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panta rhei

Arc centres of polylines

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I thought this would be easy...

A user wants to place a stake (with x/y coordinates) at the centre of each arc in her polylines (plenty of them...)

The calculations seem to depend on the curvature of each arc (the famous clockwise conundrum revisited), but I can't figure out what triggers the dicotomy.

Here's what I am trying to get: dx & dy values like this (see attachment):

The code looks like this

PROCEDURE CentrePoints; 
obHd : HANDLE; 
clockWise : BOOLEAN; 
x, y, dx, dy, a, aR, a1, a2, r, d, l : REAL; 
v1, v2 : VECTOR; 

GETPOLYPT(obHd, 1, x1, y1); 
GETPOLYLINEVERTEX(obHd, 2, x2, y2, t, r); 
GETPOLYPT(obHd, 3, x3, y3); 

v1.x := x2-x1; v1.y := y2-y1; 
v2.x := x3-x2; v2.y := y3-y2; 
a1 := VEC2ANG(v1); 
a2 := VEC2ANG(v2); 

a := ((180-ANGBVEC(v1, v2))/2); 
aR := TAN(DEG2RAD(a)); 

d := r/aR; 
l := SQRT(r^2+d^2); 

a := DEG2RAD(a-a1);
dx := l*COS(a);  
dy := l*SIN(a); 

LOCUS(x2-dx, y2+dy);

MESSAGE(clockWise); { if FALSE, this works } 



and works when the clockwiseness is False.

Also, I may be on the wrong track entirely.

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Hi Petri,

???You almost had it. With a few minor changes it now works.


PROCEDURE CentrePoints;


???obHd : HANDLE;

???clockWise : BOOLEAN;

???t : INTEGER;

???x, y, dx, dy, a, aR, a1, a2, r, d, l : REAL;

???x1, y1, x2, y2, x3, y3 : REAL;???{ added these to make it compile }

???v1, v2 : VECTOR;


???obHd := FSACTLAYER;

???GETPOLYPT(obHd, 1, x1, y1);

???GETPOLYLINEVERTEX(obHd, 2, x2, y2, t, r);

???GETPOLYPT(obHd, 3, x3, y3);


???v1.x := x1-x2; v1.y := y1-y2;??????{ make vector v1 point away from point 2 }

???v2.x := x3-x2; v2.y := y3-y2;??????{ yes, points away from point 2 }

???a1 := VEC2ANG(v1);

{??a2 := VEC2ANG(v2);}????????????????{ don't need this anymore }

???a := ANGBVEC(v1, v2)/2;??????????{ remove 180 from calculation, as v1 is now reversed }

???aR := TAN(DEG2RAD(a));

???d := r/aR;

???l := SQRT(r^2+d^2);


???{ use clockWise condition to add or subtract angle a to/from angle a1 }

???clockWise := GETOBJECTVARIABLEBOOLEAN(obHd, 652);

???if clockWise then a := DEG2RAD(a1+a)

???else a := DEG2RAD(a1-a);


???dx := l*COS(a);

???dy := l*SIN(a);

???LOCUS(x2+dx, y2+dy);



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Thank you very much, Ray! Got it to work.

Some puzzling questions still remain. In a polyline with more than one arc, there seems to be the curvature issue for each. Oddly enough, it also seems that if the polyline is clockwise, all works fine here in the lab at least. (Fortunately I have a ?reverse direction? command in my kit and this solves the situation.)

Another one is that if the radius is ?illegal? (too large), the polyline data contains the specified radius and there doesn't seem to be a way to inquire the radius actually applied.

(Maybe I have to decompose a copy, check the radii and adjust them?)

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This is the response that I received from Nemetschek's CTO regarding increasing arc polyline radius when the tangent distance of the arc is > than 1/2 the distance between intersection points.: "The fix is Deep in the code, and it is risky to fix at this point. The work around is explained in the attached file: I?ve created the desired poly by setting the first arc then decomposing and composing the polyline, And finally set the radius of the second arc."

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