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ThreePtCenter

Description

Returns the center of a circle passing thru 3 given points.

FUNCTION ThreePtCenter(
				pt1 : VECTOR;
				pt2 : VECTOR;
				pt3 : VECTOR): VECTOR;
def vs.ThreePtCenter(pt1, pt2, pt3):
    return VECTOR

Parameters

Name Type Description
pt1 VECTOR
pt2 VECTOR
pt3 VECTOR

Remarks

(_c_, 2022.01.18) In VS Python this routine returns a 3-dimensional tuple. Warning: Most Math - Vector routines require a 3-dimensional tuple, failing to init a third item in VW before 2023 (vs.Vec2Ang, for example, returns gibberish on 2-d tuples).

Examples

VectorScript

{ finds the tangent angle between two poly sides }
PROCEDURE Example;
VAR
    polyObj : HANDLE;
    p1, p2, p3, c, t : VECTOR;
    ang : REAL;

BEGIN
polyObj := FSActLayer; { take care to have a polygon selected }
IF polyObj <> NIL THEN BEGIN { not checking here for obj type, but you should }
    GetPolyPt( polyObj, 1, p1.x, p1.y );
    GetPolyPt( polyObj, 2, p2.x, p2.y );
    GetPolyPt( polyObj, 3, p3.x, p3.y );

    c := ThreePtCenter( p1, p2, p3 );
    Locus( c.x, c.y );

    t := Perp( p2 - c );
    ang := Vec2Ang( t );
    AlrtDialog( Concat('Angle of tangent at pt2: ', Chr(13), Num2Str(3, ang)) ); 
END;
Run(Example);

Python

# finds the tangent angle between two poly sides
polyObj = vs.FSActLayer() # take care to have a polygon selected
if polyObj != vs.Handle( 0 ): # not checking here for obj type, but you should
    p1 = vs.GetPolyPt( polyObj, 1 ) 
    p2 = vs.GetPolyPt( polyObj, 2 )
    p3 = vs.GetPolyPt( polyObj, 3 ) 

    c = vs.ThreePtCenter( p1, p2, p3 )
    vs.Locus( c )

    t = vs.Perp( p2[0] - c[0], p2[1] - c[1], 0 ) 
    ang = vs.Vec2Ang( t )
    vs.AlrtDialog( f'Angle of tangent at pt2:\r{ang:.3f}' ) # precision = 3, coercing float
BEGIN
	pt1 := ThreePtCenter(PolyPoints[I].pt, PolyPoints[I+1].pt, PolyPoints[I-1].pt);
	pt2 := PolyPoints[I-1].pt;
	pt3 := PolyPoints[I+1].pt;

to reduce the number of errors in long nearly parallel segments. I really need to
replace the proportional algorithm with a user-definable fixed deviation factor.
But it's too late in the 10 cycle to change the interfaces, and I'm not sure
if one factor would DO it, or IF it would take more than one.}
cen_pt := ThreePtCenter(pt1, pt2, pt3);
rad := Dist(cen_pt, pt1);

to reduce the number of errors in long nearly parallel segments. I really need to
replace the proportional algorithm with a user-definable fixed deviation factor.
But it's too late in the 10 cycle to change the interfaces, and I'm not sure
if one factor would DO it, or IF it would take more than one.}
cen_pt := ThreePtCenter(pt1, pt2, pt3);
rad := Dist(cen_pt, pt1);
IF ((EqPercent(Dist((pt1 + pt2) / 2, cen_pt), rad, 4)) &
	 (EqPercent(Dist((pt2 + pt3) / 2, cen_pt), rad, 4)) &
	 (EqPercent(Dist(pt1, pt2), Dist(pt2, pt3), 50))) THEN BEGIN
import vs

# Returns the center of a circle passing thru 3 given points.
pt1 = (0, 0)
pt2 = (1, 1)
pt3 = (2, 2)

vec = vs.ThreePtCenter(pt1, pt2, pt3)
vs.Message('ThreePtCenter returned: ' + str(vec))

Version

Availability: from Vectorworks 2014

Category