intersection two 2 cylinders - formula

intersection.txt

Here is the formula for calculating the intersection points of 2 cylinders where the centerlines of the cylinders intersect.

Definitions:

    Brad = Branch Radius
    Mrad = Main Radius
    TX = the X coord of the intersection
    TY = the Y coord of the intersection
    TZ = the Z coord of the intersection

    deginrad = the Degrees in Radians of the position we are at in the branch's circluar path

    ANG = the Angle of the variation of the branch from 90 degrees

First here is the basic easy formula for the intersection of a 90 degree set of cylinders:

    TX = Cos(deginrad) * Brad
    TY = Sin(deginrad) * Brad
    TZ = Sqr(Abs(Mrad ^ 2 - TY ^ 2))

Second is the formula that lets you set the angle of the branch and get the points you need:

    TY = Sin(deginrad) * Brad
    TZ = Sqr(Abs(Mrad ^ 2 - TY ^ 2))
    TX = (Cos(deginrad) * Brad / Cos(Ang)) + (Tan(Ang) * TZ)

Hope this helps.



from math import pi, cos, sin, tan, sqrt, radians
brad = 1.0
mrad = 1.125
ang = radians(0.0)
for degs in range(360):
	rads = radians(degs)

	tx = round(cos(rads) * brad,3)
	ty = round(sin(rads) * brad, 3)
	tz = round(sqrt(abs(mrad**2 - ty**2)), 3)

	#ty = round(sin(rads) * brad, 3)
	#tz = round(sqrt(abs(mrad**2 - ty**2)), 3)
	#tx = round((cos(rads) * brad / cos(ang)) + (tan(ang) * tz), 3)

	print(str(tx) + ' ' + str(ty) + ' ' + str(tz))