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Paolo

Tangent on a polyline control point

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I am working on a script that converts Vectorworks polylines into SVG paths and I have managed to "translate" everything except for the cubic splines vertexes.

I know that a cubic splines vertex control point is equivalent to two bezier vertexes, simply crossing the tangent lines, see figure.

1128158651_Schermata2020-11-19alle10_31_31.thumb.png.e917e9ebde8f34e039ca4ef8770879bc.png

The problem is: how I determine the tangent exactly in a polyline vertex?

The only way seems to go with this one…

def vs.PointAlongPoly(h, dist):
    return (BOOLEAN, pt, tangent)

…but I cannot know what distance the control point has.

Furthermore, testing this (and the similar PointAlongPolyN), I get inaccurate results placing of the points on the curve.

I know (from past experiences) that this function calculates distances on the poly just "polygonizing" the curve, but the conversion resolution is unknown (and not settable).

 

 

Thank you for the help.

Paolo

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I have found a way, it works, but has some inaccuracy (due to the PointAlongPoly precision), but I can leave with it.

Of course, if there is a better solution it will welcome!

import math

def angleBetweenPoints(p1, p2):
#given 2 point coordinates it retrieves the angle of the line passing between them
	orientation = None
	
	if p1[0]==p2[0]:
		if p1[1] <= p2[1]:
			orientation = 90
		else:
			orientation = 270
			
	if p1[1]==p2[1]:
		if p1[0] <= p2[0]:
			orientation =  0
		else:
			orientation = 180
			
	if (p1[0]!=p2[0]) and (p1[1]!=p2[1]):
		if p1[0]<p2[0]:
			quadrant = 0
		else:
			quadrant = 180
		orientation = quadrant+vs.Rad2Deg(vs.ArcTan((p1[1]-p2[1])/(p1[0]-p2[0])))
	return orientation

def tangentAtIndex(h, index, resolution):
	minDist = 1e308 #a very large number initially
	tangent = None
	
	ptVt, vertexType, arcRadius = vs.GetPolylineVertex(h, index)
	
	ht = vs.ConvertToPolygon(h, resolution)
	#cycle searching min distance
	for i in range(1, vs.GetVertNum(ht)+1):
		pi = vs.GetPolyPt(ht, i)
		dist = vs.Distance(ptVt[0], ptVt[1], pi[0], pi[1])
		if dist < minDist:
			minDist = dist
			if (i > 1) and (i+1 < vs.GetVertNum(ht)):
				pt1 = vs.GetPolyPt(ht, i-1)
				pt3 = vs.GetPolyPt(ht, i+1)
				c = vs.ThreePtCenter(pt1, pi, pt3)
				tangent = angleBetweenPoints(c, pi)+90
			else:
				if i == 1:
					#angle between 1 and 2
					pt1 = vs.GetPolyPt(ht, 1)
					pt2 = vs.GetPolyPt(ht, 2)
					tangent = angleBetweenPoints(pt1, pt2)
				if i == vs.GetVertNum(ht):
					#angle between latest and latest-1
					pt1 = vs.GetPolyPt(ht, vs.GetVertNum(ht))
					pt2 = vs.GetPolyPt(ht, vs.GetVertNum(ht)-1)
					tangent = angleBetweenPoints(pt1, pt2)

	vs.DelObject(ht)
	return tangent

  
#test a selected polyline

h = vs.FSActLayer()

for i in range(1, vs.GetVertNum(h)+1):

	t = tangentAtIndex(h, i, 512)
	p, vertexType, arcRadius = vs.GetPolylineVertex(h, i)
	vs.Locus(p[0], p[1])
	vs.MoveTo(p[0]-1*math.cos(vs.Deg2Rad(t)), p[1]-1*math.sin(vs.Deg2Rad(t)))
	vs.LineTo(p[0]+1*math.cos(vs.Deg2Rad(t)), p[1]+1*math.sin(vs.Deg2Rad(t)))

1907764704_Schermata2020-11-19alle12_07_17.thumb.png.831f6e0a75545d32090121c412ee0c2e.png

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