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Metalworking (rec.crafts.metalworking) Discuss various aspects of working with metal, such as machining, welding, metal joining, screwing, casting, hardening/tempering, blacksmithing/forging, spinning and hammer work, sheet metal work. |
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A Planar Geometry Problem
On May 3, 12:59*pm, Tim Wescott wrote:
Consider two circles, of arbitrary diameter, and a point, all on a plane. I want to inscribe an arc that is tangent to both circles, and which passes through the point. Anyone know a way to construct the arc? *I'm not snickering in the background here as I pose puzzles -- this is a drafting problem that I'm running into quite a lot lately. -- Tim Wescott Wescott Design Serviceshttp://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details athttp://www.wescottdesign.com/actfes/actfes.html My approch: One assues three circles. C1, C2 and Carc which can be defined by x1,y1, R1 x2,y2,R2 and xa,ya,Ra Carc is the curve you are looking for a tanjent unit vector on each circule is defiend as ((2(x-xn)x) i +(2(y-Yn)y )j)/(Sqrt( ((2(x-xn))^2 +(2(y-Yn)y)^2) where i and j are unit vectors in the x and y direction A tanjent condition is acheved when the C1, Carc share the same point and tanjent vectors are colinear. Plug the equations into Mathmaica and pray |
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