtx source yet).