topic Re: Another math challenge in Libraries & objects

Another math challenge

Rob — Fri, 23 Feb 2007 01:44:48 GMT

I just do not know how to tackle this problem and/or if it is solvable with given variables. Basically I would like to calculate the coordinates of the tangential fillet center of two segments.
if someone could help I would appreciate
ta

X1,Y1,X2,Y2,X3,Y3 - known
Xa,Ya,Xb,Yb - known
Xc,Yc - ???

Re: Another math challenge

Frank Beister — Fri, 23 Feb 2007 09:44:50 GMT

You should be able to calculate it by pythagoras and TAN. I have added some length (L,r), which are known out of your settings

Re: Another math challenge

Rob — Fri, 23 Feb 2007 10:03:02 GMT

I appologise, I have forgotten to mention that alpha is not known, it's there just to demonstrate the centerline of the angle.

Re: Another math challenge

Frank Beister — Fri, 23 Feb 2007 10:36:46 GMT

Are you shure that the both distances L are identical? Elsewhere the center line and alpha is not the only problem. 😉

Re: Another math challenge

Rob — Fri, 23 Feb 2007 10:41:39 GMT

yep, the L distances are identical

Re: Another math challenge

Laszlo Nagy — Sat, 24 Feb 2007 13:34:26 GMT

I think if you know the coordinates of all three corners of the triangle, you should be able to find out any of the angles of the triangle. Alpha will be half of the angle at point 2.

Re: Another math challenge

Rob — Sun, 25 Feb 2007 09:34:32 GMT

I think if you know the coordinates of all three corners of the triangle, you should be able to find out any of the angles of the triangle. Alpha will be half of the angle at point 2.

thanks laszlo for your suggeston, it did not solve the problem, however it gave me the starting idea and finally solution after couple hours of sketching and calculating.

Re: Another math challenge

LiHigh — Mon, 26 Feb 2007 10:33:49 GMT

You can also avoid Alpha:

!-------------------------------------------------------
! (X0, Y0) is the center of the arc
! D = distance betwen center and point (X2,Y2)
!--------------------------------------------------------

R^2 = (Xa-X0)^2 + (Ya-Y0)^2
R^2 = (Xb-X0)^2 + (Yb-Y0)^2

L^2 = (Xa-X2)^2 + (Ya-Y2)^2
L^2 = (Xb-X2)^2 + (Yb-Y2)^2

D^2 = R^2 + L^2

5 unkowns & 5 Equations, solvable.......

Re: Another math challenge

Anonymous — Wed, 20 Jan 2010 18:48:57 GMT

I know the post I'm adding to is old, but it's related.

I was working on a much simplified detail symbol which shows the clip polygon with filleted corners. I managed to figure out how to draw the clip polygon, . Simple enough, you just put the clip coordinates into memory and draw a polygon but I could not figure out how to add the nodes to create filleted coners.

I attached the library part, but following is the"for next" loop that extracts the clip polygon.

add2 AC_RefCoord[1][1], AC_RefCoord[1][2]
for i=1 to AC_ClippNodes
if i<>AC_ClippNodes then
put AC_ClippCoord[1],AC_ClippCoord[2],1

next i

poly2_ AC_ClippNodes, 1,
get(nsp)